11institutetext:  Department of Computer and Information Science, University
of Macau, Macau, China
11email<EMAIL_ADDRESS>
# Mixed Prototype Consistency Learning for Semi-supervised Medical Image
Segmentation

Lijian Li 11 0009-0006-2009-3269

###### Abstract

Recently, prototype learning has emerged in semi-supervised medical image
segmentation and achieved remarkable performance. However, the scarcity of
labeled data limits the expressiveness of prototypes in previous methods,
potentially hindering the complete representation of prototypes for class
embedding. To address this problem, we propose the Mixed Prototype Consistency
Learning (MPCL) framework, which includes a Mean Teacher and an auxiliary
network. The Mean Teacher generates prototypes for labeled and unlabeled data,
while the auxiliary network produces additional prototypes for mixed data
processed by CutMix. Through prototype fusion, mixed prototypes provide extra
semantic information to both labeled and unlabeled prototypes. High-quality
global prototypes for each class are formed by fusing two enhanced prototypes,
optimizing the distribution of hidden embeddings used in consistency learning.
Extensive experiments on the left atrium and type B aortic dissection datasets
demonstrate MPCL’s superiority over previous state-of-the-art approaches,
confirming the effectiveness of our framework. The code will be released soon.

###### Keywords:

Semi-supervised Medical Image Segmentation Mixed Prototype Learning
Consistency learning

##  1 Introduction

Recently, supervised medical image segmentation has achieved remarkable
improvements by introducing deep learning methods. However, widely applying
such techniques in real medical diagnosis is continually hindered by the
scarcity of labeled data. Thus, researchers propose the concept of semi-
supervised medical image segmentation to alleviate dependence of models on
abundant manual annotations which require a significant amount of time and
labor. SS-MIS methods are capable of achieving relatively great performance by
extracting precious information from unlabeled data to assist model in
training with a small amount of annotated data.

There are three common categories of semi-supervised learning techniques
utilized in SS-MIS methods, including consistency-based, pseudo-label-based,
and prototype-based learning approaches. As for pseudo-label-based methods
[82, 15, 178, 33], they aim to generate pseudo-labels for unlabeled data to
provide auxiliary supervisions similar to annotated data. Some studies
introduce uncertainty estimation methods like Monte Carlo dropout [174] and
ensemble-based methods [130] to mitigate interference information contained in
unlabeled data so as to generate more reliable pseudo-labels. Besides,
researchers also quantify the level of uncertainty and set a threshold to
select high-confidence pseudo-labels by utilizing some measurements like
information entropy. Xiang et al. [161] considers both epistemic uncertainty
(EU) and aleatoric uncertainty (AU) to generate a better uncertainty mask to
promote model learning. Consistency-based methods [14, 124, 25, 165, 78, 56,
98] comply with a learning pattern that guides model to generate consistent
predictions for both raw data and enhanced or interfered data. A unified
consistency loss is adopted to optimize model learning. Chen et al. [33]
proposes a learning strategy named cross pseudo supervision (CPS) to enable
pseudo labels generated by two perturbed segmentation networks to supervise
mutually. Luo et al. [98] introduces a dual-task consistency regularization
(DTC) to enforce consistency between pixel-level and geometry-level
segmentation maps for labeled and unlabeled data. However, slight or
inappropriate perturbations may provide erroneous supervisory signals so as to
produce suboptimal segmentation performance. In regard to prototype learning
methods [150, 154, 181], they are intended to impose a consistency constraint
between prototypes generated by feature matching operations and corresponding
model’s predictions to improve segmentation performance. Xu et al. [166]
devises a cyclic prototypical consistency learning framework (CPCL) that is
composed of a labeled-to-unlabeled (L2U) prototypical forward process and an
unlabeled-to-labeled (U2L) backward process. However, current prototype
learning methods always generate prototypes for labeled and unlabeled data
separately and fuse two kinds of prototypes to obtain more comprehensive
prototypes. They are limited by the quantity and quality of prototypes so that
the representation capability of global prototypes will be impaired. In
response to the insufficient amount of annotated data, researchers usually use
interpolation-based semi-supervised learning methods to solve this problem.
For example, CutMix [176], also known as Copy-Paste (CP), achieves data
augmentation by copying image crops from labeled data as foreground onto
another image. It has been verified that the predictions of mixed data can
provide useful information to alleviate the distribution mismatch and class
imbalance problems.

Briefly, previous prototype-based methods are hindered by the small quantity
of prototypes and their low quality. To eliminate this problem, in this paper,
we propose a Mixed Prototype Consistency Learning (MPCL) framework that
introduces a Mean Teacher structure and an auxiliary network to enhance the
prototype generation process. Firstly, the teacher and student networks are
utilized to train unlabeled and labeled data respectively and generate
corresponding prototypes by employing the masked average pooling approach
[142]. The pseudo-labels for unlabeled data are optimized by an uncertainty
estimation mechanism based on entropy. Then, we adopt CutMix [176] to generate
mixed labeled data and devise an auxiliary network to generate auxiliary
prototypes containing beneficial semantic information for mixed data. With
auxiliary prototypes, labeled prototypes will be fused with them to enrich
their common semantic information. Besides, we also fuse mixed prototypes with
unlabeled prototypes to enhance semantic information interaction resulting in
bridging the distribution gap between labeled and unlabeled data. Then, the
enhanced labeled and unlabeled prototypes are fused to generate high-quality
global prototypes, which have more powerful capabilities to represent the
distribution of feature embeddings. Finally, we utilize cosine similarity to
obtain the similarity maps between prototypes and feature embeddings for
labeled or unlabeled data, which are regarded as novel segmentation masks and
utilized to conduct consistency learning with labels and reliable pseudo-
labels. In sum, the main contributions of this work are summarized as follows:

  * 1)

We introduce an auxiliary network to provide extra prototypes for mixed data
formed by CutMix to assist model learning, which not only increases the number
of prototypes model can consider but also improves the quality of global
prototypes.

  * 2)

A novel prototype-based framework named mixed prototype learning is proposed,
which utilizes extra prototypes to enrich semantic information of labeled and
unlabeled prototypes so as to generate high-quality global prototypes to
optimize the distribution of hidden embeddings employed in consistency
learning.

  * 3)

The results of extensive experiments conducted on Left Atrium and Aortic
Dissection datasets verify that the proposed MPL framework outperforms
previous SOTA SSL methods

##  2 Related works

Semi-supervised Medical Image Segmentation Recently, a large quantity of semi-
supervised learning methods have been introduced into the field of medical
image segmentation and achieved quite considerable breakthroughs. The existing
semi-supervised medical image segmentation methods generally utilize an
encoder-decoder segmentation network like V-Net as their backbone and mainly
focus on devising an excellent learning strategy. Consistency learning is one
of the most commonly used strategies. Most consistency learning-based methods
adopt the structure of Mean Teacher and design various regularization methods
to maintain the consistency of pseudo-labels generated by teacher and student
networks. For example, Yu et al. [174] applies an uncertainty-guided learning
strategy based on the framework of Mean Teacher to enable student network to
learn more reliable targets, which are optimized by some uncertainty
estimation methods like Monte Carlo Dropout. Wu et al. [158] devise a mutual
consistency network (MC-Net) to mitigate uncertain information that model
brings through imposing a consistency constraint on two predictions generated
by two identical decoders. Xia et al. [160] attempts to enforce the
consistency of predictions for multi-view unlabeled data. Ouali et al. [110]
proposes a cross consistency training strategy that enforces consistency
between the predictions of main decoder and multiple auxiliary decoders whose
inputs are processed by some perturbations. Besides, Luo et al. [101] devises
a novel uncertainty rectifying strategy to ensure the consistency of pyramid
predictions at different scales. Zhu et al. [193] utilizes a hybrid
uncertainty to eliminate unreliable knowledge in the hybrid prediction and
leverage beneficial information to assist model learning. Recently, prototype
alignment based on feature matching operations has been applied in semi-
supervised medical image segmentation, which aims to obtain data structure
information from both labeled and unlabeled data and improve the distribution
of feature embeddings across distinct classes. For instance, Zhang et al.
[187] proposes a self-aware and cross-sample prototypical learning network
(SCP-Net) to leverage semantic interaction information from two different
prototypes and a self-aware consistency loss to improve the reliability of
model. Wu et al. [156] enhances the cohesion of each category distribution by
aligning the features of specific categories with their high-quality
prototypes, thereby achieving better separation of categories. Zhang et al.
[181] proposes a progressively self-correcting strategy for pseudo-labels that
calculates the feature distances from prototypes and leverages them as class-
wise likelihoods to correct pseudo-labels. Zhang et al. [182] introduces the
masked average pooling strategy to obtain prototypes of images and utilizes
cosine similarity to conduct pixel-level feature-to-prototype matching.
Adversarial learning is also an advanced technique that has been widely
applied in medical image segmentation. For example, Peiris et al. [112]
combines adversarial learning and multi-view learning to obtain confident
prediction masks for unlabeled data. Wang et al. [144] devises a Constrained
Adversarial Training (CAT) method which introduces various constraints like
connectivity and convexity to generate anatomically plausible segmentations.

Interpolation-based Semi-supervised Learning To address the problem of the
scarcity of labeled data, interpolation-based regularization is applied to
semi-supervised semantic segmentation and achieves tremendous success. Mixup
[179] and CutMix [176] are two fundamental tasks that assist model training by
mixing entire images and mixing image crops, respectively. There are numerous
variants designed for specific problems based on them. For example, Tu et al.
[138] leverages mixup to transfer knowledge from labeled data into unlabeled
data so as to generate more reliable pseudo labels. Dvornik et al. [51]
employs visual context information to find appropriate locations to place new
objects on images so as to perform data augmentation. Bai et al. [16] proposes
a bidirectional copy-paste (BCP) strategy to mix labeled and unlabeled crossly
to enable student network to learn more conjoint semantic information, which
is regarded as mixed supervisory signals to assist model learning. Berthelot
et al. [22] gradually expands the annotated set by regarding unlabeled data
with high-quality pseudo-labels as annotated data.

##  3 Methodology

###  3.1 Problem Definition

In the task of semi-supervised medical image segmentation, we have a whole
dataset $\mathbb{D}$ including an annotated subset and an unannotated subset,
which are defined as $\mathbb{D}_{l},\mathbb{D}_{u}$ respectively. The
annotated subset consists of $N$ images and corresponding labels denoted as
$\mathbb{D}_{l}=\\{(x^{a},y^{a})\\}_{a=1}^{N}$, and the unlabeled subset only
contains $M$ images denoted as $\mathbb{D}_{u}=\\{(x^{a})\\}_{a=N+1}^{N+M}$.
Besides, the dimensions of each image are $H\times W\times D$ which represent
height, width and depth. Therefore, we denote a single image as
$x^{a}\in\mathbb{R}^{H\times W\times D}$. For each label, it is defined as
$y^{a}\in\\{0,1,...,C-1\\}^{H\times W\times D}$. The batch size for both
labeled and unlabeled is 2, which is denoted as $\mathcal{B}$.The proposed
mixed prototype learning framework is composed of a Mean Teacher structure and
an auxiliary network, whose overview structure is illustrated in Figure 1. The
student network and auxiliary network are optimized by optimizers like
stochastic gradient descent (SGD). Then, the parameters of teacher network are
updated by exponential moving average (EMA) of student network.

Figure 1: The figure illustrates the structure of the proposed Mixed Prototype
Consistency Learning framework, which is composed of a Mean Teacher structure
and an auxiliary network. The student and teacher networks are utilized to
generate labeled and unlabeled prototypes $p^{c}_{l},p^{c}_{u}$, respectively.
And the auxiliary network produces mixed prototypes $p^{c}_{m}$ for mixed data
processed by CutMix. The mixed prototype fusion module includes three fusion
processes. The labeled and unlabeled prototypes will be fused with mixed
prototypes to enhance their semantic information. Finally, a high-quality
global prototype representation $p^{c}$ is formed by fusing labeled and
unlabeled prototypes, which optimizes the distribution of hidden embeddings in
consistency learning.

###  3.2 Supervised Loss

To simply mitigate the uncertainty of predictions for labeled data that model
brings, we employ four different loss functions, such as focal loss, Dice
loss, cross entropy loss and IoU loss, to process different outputs from an
identical group of classifiers. Besides, different from [161], we also utilize
cross entropy loss function to process the average of four distinct
predictions to further eliminate disparity between the four classifiers’
results. Therefore, the supervised loss for labeled data is the sum of average
of four different losses and the fused cross entropy loss, which is defined as
follows:

$L_{seg}^{l}=(L_{ce}^{l}+L_{dice}^{l}+L_{focal}^{l}+L_{IoU}^{l})/4+L^{l}_{f}$
(1)

where $L_{ce},L_{dice},L_{focal},L_{IoU}$ represent cross entropy loss, dice
loss, focal loss and IoU loss for labeled data respectively and $L_{f}$
denotes the fused cross entropy loss. For the auxiliary network, identical
supervised loss functions are constructed to train mixed data processed by
CutMix which is to copy crop from one image onto another image. Therefore, the
mixed data is defined as
$\mathbb{D}_{m}=\\{(x_{m}^{b},y_{m}^{b})\\}_{b=1}^{N/2}$ where the number of
mixed images is $N/2$.

$L_{seg}=L_{seg}^{l}+L_{seg}^{m}$ (2)

where $L_{seg}$ denotes the final supervised loss and $L_{seg}^{m}$ represents
the supervised loss for mixed data.

The pseudo-label for the $p$-th voxel in the $a$-th unlabeled image is denoted
as $pl_{u,a}^{p}\in\mathcal{R}^{C}$. Similarly, the average of multiple
different predictions for unlabeled images will be utilized to generate pseudo
labels $pl_{u}$. To progressively improve the reliability of pseudo-labels, we
adopt uncertainty measurement based on entropy to estimate the quality of
pseudo-label for each voxel. According to the properties of entropy, the lower
entropy of a voxel, the lower its uncertainty which also means that the voxel
is more reliable. The uncertainty for $p$-th voxel is defined as follows:

$U(pl_{u,a}^{p})=-\sum_{c=0}^{C-1}pl_{u,a}^{p}(c)\log pl_{u,a}^{p}(c)$ (3)

With the uncertainty map, reliable map for each voxel can be naturally
inferred which is regarded as weight assigned to each voxel. Therefore, the
reliable pseudo labels for unlabeled data can be obtained by multiplying the
reliable map with raw pseudo labels. The process can be defined as follows:

$\hat{pl}_{u,a}^{p}=\frac{1}{H\times W\times
D}(1-\frac{U(pl_{u,a}^{p})}{\sum_{p=1}^{H\times W\times
D}U(pl_{u,a}^{p})})\otimes pl_{u,a}^{p}$ (4)

where $\hat{pl}_{u,a}^{p}$ represents reliable pseudo-label for $p$-th voxel,
and $\otimes$ denotes element-wise multiplication operation.

###  3.3 Mixed Prototype Learning

Prototype Generation. Different from utilizing aforementioned predictions,
prototypes for labeled and unlabeled data are generated by feature embeddings
from the $k$-rd layer decoder of student and teacher networks separately.
Through trilinear interpolation, prototypes are upsampled to the same size as
segmentation labels. Here, we set the feature maps produced by the $k$-rd
layer of student network and teacher network to be $f_{k,a}^{l,p}$ and
$f_{k,a}^{u,p}$. Referencing [142], we directly utilize labels to mask feature
maps and then adopt masked average pooling to obtain the prototype for each
class. The labeled prototype for class $c$ is defined as follows:

$p^{c}_{l}=\frac{1}{\mathcal{B}}\sum_{a=1}^{\mathcal{B}}\frac{\sum_{p=1}^{H\times
W\times D}f_{k,a}^{l,p}\mathbbm{1}[y^{a}_{p}=c]}{\sum_{p=1}^{H\times W\times
D}\mathbbm{1}[y^{a}_{p}=c]}$ (5)

Different from the generation of labeled prototypes, we utilize uncertainty
measurement of each voxel to optimize feature maps $f_{k,a}^{u,p}$. Before
conducting the operation of masked attention pooling, the feature maps are
weighted by corresponding uncertainty maps. The unlabeled prototype for class
$c$ is formulated as follows:

$p^{c}_{u}=\frac{1}{\mathcal{B}}\sum_{a=1}^{\mathcal{B}}\frac{1}{H\times
W\times D}\frac{\sum_{p=1}^{H\times W\times
D}(1-\frac{U(f_{k,a}^{u,p})}{\sum_{p}U(f_{k,a}^{u,p})})f_{k,a}^{u,p}\mathbbm{1}[y^{a}_{p}=c]}{\sum_{p=1}^{H\times
W\times D}\mathbbm{1}[y^{a}_{p}=c]}$ (6)

Due to the limited annotated data, the annotated prototypes cannot fully
express the feature embeddings of specific classes. Considering the problem,
we utilize an auxiliary network to process mixed data and produce mixed
prototypes according to the prototype generation method for labeled data. The
feature maps from auxiliary network are represented as $f_{k,b}^{m,p}$. And
the batch size for mixed data is $\mathcal{B}^{m}=\frac{\mathcal{B}}{2}$. The
definition of mixed prototype $p^{c}_{m}$ is as follows:

$p^{c}_{m}=\frac{1}{\mathcal{B}^{m}}\sum_{b=1}^{\mathcal{B}^{m}}\frac{\sum_{p=1}^{H\times
W\times D}f_{k,b}^{m,p}\mathbbm{1}[y^{b}_{m,p}=c]}{\sum_{p=1}^{H\times W\times
D}\mathbbm{1}[y^{b}_{m,p}=c]}$ (7)

We utilize the mixed prototypes as additional knowledge to enhance the
semantic information of both labeled and unlabeled prototypes.

Mixed Prototype Fusion. For the fusion of different categories of prototypes,
we first fuse mixed prototypes with labeled prototypes to provide labeled
prototypes with more semantic information to enhance their capabilities to
express class embeddings. The fusion process is defined as follows:

$p^{c}_{lm}=\lambda_{1}p^{c}_{l}+\lambda_{2}p^{c}_{m}$ (8)

where $p^{c}_{lm}$ represents the prototypes generated after the fusion of
mixed and labeled prototypes, and $\lambda_{1}$ and $\lambda_{2}$ are the
coefficients to adjust the fusion ratio of mixed and labeled prototypes.

In addition, we will also integrate mixed prototypes with unlabeled prototypes
to enable model to learn more common semantics from labeled and unlabeled
data, which bridges the huge distribution gap between both data and promotes
distribution alignment. The unlabeled prototypes enhanced by mixed prototypes
are denoted as $p^{c}_{um}$.

$p^{c}_{um}=\lambda_{3}p^{c}_{u}+\lambda_{4}p^{c}_{m}$ (9)

where $\lambda_{3}$ and $\lambda_{4}$ denote the coefficients for the fusion
of unlabeled and mixed prototypes. Then, we fuse the optimized labeled and
unlabeled prototypes to generate high-quality global prototypes $p^{c}$, which
further bridge the distribution gap between labeled and unlabeled data and
have better expression ability for feature embeddings. We adopt Temporal
Ensembling approach that is capable of gradually improving the quality of
predictions and prototypes during the training process to progressively update
the fusion percentage of distinct prototypes. Time-dependent Gaussian warming
up function [136] is a prevalent technique that includes a vital parameter
$\lambda_{con}$ ranging from 0 to 1. As the training progresses, the
coefficients for labeled and unlabeled prototypes enable model to continually
focus on the mixed prototypes while maintaining labeled prototypes as the
capital information sources.

$p^{c}=((2-\lambda_{con})p^{c}_{lm}+\lambda_{con}p^{c}_{um})/2$ (10)

###  3.4 Loss functions

With the global prototypes, the next step is to build relationships between
prototypes and features from teacher and student networks. We utilize cosine
distance to measure the similarity [182]. Then, the likelihood of voxels in
each class is approximated using feature-to-prototype similarity maps. To
conduct consistency learning, we utilize cross entropy loss function to narrow
the distance between prototype-based predictions for labeled data and labels.
For prototype-based predictions for unlabeled data, they are regarded as
beneficial information and are expected to close to pseudo labels
$\hat{pl}_{u,a}^{p}$ to improve their qualities. The consistency losses based
on prototypes for labeled and unlabeled data are defined as follows:

$L_{lc}=L_{ce}(s_{l,a},y_{a}),\qquad L_{uc}=\sum_{p=1}^{H\times W\times
D}L_{ce}(s_{u,a}^{p},\hat{pl}_{u,a}^{p})$ (11)

where $s_{a}^{l}$ and $s_{a}^{u}$ denote the similarity maps between labeled
prototypes and features for labeled and unlabeled data respectively. Finally,
the total loss of the proposed mixed prototype learning is combined with all
supervised losses and two consistency losses, which is shown in below
equation:

$L=L_{seg}+L_{lc}+\lambda_{con}L_{uc}$ (12)

##  4 Experiments

###  4.1 Datasets and Metrics

Two public datasets are utilized to evaluate the performance of our model,
including the left atrium (LA) dataset [163] and a multi-center dataset for
type B aortic dissection (TBAD). For both datasets, we normalize the voxel
intensities to zero mean and unit variance.

LA dataset [163] is comprised of 100 3D gadolinium-enhanced magnetic resonance
(MR) imaging volumes, each of which has identical spatial resolution of
$0.625\times 0.625\times 0.625$$mm^{3}$ and distinct dimensions. The dataset
is methodically partitioned to allocate 80 samples for the training set and 20
samples for the validation set. For training, samples in training set are
randomly cropped into $112\times 112\times 80$ patches. For inference, a
sliding window of the same dimensions is employed, along with a stride of
$18\times 18\times 4$, to generate the final segmentation outcomes.

TBAD dataset [171] consists of 124 computed tomography angiography (CTA) scans
having three annotations (whole aorta, true lumen (TL), and false lumen (FL)).
In the dataset, 100 and 24 scans are utilized for training and testing,
respectively. Besides, for the preprocessing of data, we utilize the same
techniques as in [97].

Metrics. We evaluate our model with four common metrics: Dice coefficient
(Dice), Jaccard Index (Jac), 95% Hausdorff Distance (95HD), and Average
Symmetric Surface Distance (ASD). Two former and latter metrics are regionally
sensitive and edge-sensitive, respectively.

###  4.2 Implementation details

We employ V-Net [105] as backbone. And the student network and auxiliary
network are trained for 10k iterations and optimized by an Adam optimizer with
a learning rate of 0.01, while the parameters of teacher network are updated
using exponential moving average (EMA). The batch size is set to 4, containing
2 annotated and unannotated samples. During the training stage, we augment the
TBAD dataset with the same approaches like rotation following [97] and use
3-fold cross-validation. And $k$ is set to 1, which is the optimal number of
decoder layer to generate prototypes in student, teacher and auxiliary
networks. Besides, the fusion coefficients for labeled prototypes
$\lambda_{1}$ and $\lambda_{2}$ are equal. The same setting also appears on
the fusion coefficients of unlabeled prototypes $\lambda_{3}$ and
$\lambda_{4}$. The default loss function utilized in consistency learning is
cross entropy. CutMix is set to be the default data augmentation technique.
The whole MPCL framework is implemented by PyTorch and trained with an RTX
4090 GPU.

Table 1: Experimental Results Comparison on the LA Dataset Method | Scans Used | Metrics
---|---|---
Labeled | Unlabled |  Dice$\uparrow$ |  Jaccard$\uparrow$ |  95HD$\downarrow$ |  ASD$\downarrow$
V-Net | 4(5%) | 0 | 52.55 | 39.60 | 47.05 | 9.87
V-Net | 8(10%) | 0 | 82.74 | 71.72 | 13.35 | 3.26
V-Net | 80(All) | 0 | 91.47 | 84.36 | 5.48 | 1.51
UA-MT | 16(20%) | 64(80%) | 88.88 | 80.21 | 7.32 | 2.26
SASSNet | 89.54 | 81.24 | 8.24 | 1.99
DTC | 89.42 | 80.98 | 7.32 | 2.10
URPC | 88.43 | 81.15 | 8.21 | 2.35
MC-Net | 90.12 | 82.12 | 11.28 | 2.30
SS-Net | 89.25 | 81.62 | 6.45 | 1.80
BCP | 90.34 | 82.50 | 6.75 | 1.77
Co-BioNet | 91.26 | 83.99 | 5.17 | 1.64
MPCL |  |  | 91.98 | 85.02 | 4.77 | 1.58
Table 2: Comparison with state-of-the-art models on Aortic Dissection dataset Dataset | Scans Used | Metrics
---|---|---
Dice$\uparrow$ |  Jaccard$\uparrow$ |  95HD$\downarrow$ |  ASD$\downarrow$
Model | Labeled | Unlabled | TL | FL | Mean | TL | FL | Mean | TL | FL | Mean | TL | FL | Mean
V-Net | (20%) | (80%) | 55.51 | 48.98 | 52.25 | 39.81 | 34.79 | 37.30 | 7.24 | 10.17 | 8.71 | 1.27 | 3.19 | 2.23
(100%) | (0%) | 75.98 | 64.02 | 70.00 | 61.89 | 50.05 | 55.97 | 3.16 | 7.56 | 5.36 | 0.48 | 2.44 | 1.46
MT | (20%) | (80%) | 57.62 | 49.95 | 53.78 | 41.57 | 35.52 | 38.54 | 6.00 | 8.98 | 7.49 | 0.97 | 2.77 | 1.87
UA-MT | 70.91 | 60.66 | 65.78 | 56.15 | 46.24 | 51.20 | 4.44 | 7.94 | 6.19 | 0.83 | 2.37 | 1.60
FUSSNet | 79.73 | 65.32 | 72.53 | 67.31 | 51.74 | 59.52 | 3.46 | 7.87 | 5.67 | 0.61 | 2.93 | 1.77
URPC | 81.84 | 69.15 | 75.50 | 70.35 | 57.00 | 63.68 | 4.41 | 9.13 | 6.77 | 0.93 | 1.11 | 1.02
UPCoL | 82.65 | 69.74 | 76.19 | 71.49 | 57.42 | 64.45 | 2.82 | 6.81 | 4.82 | 0.43 | 2.22 | 1.33
MPCL | (20%) | (80%) | 83.83 | 76.05 | 79.94 | 73.00 | 63.63 | 71.94 | 2.24 | 5.02 | 3.63 | 0.33 | 1.15 | 0.74
Figure 2: The visualizations of experimental results on Left Atrium and Aortic
Dissection datasets. MPCL denotes the proposed mixed prototypes consistency
learning. GT denotes the ground truth labels. Baseline represents the method
of URPC. ITK-SNAP [177] is the tool to visualize 3D medical image.

###  4.3 Discussions

Results on Left Atrium dataset. The table 1 presents a comparison of various
state-of-the-art models on the Left Atrium dataset, focusing on their
performance with a labeled ratio of 20%. The models compared are UA-MT [173],
SASSNet [86], DTC [98], URPC [102], MC-Net [158], SS-Net [156], Co-BioNet
[113], BCP [16]. Obviously, across all metrics (Dice, Jaccard, 95HD, ASD), the
proposed model consistently outperforms previous state-of-the-art models on
the Left Atrium dataset. For a 20% labeled ratio, the proposed MPCL attains
the highest Dice score (91.98) and Jaccard index (85.02), along with the
lowest 95HD (4.77) and ASD (1.58) among all models compared. In order to
better observe the effectiveness improvement of the proposed MPCL framework,
we visualize the predictions of MPCL on LA dataset and compare them with the
predictions of URPC model and ground truth labels in Fig. 2. Obviously, the
visualization results of MPCL’s predictions are far superior to those of
baseline’s predictions, with a very high similarity to corresponding labels.
To be specific, for the first and third examples in Fig. 2, the predictions of
baseline lack a section of content compared with the ground truth labels.
However, the predictions of MPCL effectively compensate for the missing parts,
with only slight differences in overall shape from the label, which reflects
the improvements of MPCL on Dice and Jaccard score metrics.

Results on Aortic Dissection dataset. In the Aortic Dissection dataset
comparison illustrated in table 2, the proposed MPCL framework also excels,
showing remarkable performance improvements at lower labeled data scenarios
(like 20% labeled data) compared with previous methods including MT [136], UA-
MT [173], FUSSNet [161], URPC [102] and UPCoL [97]. MPCL achieves the highest
Dice (up to 79.94%), Jaccard (up to 71.94%), and significantly lower 95HD
(down to 3.63) and ASD (down to 0.74) metrics, showing robust capability of
capturing sophisticated geometric information like the vessel walls between
True Lumen (TL) and False Lumen (FL). Similarly, we also visualize the
predictions of MPCL and baseline on Aortic Dissection dataset and compare them
with ground truth labels in Fig. 2. According to the visualization results,
baseline is inclined to predict an incomplete structure or generate redundant
parts, which can be observed in the five and seventh examples in Fig. 2.
Compared with baseline, the predicted shape of MPCL appears more aggregated
and more consistent with the labels. Besides, the accuracy of category
prediction of MPCL is also higher based on the color distribution of the
predicted images.

###  4.4 Ablation studies

We conduct extensive ablation studies to explore the effectiveness of each
component of the proposed framework and various optimal parameter settings.
There are five distinct ablation studies targeting data augmentation
techniques, prototype fusion steps, prototype fusion coefficients, parameter
k, and loss functions used in consistency learning.

Table 3: Ablation studies of data augmentation techniques used for generation of mixed data on the LA Dataset Method | Scans Used | Metrics
---|---|---
Labeled | Unlabled |  Dice$\uparrow$ |  Jaccard$\uparrow$ |  95HD$\downarrow$ |  ASD$\downarrow$
CutMix | 8(20%) | 0 | 91.98 | 85.02 | 4.77 | 1.58
Mixup | 8(20%) | 0 | 91.01 | 83.62 | 5.27 | 1.78
Cutout | 8(20%) | 0 | 91.58 | 84.52 | 5.00 | 1.52
fMix | 8(20%) | 0 | 91.44 | 84.29 | 5.06 | 1.72

As aforementioned, we utilize CutMix as the default data augmentation method
for the generation of mixed prototypes. Here, we attempt to explore the impact
of different data augmentation methods on model performance. The table 3
presents the results of an ablation study that evaluates the impact of
different data augmentation techniques on LA dataset. The study focuses on
four augmentation methods: CutMix, Mixup, Cutout [46], and fMix [68]. CutMix
appears to be the most effective data augmentation technique for this dataset,
achieving the highest Dice and Jaccard scores (91.98% and 85.02%,
respectively) and the lowest Hausdorff Distance at 4.77. Cutout results in the
lowest ASD score (1.52), indicating that mixed data processed by Cutout is
capable of providing edge-related semantic information to global prototypes
that enable model to achieve more precise surface delineation. Mixup and fMix
show competitive performance but lag slightly behind CutMix and Cutout in
these evaluations.

Table 4: Ablation studies of prototype fusion steps on the LA Dataset. N-N denotes that the fusion processes related to mixed prototypes are removed. M-L represents that the fusion of mixed and labeled prototypes is removed. M-UL denotes that the fusion of mixed and unlabeled prototypes is removed. L-UL represents that the fusion of labeled and unlabeled prototypes is removed. Method | Scans Used | Metrics
---|---|---
Labeled | Unlabled |  Dice$\uparrow$ |  Jaccard$\uparrow$ |  95HD$\downarrow$ |  ASD$\downarrow$
N-N | 8(20%) | 0 | 90.78 | 82.96 | 8.72 | 3.05
M-L | 8(20%) | 0 | 91.38 | 84.22 | 7.82 | 2.46
M-UL | 8(20%) | 0 | 91.32 | 84.15 | 7.56 | 2.33
L-UL | 8(20%) | 0 | 91.07 | 83.86 | 8.25 | 2.84
MPCL | 8(20%) | 0 | 91.98 | 85.02 | 4.77 | 1.58

We also attempt to explore the effects of different prototype fusion steps,
which include N-N (no fusion of mixed prototypes), M-L (no fusion of mixed and
labeled prototypes), M-UL (no fusion of mixed and unlabeled prototypes), L-UL
(no fusion of labeled and unlabeled prototypes), and MPCL (a method combining
all prototypes effectively, shown as the best performing setup) within the
MPCL framework. The table 4 presents the experimental results on LA dataset.
As is shown in table 4, N-N performs the worst, indicating the importance of
mixed prototypes in enhancing segmentation performance. M-UL and M-L show
intermediate performance, suggesting that while the combination of all fusion
processes contributes to model performance, the impact of individual fusion is
not as critical as the complete fusion process in MPCL. L-UL appears to have
an apparent performance degradation, indicating that the global prototypes
have better capabilities to optimize hidden embeddings from teacher and
student networks in consistency learning, resulting in better segmentation
performance.

Table 5: Ablation studies of coefficients for prototype fusion on the LA dataset. $\gamma_{1}=\frac{\lambda_{1}}{\lambda_{2}}$, $\gamma_{2}=\frac{\lambda_{3}}{\lambda_{4}}$. $\gamma_{1}$ denotes the fusion ratio of labeled and mixed prototypes. $\gamma_{2}$ denotes the fusion percentage of unlabeled and mixed prototypes. $\gamma_{1}$ | Scans Used | Metrics
---|---|---
Labeled | Unlabled |  Dice$\uparrow$ |  Jaccard$\uparrow$ |  95HD$\downarrow$ |  ASD$\downarrow$
0.5 | 8(20%) | 0 | 91.51 | 84.39 | 5.05 | 1.69
1 | 8(20%) | 0 | 91.98 | 85.02 | 4.77 | 1.58
2 | 8(20%) | 0 | 91.49 | 84.37 | 5.16 | 1.70
3 | 8(20%) | 0 | 91.53 | 84.43 | 4.94 | 1.57
$\gamma_{2}$ | Scans Used | Metrics
Labeled | Unlabled |  Dice$\uparrow$ |  Jaccard$\uparrow$ |  95HD$\downarrow$ |  ASD$\downarrow$
0.5 | 8(20%) | 0 | 91.43 | 84.21 | 5.15 | 1.74
1 | 8(20%) | 0 | 91.98 | 85.02 | 4.77 | 1.58
2 | 8(20%) | 0 | 91.65 | 84.57 | 5.02 | 1.66
3 | 8(20%) | 0 | 91.54 | 84.32 | 4.98 | 1.62

When performing prototype fusion, different fusion ratios may have a
significant impact on model performance. Therefore, we also conduct ablation
studies to explore the impact of varying coefficients on prototype fusion. The
table 5 displays the experimental results. The experiments involve varying
$\gamma_{1}$ and $\gamma_{2}$ across four different values (0.5, 1, 2, 3) to
observe their impact. Obviously, the optimal value for both $\gamma_{1}$ and
$\gamma_{2}$ appears to be 1, suggesting that an equal balance among labeled,
unlabeled and mixed prototypes is most beneficial for model performance.
Increasing $\gamma_{2}$ from 1 leads to a decrease in performance across all
metrics, although the declines are less pronounced compared to changes in
$\gamma_{1}$, indicating that the model might be slightly more sensitive to
changes in the balance between labeled and mixed prototypes than between
unlabeled and mixed prototypes.

Table 6: Ablation studies of the parameter $k$ on the LA dataset. The features from the $k$-rd decoder layer are utilized to generate prototypes. Time represents how many seconds it takes to train a model for one epoch k | Scans Used | Metrics | Time(s/epoch)
---|---|---|---
Labeled | Unlabeled |  Dice$\uparrow$ |  Jaccard$\uparrow$ |  95HD$\downarrow$ |  ASD$\downarrow$
1 | 8(20%) | 0 | 91.98 | 85.02 | 4.77 | 1.58 | 38.9
2 | 8(20%) | 0 | 91.40 | 84.23 | 5.11 | 1.87 | 35.1
3 | 8(20%) | 0 | 91.38 | 84.17 | 5.77 | 1.85 | 32.4
4 | 8(20%) | 0 | 90.74 | 83.15 | 6.18 | 2.00 | 30.5
Table 7: Ablation studies of consistency loss on the LA dataset. KL-Div denotes the KL divergence loss. MSE denotes the mean square error loss. MAE denotes the mean average error loss. CE represents the cross-entropy loss. Method | Scans Used | Metrics
---|---|---
Labeled | Unlabled |  Dice$\uparrow$ |  Jaccard$\uparrow$ |  95HD$\downarrow$ |  ASD$\downarrow$
KL-Div | 8(20%) | 0 | 91.50 | 84.45 | 5.17 | 1.73
MSE | 8(20%) | 0 | 91.31 | 84.02 | 7.32 | 1.85
MAE | 8(20%) | 0 | 91.10 | 83.69 | 7.83 | 2.24
CE | 8(20%) | 0 | 91.98 | 85.02 | 4.77 | 1.58

Due to the use of trilinear interpolation to upsample prototypes to the same
size as segmentation labels, prototypes generated by feature embeddings from
different decoder layers may affect the training time and performance of the
model. The table 6 shows the results of an ablation study examining the impact
of using features from different decoder layers (denoted by the parameter k)
for prototype generation. In light of these experimental results, as the value
of k increases, there is a consistent decline in model performance across all
metrics. This suggests that features from deeper layers, while potentially
more abstract or higher-level, may not capture the necessary details for
optimal prototype generation. The results also reflect a critical trade-off
between segmentation accuracy and training efficiency when selecting which
decoder layer’s features to use for prototype generation. While utilizing
features from the first decoder layer offers the best segmentation
performance, it also requires the longest training time at 38.9 seconds per
epoch. Conversely, features from deeper layers reduce training time, but at
the cost of decreased accuracy and precision. Using features from the fourth
layer (k = 4) to generate prototypes is the most time-efficient (30.5 seconds
per epoch).

Finally, the table 7 presents the outcomes of an ablation study examining the
effect of different consistency loss functions. According to the results,
utilizing cross-entropy loss as consistency loss outperforms those using other
loss functions across all metrics, achieving the highest Dice and Jaccard
scores (91.98% and 85.02%, respectively) and the lowest 95HD and ASD scores
(4.77 and 1.58, respectively). However, both MSE and MAE losses result in
lower Dice and Jaccard scores compared to KL-Div and CE losses. This could
indicate that these loss functions are less suited for capturing the nuances
of medical image segmentation tasks.

##  5 Conclusions

The article introduces a novel framework named Mixed Prototype Consistency
Learning (MPCL) for semi-supervised medical image segmentation. MPCL
integrates a Mean Teacher structure and an auxiliary network to address the
limitations of previous prototype-based methods caused by the small quantity
and low quality of prototypes. This framework introduces mixed prototypes with
additional semantic information to enhance labeled and unlabeled prototypes
through prototype fusion, further optimizing the quality and expressiveness of
global prototypes, which significantly improve segmentation performance.
Extensive experiments on the left atrium and type B aortic dissection datasets
demonstrate MPCL’s superiority over state-of-the-art approaches, showcasing
its effectiveness in medical image segmentation tasks.

## References

  * [1] Abdusalomov, A.B., Nasimov, R., Nasimova, N., Muminov, B., Whangbo, T.K.: Evaluating synthetic medical images using artificial intelligence with the gan algorithm. Sensors 23(7), 3440 (2023)
  * [2] Ahmed, Z., Mohamed, K., Zeeshan, S., Dong, X.: Artificial intelligence with multi-functional machine learning platform development for better healthcare and precision medicine. Database 2020, baaa010 (2020)
  * [3] Alpher, F.: Frobnication. IEEE TPAMI 12(1), 234–778 (2002)
  * [4] Alpher, F., Fotheringham-Smythe, F.: Frobnication revisited. Journal of Foo 13(1), 234–778 (2003)
  * [5] Alpher, F., Fotheringham-Smythe, F., Gamow, F.: Can a machine frobnicate? Journal of Foo 14(1), 234–778 (2004)
  * [6] Alpher, F., Gamow, F.: Can a computer frobnicate? In: CVPR. pp. 234–778 (2005)
  * [7] Amini, A., Schwarting, W., Soleimany, A., Rus, D.: Deep evidential regression. Advances in Neural Information Processing Systems 33, 14927–14937 (2020)
  * [8] Anonymous: The frobnicatable foo filter (2024), ECCV submission ID 00324, supplied as supplemental material 00324.pdf
  * [9] Anonymous: Frobnication tutorial (2024), supplied as supplemental material tr.pdf
  * [10] Antonelli, M., Reinke, A., Bakas, S., Farahani, K., Kopp-Schneider, A., Landman, B.A., Litjens, G., Menze, B., Ronneberger, O., Summers, R.M., et al.: The medical segmentation decathlon. Nature communications 13(1), 4128 (2022)
  * [11] Arazo, E., Ortego, D., Albert, P., O’Connor, N.E., McGuinness, K.: Pseudo-labeling and confirmation bias in deep semi-supervised learning. In: 2020 International Joint Conference on Neural Networks, IJCNN 2020, Glasgow, United Kingdom, July 19-24, 2020. pp. 1–8. IEEE (2020). https://doi.org/10.1109/IJCNN48605.2020.9207304, https://doi.org/10.1109/IJCNN48605.2020.9207304
  * [12] Ashfaq, A., Lingman, M., Sensoy, M., Nowaczyk, S.: DEED: deep evidential doctor. Artif. Intell. 325, 104019 (2023). https://doi.org/10.1016/J.ARTINT.2023.104019, https://doi.org/10.1016/j.artint.2023.104019
  * [13] Avidan, S., Brostow, G., Cissé, M., Farinella, G.M., Hassner, T. (eds.): Computer Vision – ECCV 2022. Springer (2022). https://doi.org/10.1007/978-3-031-19769-7
  * [14] Bachman, P., Alsharif, O., Precup, D.: Learning with pseudo-ensembles. In: Ghahramani, Z., Welling, M., Cortes, C., Lawrence, N.D., Weinberger, K.Q. (eds.) Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems 2014, December 8-13 2014, Montreal, Quebec, Canada. pp. 3365–3373 (2014), https://proceedings.neurips.cc/paper/2014/hash/66be31e4c40d676991f2405aaecc6934-Abstract.html
  * [15] Bai, W., Oktay, O., Sinclair, M., Suzuki, H., Rajchl, M., Tarroni, G., Glocker, B., King, A.P., Matthews, P.M., Rueckert, D.: Semi-supervised learning for network-based cardiac MR image segmentation. In: Descoteaux, M., Maier-Hein, L., Franz, A.M., Jannin, P., Collins, D.L., Duchesne, S. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2017 - 20th International Conference, Quebec City, QC, Canada, September 11-13, 2017, Proceedings, Part II. Lecture Notes in Computer Science, vol. 10434, pp. 253–260. Springer (2017). https://doi.org/10.1007/978-3-319-66185-8_29, https://doi.org/10.1007/978-3-319-66185-8_29
  * [16] Bai, Y., Chen, D., Li, Q., Shen, W., Wang, Y.: Bidirectional copy-paste for semi-supervised medical image segmentation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 11514–11524 (2023)
  * [17] Bai, Y., Chen, D., Li, Q., Shen, W., Wang, Y.: Bidirectional copy-paste for semi-supervised medical image segmentation. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023. pp. 11514–11524. IEEE (2023). https://doi.org/10.1109/CVPR52729.2023.01108, https://doi.org/10.1109/CVPR52729.2023.01108
  * [18] Balaji, K.: Image augmentation based on variational autoencoder for breast tumor segmentation. Academic Radiology (2023)
  * [19] Basak, H., Yin, Z.: Pseudo-label guided contrastive learning for semi-supervised medical image segmentation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 19786–19797 (2023)
  * [20] Basak, H., Yin, Z.: Pseudo-label guided contrastive learning for semi-supervised medical image segmentation. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023. pp. 19786–19797. IEEE (2023). https://doi.org/10.1109/CVPR52729.2023.01895, https://doi.org/10.1109/CVPR52729.2023.01895
  * [21] Bernard, O., Lalande, A., Zotti, C., Cervenansky, F., Yang, X., Heng, P.A., Cetin, I., Lekadir, K., Camara, O., Ballester, M.A.G., et al.: Deep learning techniques for automatic mri cardiac multi-structures segmentation and diagnosis: is the problem solved? IEEE transactions on medical imaging 37(11), 2514–2525 (2018)
  * [22] Berthelot, D., Carlini, N., Goodfellow, I., Papernot, N., Oliver, A., Raffel, C.A.: Mixmatch: A holistic approach to semi-supervised learning. Advances in neural information processing systems 32 (2019)
  * [23] Berthelot, D., Carlini, N., Goodfellow, I.J., Papernot, N., Oliver, A., Raffel, C.: Mixmatch: A holistic approach to semi-supervised learning. In: Wallach, H.M., Larochelle, H., Beygelzimer, A., d’Alché-Buc, F., Fox, E.B., Garnett, R. (eds.) Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada. pp. 5050–5060 (2019), https://proceedings.neurips.cc/paper/2019/hash/1cd138d0499a68f4bb72bee04bbec2d7-Abstract.html
  * [24] Bordley, R.F.: Modeling unforeseen events with similarity templates changes bayesian probabilities into pignistic probabilities. Int. J. Approx. Reason. 13(1), 83–93 (1995). https://doi.org/10.1016/0888-613X(95)00015-9, https://doi.org/10.1016/0888-613X(95)00015-9
  * [25] Bortsova, G., Dubost, F., Hogeweg, L., Katramados, I., de Bruijne, M.: Semi-supervised medical image segmentation via learning consistency under transformations. In: Shen, D., Liu, T., Peters, T.M., Staib, L.H., Essert, C., Zhou, S., Yap, P., Khan, A.R. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2019 - 22nd International Conference, Shenzhen, China, October 13-17, 2019, Proceedings, Part VI. Lecture Notes in Computer Science, vol. 11769, pp. 810–818. Springer (2019). https://doi.org/10.1007/978-3-030-32226-7_90, https://doi.org/10.1007/978-3-030-32226-7_90
  * [26] Cascante-Bonilla, P., Tan, F., Qi, Y., Ordonez, V.: Curriculum labeling: Revisiting pseudo-labeling for semi-supervised learning. In: Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2021, Thirty-Third Conference on Innovative Applications of Artificial Intelligence, IAAI 2021, The Eleventh Symposium on Educational Advances in Artificial Intelligence, EAAI 2021, Virtual Event, February 2-9, 2021. pp. 6912–6920. AAAI Press (2021). https://doi.org/10.1609/aaai.v35i8.16852, https://doi.org/10.1609/aaai.v35i8.16852
  * [27] Catak, F.O., Yue, T., Ali, S.: Uncertainty-aware prediction validator in deep learning models for cyber-physical system data. ACM Transactions on Software Engineering and Methodology (TOSEM) 31(4), 1–31 (2022)
  * [28] Chaitanya, K., Erdil, E., Karani, N., Konukoglu, E.: Local contrastive loss with pseudo-label based self-training for semi-supervised medical image segmentation. Medical Image Analysis 87, 102792 (2023)
  * [29] Chen, F., Chen, L., Kong, W., Zhang, W., Zheng, P., Sun, L., Zhang, D., Liao, H.: Deep semi-supervised ultrasound image segmentation by using a shadow aware network with boundary refinement. IEEE Trans. Medical Imaging 42(12), 3779–3793 (2023). https://doi.org/10.1109/TMI.2023.3309249, https://doi.org/10.1109/TMI.2023.3309249
  * [30] Chen, M., Gao, J., Xu, C.: Cascade evidential learning for open-world weakly-supervised temporal action localization. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023. pp. 14741–14750. IEEE (2023). https://doi.org/10.1109/CVPR52729.2023.01416, https://doi.org/10.1109/CVPR52729.2023.01416
  * [31] Chen, M., Gao, J., Xu, C.: Uncertainty-aware dual-evidential learning for weakly-supervised temporal action localization. IEEE Trans. Pattern Anal. Mach. Intell. 45(12), 15896–15911 (2023). https://doi.org/10.1109/TPAMI.2023.3308571, https://doi.org/10.1109/TPAMI.2023.3308571
  * [32] Chen, M., Gao, J., Yang, S., Xu, C.: Dual-evidential learning for weakly-supervised temporal action localization. In: ECCV 2022. Lecture Notes in Computer Science, vol. 13664, pp. 192–208. https://doi.org/10.1007/978-3-031-19772-7_12
  * [33] Chen, X., Yuan, Y., Zeng, G., Wang, J.: Semi-supervised semantic segmentation with cross pseudo supervision. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2021, virtual, June 19-25, 2021. pp. 2613–2622. Computer Vision Foundation / IEEE (2021). https://doi.org/10.1109/CVPR46437.2021.00264, https://openaccess.thecvf.com/content/CVPR2021/html/Chen_Semi-Supervised_Semantic_Segmentation_With_Cross_Pseudo_Supervision_CVPR_2021_paper.html
  * [34] Chen, Y., Yu, L., Wang, J.Y., Panjwani, N., Obeid, J.P., Liu, W., Liu, L., Kovalchuk, N., Gensheimer, M.F., Vitzthum, L.K., Beadle, B.M., Chang, D.T., Le, Q.T., Han, B., Xing, L.: Adaptive region-specific loss for improved medical image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 45(11), 13408–13421 (2023). https://doi.org/10.1109/TPAMI.2023.3289667
  * [35] Chen, Z.: Medical image segmentation based on u-net. In: Journal of Physics: Conference Series. vol. 2547, p. 012010. IOP Publishing (2023)
  * [36] Chowdary, G.J., Yin, Z.: Diffusion transformer u-net for medical image segmentation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 622–631. Springer (2023)
  * [37] Cover, T.M., Thomas, J.A.: Elements of information theory (2. ed.). Wiley (2006), http://www.elementsofinformationtheory.com/
  * [38] Cui, Y., Ren, W., Yang, S., Cao, X., Knoll, A.: Irnext: Rethinking convolutional network design for image restoration. In: Krause, A., Brunskill, E., Cho, K., Engelhardt, B., Sabato, S., Scarlett, J. (eds.) International Conference on Machine Learning, ICML 2023, 23-29 July 2023, Honolulu, Hawaii, USA. Proceedings of Machine Learning Research, vol. 202, pp. 6545–6564. PMLR (2023), https://proceedings.mlr.press/v202/cui23d.html
  * [39] Dai, X., Li, M., Zhai, P., Tong, S., Gao, X., Huang, S., Zhu, Z., You, C., Ma, Y.: Revisiting sparse convolutional model for visual recognition. In: NeurIPS (2022), http://papers.nips.cc/paper_files/paper/2022/hash/4418f6a54f4314202688d77956e731ce-Abstract-Conference.html
  * [40] Dempster, A.P.: The dempster-shafer calculus for statisticians. Int. J. Approx. Reason. 48(2), 365–377 (2008). https://doi.org/10.1016/J.IJAR.2007.03.004, https://doi.org/10.1016/j.ijar.2007.03.004
  * [41] Dempster, A.P.: Upper and lower probabilities induced by a multivalued mapping. In: Yager, R.R., Liu, L. (eds.) Classic Works of the Dempster-Shafer Theory of Belief Functions, Studies in Fuzziness and Soft Computing, vol. 219, pp. 57–72. Springer (2008). https://doi.org/10.1007/978-3-540-44792-4_3
  * [42] Dempster, A.P., Chiu, W.F.: Dempster-shafer models for object recognition and classification. Int. J. Intell. Syst. 21(3), 283–297 (2006). https://doi.org/10.1002/INT.20135, https://doi.org/10.1002/int.20135
  * [43] Deng, D., Chen, G., Yu, Y., Liu, F., Heng, P.A.: Uncertainty estimation by fisher information-based evidential deep learning. In: Proceedings of the 40th International Conference on Machine Learning. ICML’23, JMLR.org (2023)
  * [44] Deng, Y.: Deng entropy. Chaos, Solitons & Fractals 91, 549–553 (2016). https://doi.org/https://doi.org/10.1016/j.chaos.2016.07.014, https://www.sciencedirect.com/science/article/pii/S0960077916302363
  * [45] Deng, Y.: Uncertainty measure in evidence theory. Sci. China Inf. Sci. 63(11) (2020). https://doi.org/10.1007/S11432-020-3006-9, https://doi.org/10.1007/s11432-020-3006-9
  * [46] DeVries, T., Taylor, G.W.: Improved regularization of convolutional neural networks with cutout. arXiv preprint arXiv:1708.04552 (2017)
  * [47] Ding, Y., Liu, J., Xu, X., Huang, M., Zhuang, J., Xiong, J., Shi, Y.: Uncertainty-aware training of neural networks for selective medical image segmentation. In: Medical Imaging with Deep Learning. pp. 156–173. PMLR (2020)
  * [48] Dong, S., Pan, Z., Fu, Y., Xu, D., Shi, K., Yang, Q., Shi, Y., Zhuo, C.: Partial unbalanced feature transport for cross-modality cardiac image segmentation. IEEE Trans. Medical Imaging 42(6), 1758–1773 (2023). https://doi.org/10.1109/TMI.2023.3238067, https://doi.org/10.1109/TMI.2023.3238067
  * [49] Dou, Q., Liu, Q., Heng, P.A., Glocker, B.: Unpaired multi-modal segmentation via knowledge distillation. IEEE transactions on medical imaging 39(7), 2415–2425 (2020)
  * [50] Du, B., Huang, Y., Chen, J., Huang, D.: Adaptive sparse convolutional networks with global context enhancement for faster object detection on drone images. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023. pp. 13435–13444. IEEE (2023). https://doi.org/10.1109/CVPR52729.2023.01291, https://doi.org/10.1109/CVPR52729.2023.01291
  * [51] Dvornik, N., Mairal, J., Schmid, C.: Modeling visual context is key to augmenting object detection datasets. In: Proceedings of the European Conference on Computer Vision (ECCV). pp. 364–380 (2018)
  * [52] Fan, J., Gao, B., Jin, H., Jiang, L.: UCC: uncertainty guided cross-head co-training for semi-supervised semantic segmentation. CoRR abs/2205.10334 (2022). https://doi.org/10.48550/arXiv.2205.10334, https://doi.org/10.48550/arXiv.2205.10334
  * [53] Fang, K., Li, W.: Dmnet: Difference minimization network for semi-supervised segmentation in medical images. In: Martel, A.L., Abolmaesumi, P., Stoyanov, D., Mateus, D., Zuluaga, M.A., Zhou, S.K., Racoceanu, D., Joskowicz, L. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2020 - 23rd International Conference, Lima, Peru, October 4-8, 2020, Proceedings, Part I. Lecture Notes in Computer Science, vol. 12261, pp. 532–541. Springer (2020). https://doi.org/10.1007/978-3-030-59710-8_52, https://doi.org/10.1007/978-3-030-59710-8_52
  * [54] Feng, W., Ju, L., Wang, L., Song, K., Zhao, X., Ge, Z.: Unsupervised domain adaptation for medical image segmentation by selective entropy constraints and adaptive semantic alignment. In: Williams, B., Chen, Y., Neville, J. (eds.) Thirty-Seventh AAAI Conference on Artificial Intelligence, AAAI 2023, Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence, IAAI 2023, Thirteenth Symposium on Educational Advances in Artificial Intelligence, EAAI 2023, Washington, DC, USA, February 7-14, 2023. pp. 623–631. AAAI Press (2023). https://doi.org/10.1609/AAAI.V37I1.25138, https://doi.org/10.1609/aaai.v37i1.25138
  * [55] François, J., Grandvalet, Y., Denoeux, T., Roger, J.: Addendum to resample and combine: an approach to improving uncertainty representation in evidential pattern classification. Inf. Fusion 4(3), 235–236 (2003). https://doi.org/10.1016/S1566-2535(03)00020-4, https://doi.org/10.1016/S1566-2535(03)00020-4
  * [56] French, G., Laine, S., Aila, T., Mackiewicz, M., Finlayson, G.D.: Semi-supervised semantic segmentation needs strong, varied perturbations. In: 31st British Machine Vision Conference 2020, BMVC 2020, Virtual Event, UK, September 7-10, 2020. BMVA Press (2020), https://www.bmvc2020-conference.com/assets/papers/0680.pdf
  * [57] Gai, D., Zhang, J., Xiao, Y., Min, W., Chen, H., Wang, Q., Su, P., Huang, Z.: Gl-segnet: Global-local representation learning net for medical image segmentation. Frontiers in Neuroscience 17, 1153356 (2023)
  * [58] Gao, J., Chen, M., Xu, C.: Collecting cross-modal presence-absence evidence for weakly-supervised audio- visual event perception. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023. pp. 18827–18836. IEEE (2023). https://doi.org/10.1109/CVPR52729.2023.01805, https://doi.org/10.1109/CVPR52729.2023.01805
  * [59] Gao, S., Zhang, Z., Ma, J., Li, Z., Zhang, S.: Correlation-aware mutual learning for semi-supervised medical image segmentation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 98–108. Springer (2023)
  * [60] Gillmann, C., Saur, D., Wischgoll, T., Scheuermann, G.: Uncertainty-aware visualization in medical imaging-a survey. In: Computer Graphics Forum. vol. 40, pp. 665–689. Wiley Online Library (2021)
  * [61] Gordon, J., Shortliffe, E.H.: A method for managing evidential reasoning in a hierarchical hypothesis space. Artif. Intell. 26(3), 323–357 (1985). https://doi.org/10.1016/0004-3702(85)90064-5, https://doi.org/10.1016/0004-3702(85)90064-5
  * [62] Gu, R., Wang, G., Song, T., Huang, R., Aertsen, M., Deprest, J., Ourselin, S., Vercauteren, T., Zhang, S.: Ca-net: Comprehensive attention convolutional neural networks for explainable medical image segmentation. IEEE Trans. Medical Imaging 40(2), 699–711 (2021). https://doi.org/10.1109/TMI.2020.3035253, https://doi.org/10.1109/TMI.2020.3035253
  * [63] Guo, M., Yang, J., Chin, K., Wang, H., Liu, X.: Evidential reasoning approach for multiattribute decision analysis under both fuzzy and interval uncertainty. IEEE Trans. Fuzzy Syst. 17(3), 683–697 (2009). https://doi.org/10.1109/TFUZZ.2008.928599, https://doi.org/10.1109/TFUZZ.2008.928599
  * [64] Guo, P., Yang, D., Hatamizadeh, A., Xu, A., Xu, Z., Li, W., Zhao, C., Xu, D., Harmon, S.A., Turkbey, E., Turkbey, B., Wood, B.J., Patella, F., Stellato, E., Carrafiello, G., Patel, V.M., Roth, H.R.: Auto-fedrl: Federated hyperparameter optimization for multi-institutional medical image segmentation. In: Avidan, S., Brostow, G.J., Cissé, M., Farinella, G.M., Hassner, T. (eds.) Computer Vision - ECCV 2022 - 17th European Conference, Tel Aviv, Israel, October 23-27, 2022, Proceedings, Part XXI. Lecture Notes in Computer Science, vol. 13681, pp. 437–455. Springer (2022). https://doi.org/10.1007/978-3-031-19803-8_26, https://doi.org/10.1007/978-3-031-19803-8_26
  * [65] Han, Q., Wang, H., Hou, M., Weng, T., Pei, Y., Li, Z., Chen, G., Tian, Y., Qiu, Z.: Hwa-segnet: Multi-channel skin lesion image segmentation network with hierarchical analysis and weight adjustment. Computers in Biology and Medicine 152, 106343 (2023)
  * [66] Han, Z., Zhang, C., Fu, H., Zhou, J.T.: Trusted multi-view classification. arXiv preprint arXiv:2102.02051 (2021)
  * [67] Han, Z., Zhang, C., Fu, H., Zhou, J.T.: Trusted multi-view classification with dynamic evidential fusion. IEEE Trans. Pattern Anal. Mach. Intell. 45(2), 2551–2566 (2023). https://doi.org/10.1109/TPAMI.2022.3171983, https://doi.org/10.1109/TPAMI.2022.3171983
  * [68] Harris, E., Marcu, A., Painter, M., Niranjan, M., Prügel-Bennett, A., Hare, J.: Fmix: Enhancing mixed sample data augmentation. arXiv preprint arXiv:2002.12047 (2020)
  * [69] Hoyer, L., Dai, D., Van Gool, L.: Domain adaptive and generalizable network architectures and training strategies for semantic image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence 46(1), 220–235 (2024). https://doi.org/10.1109/TPAMI.2023.3320613
  * [70] Hua, Y., Shu, X., Wang, Z., Zhang, L.: Uncertainty-guided voxel-level supervised contrastive learning for semi-supervised medical image segmentation. International Journal of Neural Systems 32(04), 2250016 (2022)
  * [71] Huang, H., Xie, S., Lin, L., Tong, R., Chen, Y., Wang, H., Li, Y., Huang, Y., Zheng, Y.: Classformer: Exploring class-aware dependency with transformer for medical image segmentation. In: Williams, B., Chen, Y., Neville, J. (eds.) Thirty-Seventh AAAI Conference on Artificial Intelligence, AAAI 2023, Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence, IAAI 2023, Thirteenth Symposium on Educational Advances in Artificial Intelligence, EAAI 2023, Washington, DC, USA, February 7-14, 2023. pp. 917–925. AAAI Press (2023). https://doi.org/10.1609/AAAI.V37I1.25171, https://doi.org/10.1609/aaai.v37i1.25171
  * [72] Jain, J., Li, J., Chiu, M.T., Hassani, A., Orlov, N., Shi, H.: Oneformer: One transformer to rule universal image segmentation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 2989–2998 (2023)
  * [73] Jardim, S., António, J., Mora, C.: Image thresholding approaches for medical image segmentation-short literature review. Procedia Computer Science 219, 1485–1492 (2023)
  * [74] Jiang, H., Diao, Z., Shi, T., Zhou, Y., Wang, F., Hu, W., Zhu, X., Luo, S., Tong, G., Yao, Y.D.: A review of deep learning-based multiple-lesion recognition from medical images: classification, detection and segmentation. Computers in Biology and Medicine p. 106726 (2023)
  * [75] Jiang, M., Roth, H.R., Li, W., Yang, D., Zhao, C., Nath, V., Xu, D., Dou, Q., Xu, Z.: Fair federated medical image segmentation via client contribution estimation. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023. pp. 16302–16311. IEEE (2023). https://doi.org/10.1109/CVPR52729.2023.01564, https://doi.org/10.1109/CVPR52729.2023.01564
  * [76] Jøsang, A.: Subjective Logic - A Formalism for Reasoning Under Uncertainty. Artificial Intelligence: Foundations, Theory, and Algorithms, Springer (2016). https://doi.org/10.1007/978-3-319-42337-1, https://doi.org/10.1007/978-3-319-42337-1
  * [77] Kang, B., Deng, Y.: The maximum deng entropy. IEEE Access 7, 120758–120765 (2019). https://doi.org/10.1109/ACCESS.2019.2937679, https://doi.org/10.1109/ACCESS.2019.2937679
  * [78] Kim, J., Jang, J., Park, H.: Structured consistency loss for semi-supervised semantic segmentation. CoRR abs/2001.04647 (2020), https://arxiv.org/abs/2001.04647
  * [79] Kohler, M., Kohler, B.: Analysis of convolutional neural network image classifiers in a rotationally symmetric model. IEEE Trans. Inf. Theory 69(8), 5203–5218 (2023). https://doi.org/10.1109/TIT.2023.3262745, https://doi.org/10.1109/TIT.2023.3262745
  * [80] Kowalski, P., Zocholl, M., Jousselme, A.: Explaining the impact of source behaviour in evidential reasoning. Inf. Fusion 81, 41–58 (2022). https://doi.org/10.1016/J.INFFUS.2021.11.007, https://doi.org/10.1016/j.inffus.2021.11.007
  * [81] Kumar, K.S., Singh, N.P.: Retinal disease prediction through blood vessel segmentation and classification using ensemble-based deep learning approaches. Neural Computing and Applications 35(17), 12495–12511 (2023)
  * [82] Kwon, D., Kwak, S.: Semi-supervised semantic segmentation with error localization network. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2022, New Orleans, LA, USA, June 18-24, 2022. pp. 9947–9957. IEEE (2022). https://doi.org/10.1109/CVPR52688.2022.00972, https://doi.org/10.1109/CVPR52688.2022.00972
  * [83] Lee, D.H.: Pseudo-label : The simple and efficient semi-supervised learning method for deep neural networks. ICML 2013 Workshop : Challenges in Representation Learning (WREPL) (07 2013)
  * [84] Li, D., Yang, J., Kreis, K., Torralba, A., Fidler, S.: Semantic segmentation with generative models: Semi-supervised learning and strong out-of-domain generalization. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 8300–8311 (2021)
  * [85] Li, J., Hassani, A., Walton, S., Shi, H.: Convmlp: Hierarchical convolutional mlps for vision. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023 - Workshops, Vancouver, BC, Canada, June 17-24, 2023. pp. 6307–6316. IEEE (2023). https://doi.org/10.1109/CVPRW59228.2023.00671, https://doi.org/10.1109/CVPRW59228.2023.00671
  * [86] Li, S., Zhang, C., He, X.: Shape-aware semi-supervised 3d semantic segmentation for medical images. In: Martel, A.L., Abolmaesumi, P., Stoyanov, D., Mateus, D., Zuluaga, M.A., Zhou, S.K., Racoceanu, D., Joskowicz, L. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2020 - 23rd International Conference, Lima, Peru, October 4-8, 2020, Proceedings, Part I. Lecture Notes in Computer Science, vol. 12261, pp. 552–561. Springer (2020). https://doi.org/10.1007/978-3-030-59710-8_54, https://doi.org/10.1007/978-3-030-59710-8_54
  * [87] Li, X., Chen, H., Qi, X., Dou, Q., Fu, C.W., Heng, P.A.: H-denseunet: hybrid densely connected unet for liver and tumor segmentation from ct volumes. IEEE transactions on medical imaging 37(12), 2663–2674 (2018)
  * [88] Li, X., Peng, Y., Xu, M.: Patch-shuffle-based semi-supervised segmentation of bone computed tomography via consistent learning. Biomedical Signal Processing and Control 80, 104239 (2023)
  * [89] Li, Y., Chen, J., Xie, X., Ma, K., Zheng, Y.: Self-loop uncertainty: A novel pseudo-label for semi-supervised medical image segmentation. In: Martel, A.L., Abolmaesumi, P., Stoyanov, D., Mateus, D., Zuluaga, M.A., Zhou, S.K., Racoceanu, D., Joskowicz, L. (eds.) Medical Image Computing and Computer Assisted Intervention – MICCAI 2020. pp. 614–623. Springer International Publishing, Cham (2020)
  * [90] Li, Z., Li, Y., Li, Q., Wang, P., Guo, D., Lu, L., Jin, D., Zhang, Y., Hong, Q.: Lvit: language meets vision transformer in medical image segmentation. IEEE Transactions on Medical Imaging (2023)
  * [91] Lin, J., Xiao, Z., Wei, X., Duan, P., He, X., Dian, R., Li, Z., Li, S.: Click-pixel cognition fusion network with balanced cut for interactive image segmentation. IEEE Transactions on Image Processing 33, 177–190 (2024). https://doi.org/10.1109/TIP.2023.3338003
  * [92] Liu, L., Yager, R.R.: Classic works of the dempster-shafer theory of belief functions: An introduction. In: Yager, R.R., Liu, L. (eds.) Classic Works of the Dempster-Shafer Theory of Belief Functions, Studies in Fuzziness and Soft Computing, vol. 219, pp. 1–34. Springer (2008). https://doi.org/10.1007/978-3-540-44792-4_1, https://doi.org/10.1007/978-3-540-44792-4_1
  * [93] Liu, W.: Analyzing the degree of conflict among belief functions. Artif. Intell. 170(11), 909–924 (2006). https://doi.org/10.1016/J.ARTINT.2006.05.002, https://doi.org/10.1016/j.artint.2006.05.002
  * [94] Liu, Y., Wang, W., Luo, G., Wang, K., Li, S.: A contrastive consistency semi-supervised left atrium segmentation model. Computerized Medical Imaging and Graphics 99, 102092 (2022). https://doi.org/https://doi.org/10.1016/j.compmedimag.2022.102092, https://www.sciencedirect.com/science/article/pii/S0895611122000659
  * [95] Lowrance, J.D., Garvey, T.D., Strat, T.M.: A framework for evidential-reasoning systems. In: Kehler, T., Rosenschein, S.J. (eds.) Proceedings of the 5th National Conference on Artificial Intelligence. Philadelphia, PA, USA, August 11-15, 1986. Volume 2: Engineering. pp. 896–903. Morgan Kaufmann (1986), http://www.aaai.org/Library/AAAI/1986/aaai86-149.php
  * [96] Lu, L., Yin, M., Fu, L., Yang, F.: Uncertainty-aware pseudo-label and consistency for semi-supervised medical image segmentation. Biomedical Signal Processing and Control 79, 104203 (2023)
  * [97] Lu, W., Lei, J., Qiu, P., Sheng, R., Zhou, J., Lu, X., Yang, Y.: Upcol: Uncertainty-informed prototype consistency learning for semi-supervised medical image segmentation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 662–672. Springer (2023)
  * [98] Luo, X., Chen, J., Song, T., Wang, G.: Semi-supervised medical image segmentation through dual-task consistency. In: Thirty-Fifth AAAI Conference on Artificial Intelligence, AAAI 2021, Thirty-Third Conference on Innovative Applications of Artificial Intelligence, IAAI 2021, The Eleventh Symposium on Educational Advances in Artificial Intelligence, EAAI 2021, Virtual Event, February 2-9, 2021. pp. 8801–8809. AAAI Press (2021). https://doi.org/10.1609/aaai.v35i10.17066, https://doi.org/10.1609/aaai.v35i10.17066
  * [99] Luo, X., Chen, J., Song, T., Wang, G.: Semi-supervised medical image segmentation through dual-task consistency. In: Proceedings of the AAAI Conference on Artificial Intelligence. vol. 35, pp. 8801–8809 (2021)
  * [100] Luo, X., Liao, W., Chen, J., Song, T., Chen, Y., Zhang, S., Chen, N., Wang, G., Zhang, S.: Efficient semi-supervised gross target volume of nasopharyngeal carcinoma segmentation via uncertainty rectified pyramid consistency. In: de Bruijne, M., Cattin, P.C., Cotin, S., Padoy, N., Speidel, S., Zheng, Y., Essert, C. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2021 - 24th International Conference, Strasbourg, France, September 27 - October 1, 2021, Proceedings, Part II. Lecture Notes in Computer Science, vol. 12902, pp. 318–329. Springer (2021). https://doi.org/10.1007/978-3-030-87196-3_30, https://doi.org/10.1007/978-3-030-87196-3_30
  * [101] Luo, X., Liao, W., Chen, J., Song, T., Chen, Y., Zhang, S., Chen, N., Wang, G., Zhang, S.: Efficient semi-supervised gross target volume of nasopharyngeal carcinoma segmentation via uncertainty rectified pyramid consistency. In: Medical Image Computing and Computer Assisted Intervention–MICCAI 2021: 24th International Conference, Strasbourg, France, September 27–October 1, 2021, Proceedings, Part II 24. pp. 318–329. Springer (2021)
  * [102] Luo, X., Wang, G., Liao, W., Chen, J., Song, T., Chen, Y., Zhang, S., Metaxas, D.N., Zhang, S.: Semi-supervised medical image segmentation via uncertainty rectified pyramid consistency. Medical Image Analysis 80, 102517 (2022)
  * [103] Meinert, N., Gawlikowski, J., Lavin, A.: The unreasonable effectiveness of deep evidential regression. In: Williams, B., Chen, Y., Neville, J. (eds.) Thirty-Seventh AAAI Conference on Artificial Intelligence, AAAI 2023, Thirty-Fifth Conference on Innovative Applications of Artificial Intelligence, IAAI 2023, Thirteenth Symposium on Educational Advances in Artificial Intelligence, EAAI 2023, Washington, DC, USA, February 7-14, 2023. pp. 9134–9142. AAAI Press (2023). https://doi.org/10.1609/AAAI.V37I8.26096, https://doi.org/10.1609/aaai.v37i8.26096
  * [104] Meng, Y., Zhang, H., Zhao, Y., Gao, D., Hamill, B., Patri, G., Peto, T., Madhusudhan, S., Zheng, Y.: Dual consistency enabled weakly and semi-supervised optic disc and cup segmentation with dual adaptive graph convolutional networks. IEEE Transactions on Medical Imaging 42(2), 416–429 (2022)
  * [105] Milletari, F., Navab, N., Ahmadi, S.A.: V-net: Fully convolutional neural networks for volumetric medical image segmentation. In: 2016 fourth international conference on 3D vision (3DV). pp. 565–571. Ieee (2016)
  * [106] Milletari, F., Navab, N., Ahmadi, S.: V-net: Fully convolutional neural networks for volumetric medical image segmentation. In: Fourth International Conference on 3D Vision, 3DV 2016, Stanford, CA, USA, October 25-28, 2016. pp. 565–571. IEEE Computer Society (2016). https://doi.org/10.1109/3DV.2016.79, https://doi.org/10.1109/3DV.2016.79
  * [107] Minaee, S., Boykov, Y., Porikli, F., Plaza, A., Kehtarnavaz, N., Terzopoulos, D.: Image segmentation using deep learning: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence 44(7), 3523–3542 (2021)
  * [108] Minaee, S., Boykov, Y., Porikli, F., Plaza, A., Kehtarnavaz, N., Terzopoulos, D.: Image segmentation using deep learning: A survey. IEEE Transactions on Pattern Analysis and Machine Intelligence 44(7), 3523–3542 (2022). https://doi.org/10.1109/TPAMI.2021.3059968
  * [109] Najjar, R.: Redefining radiology: A review of artificial intelligence integration in medical imaging. Diagnostics 13(17), 2760 (2023)
  * [110] Ouali, Y., Hudelot, C., Tami, M.: Semi-supervised semantic segmentation with cross-consistency training. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 12674–12684 (2020)
  * [111] Ouali, Y., Hudelot, C., Tami, M.: Semi-supervised semantic segmentation with cross-consistency training. In: 2020 IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2020, Seattle, WA, USA, June 13-19, 2020. pp. 12671–12681. Computer Vision Foundation / IEEE (2020). https://doi.org/10.1109/CVPR42600.2020.01269, https://openaccess.thecvf.com/content_CVPR_2020/html/Ouali_Semi-Supervised_Semantic_Segmentation_With_Cross-Consistency_Training_CVPR_2020_paper.html
  * [112] Peiris, H., Chen, Z., Egan, G., Harandi, M.: Duo-segnet: adversarial dual-views for semi-supervised medical image segmentation. In: Medical Image Computing and Computer Assisted Intervention–MICCAI 2021: 24th International Conference, Strasbourg, France, September 27–October 1, 2021, Proceedings, Part II 24. pp. 428–438. Springer (2021)
  * [113] Peiris, H., Hayat, M., Chen, Z., Egan, G., Harandi, M.: Uncertainty-guided dual-views for semi-supervised volumetric medical image segmentation. Nature Machine Intelligence 5(7), 724–738 (2023)
  * [114] Peng, J., Estrada, G., Pedersoli, M., Desrosiers, C.: Deep co-training for semi-supervised image segmentation. Pattern Recognit. 107, 107269 (2020). https://doi.org/10.1016/J.PATCOG.2020.107269, https://doi.org/10.1016/j.patcog.2020.107269
  * [115] Qiu, L., Cheng, J., Gao, H., Xiong, W., Ren, H.: Federated semi-supervised learning for medical image segmentation via pseudo-label denoising. IEEE Journal of Biomedical and Health Informatics (2023)
  * [116] Qiu, Z., Hu, Y., Chen, X., Zeng, D., Hu, Q., Liu, J.: Rethinking dual-stream super-resolution semantic learning in medical image segmentation. IEEE Transactions on Pattern Analysis and Machine Intelligence (2023)
  * [117] Qureshi, I., Yan, J., Abbas, Q., Shaheed, K., Riaz, A.B., Wahid, A., Khan, M.W.J., Szczuko, P.: Medical image segmentation using deep semantic-based methods: A review of techniques, applications and emerging trends. Information Fusion 90, 316–352 (2023)
  * [118] Rahman, A., Valanarasu, J.M.J., Hacihaliloglu, I., Patel, V.M.: Ambiguous medical image segmentation using diffusion models. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 11536–11546 (2023)
  * [119] Rangnekar, A., Kanan, C., Hoffman, M.: Semantic segmentation with active semi-supervised learning. In: Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision. pp. 5966–5977 (2023)
  * [120] Rizve, M.N., Duarte, K., Rawat, Y.S., Shah, M.: In defense of pseudo-labeling: An uncertainty-aware pseudo-label selection framework for semi-supervised learning. In: 9th International Conference on Learning Representations, ICLR 2021, Virtual Event, Austria, May 3-7, 2021. OpenReview.net (2021), https://openreview.net/forum?id=-ODN6SbiUU
  * [121] Ronneberger, O., Fischer, P., Brox, T.: U-net: Convolutional networks for biomedical image segmentation. In: Navab, N., Hornegger, J., III, W.M.W., Frangi, A.F. (eds.) Medical Image Computing and Computer-Assisted Intervention - MICCAI 2015 - 18th International Conference Munich, Germany, October 5 - 9, 2015, Proceedings, Part III. Lecture Notes in Computer Science, vol. 9351, pp. 234–241. Springer (2015). https://doi.org/10.1007/978-3-319-24574-4_28, https://doi.org/10.1007/978-3-319-24574-4_28
  * [122] Roth, H.R., Lu, L., Farag, A., Shin, H.C., Liu, J., Turkbey, E.B., Summers, R.M.: Deeporgan: Multi-level deep convolutional networks for automated pancreas segmentation. In: Medical Image Computing and Computer-Assisted Intervention–MICCAI 2015: 18th International Conference, Munich, Germany, October 5-9, 2015, Proceedings, Part I 18. pp. 556–564. Springer (2015)
  * [123] Roy, S., Koehler, G., Ulrich, C., Baumgartner, M., Petersen, J., Isensee, F., Jaeger, P.F., Maier-Hein, K.H.: Mednext: transformer-driven scaling of convnets for medical image segmentation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 405–415. Springer (2023)
  * [124] Sajjadi, M., Javanmardi, M., Tasdizen, T.: Regularization with stochastic transformations and perturbations for deep semi-supervised learning. In: Lee, D.D., Sugiyama, M., von Luxburg, U., Guyon, I., Garnett, R. (eds.) Advances in Neural Information Processing Systems 29: Annual Conference on Neural Information Processing Systems 2016, December 5-10, 2016, Barcelona, Spain. pp. 1163–1171 (2016), https://proceedings.neurips.cc/paper/2016/hash/30ef30b64204a3088a26bc2e6ecf7602-Abstract.html
  * [125] Sensoy, M., Kaplan, L., Kandemir, M.: Evidential deep learning to quantify classification uncertainty. Advances in neural information processing systems 31 (2018)
  * [126] Sensoy, M., Kaplan, L.M., Kandemir, M.: Evidential deep learning to quantify classification uncertainty. In: Bengio, S., Wallach, H.M., Larochelle, H., Grauman, K., Cesa-Bianchi, N., Garnett, R. (eds.) Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montréal, Canada. pp. 3183–3193 (2018), https://proceedings.neurips.cc/paper/2018/hash/a981f2b708044d6fb4a71a1463242520-Abstract.html
  * [127] Shafer, G.: A mathematical theory of evidence turns 40. Int. J. Approx. Reason. 79, 7–25 (2016). https://doi.org/10.1016/j.ijar.2016.07.009, https://doi.org/10.1016/j.ijar.2016.07.009
  * [128] Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(3), 379–423 (1948). https://doi.org/10.1002/J.1538-7305.1948.TB01338.X, https://doi.org/10.1002/j.1538-7305.1948.tb01338.x
  * [129] Shannon, C.E.: A mathematical theory of communication. ACM SIGMOBILE Mob. Comput. Commun. Rev. 5(1), 3–55 (2001). https://doi.org/10.1145/584091.584093, https://doi.org/10.1145/584091.584093
  * [130] Shi, Y., Zhang, J., Ling, T., Lu, J., Zheng, Y., Yu, Q., Qi, L., Gao, Y.: Inconsistency-aware uncertainty estimation for semi-supervised medical image segmentation. IEEE transactions on medical imaging 41(3), 608–620 (2021)
  * [131] Shi, Y., Zhang, J., Ling, T., Lu, J., Zheng, Y., Yu, Q., Qi, L., Gao, Y.: Inconsistency-aware uncertainty estimation for semi-supervised medical image segmentation. IEEE Transactions on Medical Imaging 41(3), 608–620 (2022). https://doi.org/10.1109/TMI.2021.3117888
  * [132] Shi, Y., Zhang, J., Ling, T., Lu, J., Zheng, Y., Yu, Q., Qi, L., Gao, Y.: Inconsistency-aware uncertainty estimation for semi-supervised medical image segmentation. IEEE Trans. Medical Imaging 41(3), 608–620 (2022). https://doi.org/10.1109/TMI.2021.3117888, https://doi.org/10.1109/TMI.2021.3117888
  * [133] Shin, H., Kim, H., Kim, S., Jun, Y., Eo, T., Hwang, D.: SDC-UDA: volumetric unsupervised domain adaptation framework for slice-direction continuous cross-modality medical image segmentation. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2023, Vancouver, BC, Canada, June 17-24, 2023. pp. 7412–7421. IEEE (2023). https://doi.org/10.1109/CVPR52729.2023.00716, https://doi.org/10.1109/CVPR52729.2023.00716
  * [134] Smets, P.: Constructing the pignistic probability function in a context of uncertainty. In: Henrion, M., Shachter, R.D., Kanal, L.N., Lemmer, J.F. (eds.) UAI ’89: Proceedings of the Fifth Annual Conference on Uncertainty in Artificial Intelligence, Windsor, Ontario, Canada, August 18-20, 1989. pp. 29–40. North-Holland (1989), https://dslpitt.org/uai/displayArticleDetails.jsp?mmnu=1&smnu=2&article_id=1864&proceeding_id=1005
  * [135] Tang, L., Li, K., He, C., Zhang, Y., Li, X.: Source-free domain adaptive fundus image segmentation with class-balanced mean teacher. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 684–694. Springer (2023)
  * [136] Tarvainen, A., Valpola, H.: Mean teachers are better role models: Weight-averaged consistency targets improve semi-supervised deep learning results. Advances in neural information processing systems 30 (2017)
  * [137] Tragakis, A., Kaul, C., Murray-Smith, R., Husmeier, D.: The fully convolutional transformer for medical image segmentation. In: Proceedings of the IEEE/CVF Winter Conference on Applications of Computer Vision. pp. 3660–3669 (2023)
  * [138] Tu, P., Huang, Y., Zheng, F., He, Z., Cao, L., Shao, L.: Guidedmix-net: Semi-supervised semantic segmentation by using labeled images as reference. In: Proceedings of the AAAI Conference on Artificial Intelligence. vol. 36, pp. 2379–2387 (2022)
  * [139] Vu, T., Jain, H., Bucher, M., Cord, M., Pérez, P.: ADVENT: adversarial entropy minimization for domain adaptation in semantic segmentation. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2019, Long Beach, CA, USA, June 16-20, 2019. pp. 2517–2526. Computer Vision Foundation / IEEE (2019). https://doi.org/10.1109/CVPR.2019.00262, http://openaccess.thecvf.com/content_CVPR_2019/html/Vu_ADVENT_Adversarial_Entropy_Minimization_for_Domain_Adaptation_in_Semantic_Segmentation_CVPR_2019_paper.html
  * [140] Wang, K., Zhan, B., Zu, C., Wu, X., Zhou, J., Zhou, L., Wang, Y.: Semi-supervised medical image segmentation via a tripled-uncertainty guided mean teacher model with contrastive learning. Medical Image Analysis 79, 102447 (2022)
  * [141] Wang, K., Zhan, B., Zu, C., Wu, X., Zhou, J., Zhou, L., Wang, Y.: Semi-supervised medical image segmentation via a tripled-uncertainty guided mean teacher model with contrastive learning. Medical Image Anal. 79, 102447 (2022). https://doi.org/10.1016/J.MEDIA.2022.102447, https://doi.org/10.1016/j.media.2022.102447
  * [142] Wang, K., Liew, J.H., Zou, Y., Zhou, D., Feng, J.: Panet: Few-shot image semantic segmentation with prototype alignment. In: proceedings of the IEEE/CVF international conference on computer vision. pp. 9197–9206 (2019)
  * [143] Wang, P., Peng, J., Pedersoli, M., Zhou, Y., Zhang, C., Desrosiers, C.: Self-paced and self-consistent co-training for semi-supervised image segmentation. Medical Image Anal. 73, 102146 (2021). https://doi.org/10.1016/J.MEDIA.2021.102146, https://doi.org/10.1016/j.media.2021.102146
  * [144] Wang, P., Peng, J., Pedersoli, M., Zhou, Y., Zhang, C., Desrosiers, C.: Cat: Constrained adversarial training for anatomically-plausible semi-supervised segmentation. IEEE Transactions on Medical Imaging (2023)
  * [145] Wang, Q., Li, W., Gool, L.V.: Semi-supervised learning by augmented distribution alignment. In: 2019 IEEE/CVF International Conference on Computer Vision, ICCV 2019, Seoul, Korea (South), October 27 - November 2, 2019. pp. 1466–1475. IEEE (2019). https://doi.org/10.1109/ICCV.2019.00155, https://doi.org/10.1109/ICCV.2019.00155
  * [146] Wang, R., Lei, T., Cui, R., Zhang, B., Meng, H., Nandi, A.K.: Medical image segmentation using deep learning: A survey. IET Image Processing 16(5), 1243–1267 (2022)
  * [147] Wang, T., Lu, J., Lai, Z., Wen, J., Kong, H.: Uncertainty-guided pixel contrastive learning for semi-supervised medical image segmentation. In: Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence, IJCAI. pp. 1444–1450 (2022)
  * [148] Wang, Y., Zhang, Y., Tian, J., Zhong, C., Shi, Z., Zhang, Y., He, Z.: Double-uncertainty weighted method for semi-supervised learning. In: Martel, A.L., Abolmaesumi, P., Stoyanov, D., Mateus, D., Zuluaga, M.A., Zhou, S.K., Racoceanu, D., Joskowicz, L. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2020 - 23rd International Conference, Lima, Peru, October 4-8, 2020, Proceedings, Part I. Lecture Notes in Computer Science, vol. 12261, pp. 542–551. Springer (2020). https://doi.org/10.1007/978-3-030-59710-8_53, https://doi.org/10.1007/978-3-030-59710-8_53
  * [149] Wang, Y., Xiao, B., Bi, X., Li, W., Gao, X.: Mcf: Mutual correction framework for semi-supervised medical image segmentation. In: Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition. pp. 15651–15660 (2023)
  * [150] Wang, Y., Wang, H., Shen, Y., Fei, J., Li, W., Jin, G., Wu, L., Zhao, R., Le, X.: Semi-supervised semantic segmentation using unreliable pseudo-labels. In: IEEE/CVF Conference on Computer Vision and Pattern Recognition, CVPR 2022, New Orleans, LA, USA, June 18-24, 2022. pp. 4238–4247. IEEE (2022). https://doi.org/10.1109/CVPR52688.2022.00421, https://doi.org/10.1109/CVPR52688.2022.00421
  * [151] Wilson, N.: Decision-making with belief functions and pignistic probabilities. In: Clarke, M., Kruse, R., Moral, S. (eds.) Symbolic and Quantitative Approaches to Reasoning and Uncertainty, European Conference, ECSQARU’93, Granada, Spain, November 8-10, 1993, Proceedings. Lecture Notes in Computer Science, vol. 747, pp. 364–371. Springer (1993). https://doi.org/10.1007/BFb0028222, https://doi.org/10.1007/BFb0028222
  * [152] Wu, F., Zhuang, X.: Minimizing estimated risks on unlabeled data: A new formulation for semi-supervised medical image segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 45(5), 6021–6036 (2023). https://doi.org/10.1109/TPAMI.2022.3215186, https://doi.org/10.1109/TPAMI.2022.3215186
  * [153] Wu, H., Li, X., Cheng, K.T.: Exploring feature representation learning for semi-supervised medical image segmentation. IEEE Transactions on Neural Networks and Learning Systems (2023)
  * [154] Wu, L., Fang, L., He, X., He, M., Ma, J., Zhong, Z.: Querying labeled for unlabeled: Cross-image semantic consistency guided semi-supervised semantic segmentation. IEEE Trans. Pattern Anal. Mach. Intell. 45(7), 8827–8844 (2023). https://doi.org/10.1109/TPAMI.2022.3233584, https://doi.org/10.1109/TPAMI.2022.3233584
  * [155] Wu, W., Zhang, C., Woodland, P.C.: Estimating the uncertainty in emotion attributes using deep evidential regression. In: Rogers, A., Boyd-Graber, J.L., Okazaki, N. (eds.) Proceedings of the 61st Annual Meeting of the Association for Computational Linguistics (Volume 1: Long Papers), ACL 2023, Toronto, Canada, July 9-14, 2023. pp. 15681–15695. Association for Computational Linguistics (2023). https://doi.org/10.18653/V1/2023.ACL-LONG.873, https://doi.org/10.18653/v1/2023.acl-long.873
  * [156] Wu, Y., Wu, Z., Wu, Q., Ge, Z., Cai, J.: Exploring smoothness and class-separation for semi-supervised medical image segmentation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 34–43. Springer (2022)
  * [157] Wu, Y., Wu, Z., Wu, Q., Ge, Z., Cai, J.: Exploring smoothness and class-separation for semi-supervised medical image segmentation. In: Wang, L., Dou, Q., Fletcher, P.T., Speidel, S., Li, S. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2022 - 25th International Conference, Singapore, September 18-22, 2022, Proceedings, Part V. Lecture Notes in Computer Science, vol. 13435, pp. 34–43. Springer (2022). https://doi.org/10.1007/978-3-031-16443-9_4, https://doi.org/10.1007/978-3-031-16443-9_4
  * [158] Wu, Y., Xu, M., Ge, Z., Cai, J., Zhang, L.: Semi-supervised left atrium segmentation with mutual consistency training. In: de Bruijne, M., Cattin, P.C., Cotin, S., Padoy, N., Speidel, S., Zheng, Y., Essert, C. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2021 - 24th International Conference, Strasbourg, France, September 27 - October 1, 2021, Proceedings, Part II. Lecture Notes in Computer Science, vol. 12902, pp. 297–306. Springer (2021). https://doi.org/10.1007/978-3-030-87196-3_28, https://doi.org/10.1007/978-3-030-87196-3_28
  * [159] Xia, Y., Liu, F., Yang, D., Cai, J., Yu, L., Zhu, Z., Xu, D., Yuille, A., Roth, H.: 3d semi-supervised learning with uncertainty-aware multi-view co-training. In: 2020 IEEE Winter Conference on Applications of Computer Vision (WACV). pp. 3635–3644 (2020). https://doi.org/10.1109/WACV45572.2020.9093608
  * [160] Xia, Y., Yang, D., Yu, Z., Liu, F., Cai, J., Yu, L., Zhu, Z., Xu, D., Yuille, A.L., Roth, H.: Uncertainty-aware multi-view co-training for semi-supervised medical image segmentation and domain adaptation. Medical Image Anal. 65, 101766 (2020). https://doi.org/10.1016/j.media.2020.101766, https://doi.org/10.1016/j.media.2020.101766
  * [161] Xiang, J., Qiu, P., Yang, Y.: Fussnet: Fusing two sources of uncertainty for semi-supervised medical image segmentation. In: International Conference on Medical Image Computing and Computer-Assisted Intervention. pp. 481–491. Springer (2022)
  * [162] Xiong, Z., Xia, Q., Hu, Z., Huang, N., Bian, C., Zheng, Y., Vesal, S., Ravikumar, N., Maier, A., Yang, X., et al.: A global benchmark of algorithms for segmenting the left atrium from late gadolinium-enhanced cardiac magnetic resonance imaging. Medical image analysis 67, 101832 (2021)
  * [163] Xiong, Z., Xia, Q., Hu, Z., Huang, N., Bian, C., Zheng, Y., Vesal, S., Ravikumar, N., Maier, A.K., Yang, X., Heng, P., Ni, D., Li, C., Tong, Q., Si, W., Puybareau, É., Khoudli, Y., Géraud, T., Zhao, J.: A global benchmark of algorithms for segmenting the left atrium from late gadolinium-enhanced cardiac magnetic resonance imaging. Medical Image Anal. 67, 101832 (2021). https://doi.org/10.1016/j.media.2020.101832, https://doi.org/10.1016/j.media.2020.101832
  * [164] Xu, W., Shi, J., Lin, Y., Liu, C., Xie, W., Liu, H., Huang, S., Zhu, D., Su, L., Huang, Y., et al.: Deep learning-based image segmentation model using an mri-based convolutional neural network for physiological evaluation of the heart. Frontiers in Physiology 14, 351 (2023)
  * [165] Xu, Y., Shang, L., Ye, J., Qian, Q., Li, Y., Sun, B., Li, H., Jin, R.: Dash: Semi-supervised learning with dynamic thresholding. In: Meila, M., Zhang, T. (eds.) Proceedings of the 38th International Conference on Machine Learning, ICML 2021, 18-24 July 2021, Virtual Event. Proceedings of Machine Learning Research, vol. 139, pp. 11525–11536. PMLR (2021), http://proceedings.mlr.press/v139/xu21e.html
  * [166] Xu, Z., Wang, Y., Lu, D., Yu, L., Yan, J., Luo, J., Ma, K., Zheng, Y., Tong, R.K.: All-around real label supervision: Cyclic prototype consistency learning for semi-supervised medical image segmentation. IEEE J. Biomed. Health Informatics 26(7), 3174–3184 (2022). https://doi.org/10.1109/JBHI.2022.3162043, https://doi.org/10.1109/JBHI.2022.3162043
  * [167] Yager, R.R.: Non-monotonic compatibility relations in the theory of evidence. Int. J. Man Mach. Stud. 29(5), 517–537 (1988). https://doi.org/10.1016/S0020-7373(88)80010-5, https://doi.org/10.1016/S0020-7373(88)80010-5
  * [168] Yager, R.R.: Entropy and specificity in a mathematical theory of evidence. In: Yager, R.R., Liu, L. (eds.) Classic Works of the Dempster-Shafer Theory of Belief Functions, Studies in Fuzziness and Soft Computing, vol. 219, pp. 291–310. Springer (2008). https://doi.org/10.1007/978-3-540-44792-4_11, https://doi.org/10.1007/978-3-540-44792-4_11
  * [169] Yang, J., Tu, J., Zhang, X., Yu, S., Zheng, X.: Tse deeplab: An efficient visual transformer for medical image segmentation. Biomedical Signal Processing and Control 80, 104376 (2023)
  * [170] Yao, H., Hu, X., Li, X.: Enhancing pseudo label quality for semi-supervised domain-generalized medical image segmentation. In: Proceedings of the AAAI Conference on Artificial Intelligence. vol. 36, pp. 3099–3107 (2022)
  * [171] Yao, Z., Xie, W., Zhang, J., Dong, Y., Qiu, H., Yuan, H., Jia, Q., Wang, T., Shi, Y., Zhuang, J., et al.: Imagetbad: A 3d computed tomography angiography image dataset for automatic segmentation of type-b aortic dissection. Frontiers in Physiology 12, 732711 (2021)
  * [172] Yong, D.: Information volume of mass function. International Journal of Computers Communications & Control 15(6) (2020)
  * [173] Yu, L., Wang, S., Li, X., Fu, C., Heng, P.: Uncertainty-aware self-ensembling model for semi-supervised 3d left atrium segmentation. In: Shen, D., Liu, T., Peters, T.M., Staib, L.H., Essert, C., Zhou, S., Yap, P., Khan, A.R. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2019 - 22nd International Conference, Shenzhen, China, October 13-17, 2019, Proceedings, Part II. Lecture Notes in Computer Science, vol. 11765, pp. 605–613. Springer (2019). https://doi.org/10.1007/978-3-030-32245-8_67, https://doi.org/10.1007/978-3-030-32245-8_67
  * [174] Yu, L., Wang, S., Li, X., Fu, C.W., Heng, P.A.: Uncertainty-aware self-ensembling model for semi-supervised 3d left atrium segmentation. In: Medical Image Computing and Computer Assisted Intervention–MICCAI 2019: 22nd International Conference, Shenzhen, China, October 13–17, 2019, Proceedings, Part II 22. pp. 605–613. Springer (2019)
  * [175] Yuan, F., Zhang, Z., Fang, Z.: An effective cnn and transformer complementary network for medical image segmentation. Pattern Recognition 136, 109228 (2023)
  * [176] Yun, S., Han, D., Oh, S.J., Chun, S., Choe, J., Yoo, Y.: Cutmix: Regularization strategy to train strong classifiers with localizable features. In: Proceedings of the IEEE/CVF international conference on computer vision. pp. 6023–6032 (2019)
  * [177] Yushkevich, P.A., Piven, J., Cody Hazlett, H., Gimpel Smith, R., Ho, S., Gee, J.C., Gerig, G.: User-guided 3D active contour segmentation of anatomical structures: Significantly improved efficiency and reliability. Neuroimage 31(3), 1116–1128 (2006)
  * [178] Zhang, B., Wang, Y., Hou, W., Wu, H., Wang, J., Okumura, M., Shinozaki, T.: Flexmatch: Boosting semi-supervised learning with curriculum pseudo labeling. In: Ranzato, M., Beygelzimer, A., Dauphin, Y.N., Liang, P., Vaughan, J.W. (eds.) Advances in Neural Information Processing Systems 34: Annual Conference on Neural Information Processing Systems 2021, NeurIPS 2021, December 6-14, 2021, virtual. pp. 18408–18419 (2021), https://proceedings.neurips.cc/paper/2021/hash/995693c15f439e3d189b06e89d145dd5-Abstract.html
  * [179] Zhang, H., Cisse, M., Dauphin, Y.N., Lopez-Paz, D.: mixup: Beyond empirical risk minimization. arXiv preprint arXiv:1710.09412 (2017)
  * [180] Zhang, J., Zhang, S., Shen, X., Lukasiewicz, T., Xu, Z.: Multi-condos: Multimodal contrastive domain sharing generative adversarial networks for self-supervised medical image segmentation. IEEE Transactions on Medical Imaging (2023)
  * [181] Zhang, P., Zhang, B., Zhang, T., Chen, D., Wang, Y., Wen, F.: Prototypical pseudo label denoising and target structure learning for domain adaptive semantic segmentation. In: IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2021, virtual, June 19-25, 2021. pp. 12414–12424. Computer Vision Foundation / IEEE (2021). https://doi.org/10.1109/CVPR46437.2021.01223, https://openaccess.thecvf.com/content/CVPR2021/html/Zhang_Prototypical_Pseudo_Label_Denoising_and_Target_Structure_Learning_for_Domain_CVPR_2021_paper.html
  * [182] Zhang, X., Wei, Y., Yang, Y., Huang, T.S.: Sg-one: Similarity guidance network for one-shot semantic segmentation. IEEE transactions on cybernetics 50(9), 3855–3865 (2020)
  * [183] Zhang, Y., Destercke, S., Zhang, Z., Bouadi, T., Martin, A.: On computing evidential centroid through conjunctive combination: An impossibility theorem. IEEE Trans. Artif. Intell. 4(3), 487–496 (2023). https://doi.org/10.1109/TAI.2022.3180973, https://doi.org/10.1109/TAI.2022.3180973
  * [184] Zhang, Y., Yang, L., Chen, J., Fredericksen, M., Hughes, D.P., Chen, D.Z.: Deep adversarial networks for biomedical image segmentation utilizing unannotated images. In: Descoteaux, M., Maier-Hein, L., Franz, A.M., Jannin, P., Collins, D.L., Duchesne, S. (eds.) Medical Image Computing and Computer Assisted Intervention - MICCAI 2017 - 20th International Conference, Quebec City, QC, Canada, September 11-13, 2017, Proceedings, Part III. Lecture Notes in Computer Science, vol. 10435, pp. 408–416. Springer (2017). https://doi.org/10.1007/978-3-319-66179-7_47, https://doi.org/10.1007/978-3-319-66179-7_47
  * [185] Zhang, Y., Yang, L., Chen, J., Fredericksen, M., Hughes, D.P., Chen, D.Z.: Deep adversarial networks for biomedical image segmentation utilizing unannotated images. In: Medical Image Computing and Computer Assisted Intervention- MICCAI 2017: 20th International Conference, Quebec City, QC, Canada, September 11-13, 2017, Proceedings, Part III 20. pp. 408–416. Springer (2017)
  * [186] Zhang, Y.: Lung segmentation with nasnet-large-decoder net. arXiv preprint arXiv:2303.10315 (2023)
  * [187] Zhang, Z., Ran, R., Tian, C., Zhou, H., Li, X., Yang, F., Jiao, Z.: Self-aware and cross-sample prototypical learning for semi-supervised medical image segmentation. arXiv preprint arXiv:2305.16214 (2023)
  * [188] Zhao, T., Cao, K., Yao, J., Nogues, I., Lu, L., Huang, L., Xiao, J., Yin, Z., Zhang, L.: 3d graph anatomy geometry-integrated network for pancreatic mass segmentation, diagnosis, and quantitative patient management. In: Proceedings of the IEEE/CVF conference on computer vision and pattern recognition. pp. 13743–13752 (2021)
  * [189] Zhao, Y., Lu, K., Xue, J., Wang, S., Lu, J.: Semi-supervised medical image segmentation with voxel stability and reliability constraints. IEEE Journal of Biomedical and Health Informatics (2023)
  * [190] Zhou, H.Y., Guo, J., Zhang, Y., Han, X., Yu, L., Wang, L., Yu, Y.: nnformer: volumetric medical image segmentation via a 3d transformer. IEEE Transactions on Image Processing (2023)
  * [191] Zhou, Q., Deng, Y.: Fractal-based belief entropy. Inf. Sci. 587, 265–282 (2022). https://doi.org/10.1016/J.INS.2021.12.032, https://doi.org/10.1016/j.ins.2021.12.032
  * [192] Zhou, T., Li, Q., Lu, H., Cheng, Q., Zhang, X.: Gan review: Models and medical image fusion applications. Information Fusion 91, 134–148 (2023)
  * [193] Zhu, J., Bolsterlee, B., Chow, B.V., Song, Y., Meijering, E.: Hybrid dual mean-teacher network with double-uncertainty guidance for semi-supervised segmentation of mri scans. arXiv preprint arXiv:2303.05126 (2023)