Abbas Khanacw676@qmul.ac.uk1,2 Muhammad Asadmuhammad.asad@qmul.ac.uk3,2 Martin
Benningmartin.benning@ucl.ac.uk4,2 Caroline Roneyc.roney@qmul.ac.uk5,2 Gregory
Slabaughg.slabaugh@qmul.ac.uk1,2 School of Electronic Engineering and Computer
Science
Queen Mary University of London, UK
Queen Mary’s Digital Environment
Research Institute (DERI), London, UK
School of Biomedical Engineering and Imaging Sciences
King’s College London, UK
Department of Computer Science,
University College London, UK School of Engineering and Materials Science,
Queen Mary University of London, UK
Convolution and Attention-Free Segmentation

# Convolution and Attention-Free Mamba-based Cardiac Image Segmentation

###### Abstract

Convolutional Neural Networks (CNNs) and Transformer-based self-attention
models have become standard for medical image segmentation. This paper
demonstrates that convolution and self-attention, while widely used, are not
the only effective methods for segmentation. Breaking with convention, we
present a Convolution and self-Attention-Free Mamba-based semantic
Segmentation Network named CAF-MambaSegNet. Specifically, we design a Mamba-
based _Channel Aggregator_ and _Spatial Aggregator_ , which are applied
independently in each encoder-decoder stage. The Channel Aggregator extracts
information across different channels, and the Spatial Aggregator learns
features across different spatial locations. We also propose a Linearly
Interconnected Factorized Mamba (LIFM) Block to reduce the computational
complexity of a Mamba and to enhance its decision function by introducing a
non-linearity between two factorized Mamba blocks. Our goal is not to
outperform state-of-the-art results but to show how this innovative,
convolution and self-attention-free method can inspire further research beyond
well-established CNNs and Transformers, achieving linear complexity and
reducing the number of parameters. Source code and pre-trained models will be
publicly available.

##  1 Introduction

Image segmentation is an essential part of cardiac image analysis [Martin-Isla
et al.(2020)Martin-Isla, Campello, Izquierdo, Raisi-Estabragh, Baeßler,
Petersen, and Lekadir]. It can help quantify the size and shape of different
regions of interest, such as left ventricle (LV), right ventricle (RV), left
atrium (LA), right atrium (RA), myocardium (MYO), useful for monitoring
disease progression, prognosis and supporting computer-aided intervention
[Chen et al.(2020)Chen, Qin, Qiu, Tarroni, Duan, Bai, and Rueckert]. Manual
segmentation is considered a gold standard; however, with the advent of
artificial intelligence, more focus is paid to automatic methods for faster,
cheaper, and reproducible results [Litjens et al.(2019)Litjens, Ciompi,
Wolterink, de Vos, Leiner, Teuwen, and Išgum, Hesamian et al.(2019)Hesamian,
Jia, He, and Kennedy].
Convolutional neural networks (CNNs) and transformer-based self-attention
mechanisms have significantly evolved the landscape of medical image
segmentation [Yao et al.(2024)Yao, Bai, Liao, Chen, Liu, and Xie]. While CNNs
have been the commonly used choice [Aljuaid and Anwar(2022)], the current
literature suggests that self-attention-based methods generally produce better
results than CNN architectures [Khan et al.(2023)Khan, Lee, and Lee] due to
their global receptive field, ability to model long-range dependencies, and
dynamic weights mechanism [Dosovitskiy et al.(2020)Dosovitskiy, Beyer,
Kolesnikov, Weissenborn, Zhai, Unterthiner, Dehghani, Minderer, Heigold,
Gelly, et al.]. CNN-based architectures have been criticized for their limited
receptive field [Richter et al.(2021)Richter, Schöning, Wiedenroth, and
Krumnack], their limited ability to effectively capture long-range
dependencies, and their bias toward recognising textures rather than shapes
[Geirhos et al.(2018)Geirhos, Rubisch, Michaelis, Bethge, Wichmann, and
Brendel]. However, attention-based methods are computationally expensive
compared to CNNs due to their quadratic complexity [Niu et al.(2021)Niu,
Zhong, and Yu] and excessive memory requirements [Ramachandran et
al.(2019)Ramachandran, Parmar, Vaswani, Bello, Levskaya, and Shlens]. The
computer vision community has tried to reduce its computational complexity
while maintaining accuracy, including efficient additive attention [Shaker et
al.(2023)Shaker, Maaz, Rasheed, Khan, Yang, and Khan], efficient self-
attention [Gao et al.(2021)Gao, Zhou, and Metaxas], and separable self-
attention [Mehta and Rastegari(2022)]. Hybrid CNN-transformer-based
segmentation methods have also been a recent trend that harnesses relative
strengths [Tang et al.(2024)Tang, Chen, Wang, Zhou, Zhao, Gao, Du, Tan, Zhang,
and Tong, Khan et al.(2024)Khan, Asad, Benning, Roney, and Slabaugh]. These
methods consecutively combine CNN and self-attention layers to capture both
local and global features while reducing the computational complexity of self-
attention.

State space models (SSMs) [Gu et al.(2021)Gu, Goel, and Re] such as Mamba [Gu
and Dao(2023)] have recently emerged as a potential replacement for
transformers due to their ability to capture long-range dependencies under
linear complexity computation. Several architectures have been proposed to
show the power of Mamba for computer vision tasks, including Vision Mamba [Zhu
et al.(2024)Zhu, Liao, Zhang, Wang, Liu, and Wang], Visual Mamba (VMamba) [Liu
et al.(2024)Liu, Tian, Zhao, Yu, Xie, Wang, Ye, and Liu] ZigMa [Hu et
al.(2024)Hu, Baumann, Gui, Grebenkova, Ma, Fischer, and Ommer], and medical
image segmentation is no exception [Ruan and Xiang(2024), Wang et
al.(2024)Wang, Zheng, Zhang, Cui, and Li]. Most existing encoder-decoder
medical image segmentation architectures inspired by Mamba [Gu and Dao(2023)]
and vision transformers [Dosovitskiy et al.(2020)Dosovitskiy, Beyer,
Kolesnikov, Weissenborn, Zhai, Unterthiner, Dehghani, Minderer, Heigold,
Gelly, et al.] differ in how the convolution layers, self-attention, and Mamba
blocks are arranged. In this paper, we go beyond the arrangements of these
blocks and propose a novel convolution and attention-free CAF-MambaSegNet.

##  2 Related Work

UNet [Ronneberger et al.(2015)Ronneberger, Fischer, and Brox] is a pioneering
network architecture for medical image segmentation, and several subsequent
architectures, including ResUNet [Diakogiannis et al.(2020)Diakogiannis,
Waldner, Caccetta, and Wu], UNet++ [Zhou et al.(2019)Zhou, Siddiquee,
Tajbakhsh, and Liang], have extended its initial formulation. These networks
use an encoder-decoder design, where the encoder extracts information from
images, and the decoder reconstructs the segmentation map. Skip connections
[Drozdzal et al.(2016)Drozdzal, Vorontsov, Chartrand, Kadoury, and Pal] are
also vital to mitigate the vanishing gradient problem and reuse the features
from the encoder side. With the advent of the vision transformer [Dosovitskiy
et al.(2020)Dosovitskiy, Beyer, Kolesnikov, Weissenborn, Zhai, Unterthiner,
Dehghani, Minderer, Heigold, Gelly, et al.], self-attention-based methods have
become popular in medical image segmentation to overcome the limitations of
CNN-based pipelines, as mentioned before. These methods include Swin-UNet [Cao
et al.(2022)Cao, Wang, Chen, Jiang, Zhang, Tian, and Wang], which replaces the
convolutional layers with Swin-Transformer blocks [Liu et al.(2021)Liu, Lin,
Cao, Hu, Wei, Zhang, Lin, and Guo]. The Swin-UNet also follows a U-shaped
architecture, where the encoder utilises a hierarchical Swin Transformer with
shifted windows to extract context features and a symmetric decoder with
patch-expanding layers for up-sampling. The UNEt TRansformers (UNETR)
[Hatamizadeh et al.(2022)Hatamizadeh, Tang, Nath, Yang, Myronenko, Landman,
Roth, and Xu] uses a transformer-based encoder to learn sequence
representations of the input images, allowing the network to capture global
multi-scale information and a CNN-based decoder for localized information.
Similar to Swin-UNet [Cao et al.(2022)Cao, Wang, Chen, Jiang, Zhang, Tian, and
Wang], Swin-UNETR [Hatamizadeh et al.(2021)Hatamizadeh, Nath, Tang, Yang,
Roth, and Xu] is also built on a hierarchical Swin transformer. However, it
has a hybrid architecture that only uses a Swin transformer in the encoder to
extract features and a CNN-based decoder to generate the segmentation map.

Recently, Mamba has gained prominence in the computer vision field and
integrates Gated MLP [Mehta et al.(2022)Mehta, Gupta, Cutkosky, and Neyshabur]
into the SSM of H3 [Dao et al.(2023)Dao, Fu, Saab, Thomas, Rudra, and Ré].
Readers are encouraged to refer to [Patro and Agneeswaran(2024), Zhang et
al.(2024)Zhang, Zhu, Wang, Zhang, Chen, and Ye] for a more comprehensive
understanding of this topic. Here, we will list some related Mamba
architectures used for medical image segmentation. Mamba-UNet [Wang et
al.(2024)Wang, Zheng, Zhang, Cui, and Li] incorporates the VMamba-based [Liu
et al.(2024)Liu, Tian, Zhao, Yu, Xie, Wang, Ye, and Liu] encoder-decoder
structure with UNet. The Cross-Scan Module from VMamba scans the input image
in four ways to integrate information from all other locations for each
element of the features. Mamba-UNet utilizes these VMamba blocks throughout
the U-shaped architecture to capture semantic contexts from intensity images.
Vision Mamba UNet (VM-UNet) [Ruan and Xiang(2024)] extends Vision Mamba [Zhu
et al.(2024)Zhu, Liao, Zhang, Wang, Liu, and Wang] using foundation blocks
named Visual State Space. Its asymmetrical encoder-decoder structure leverages
the power of SSMs to capture contextual information while maintaining linear
computational complexity.

Nevertheless, these hybrid methods address the challenges posed by self-
attention and CNNs and utilize both local and global features in dense
prediction tasks, like segmentation. However, convolution-free methods have
been a recent trend in computer vision, and some of these approaches have
tried to utilize self-attention-based architectures only. For example, Kim et
al. [Kim et al.(2022)Kim, Kim, Lan, Zeng, and Kwak] proposed ReSTR for
referring image segmentation, where transformer-based encoders extract
features from each modality, image and text, followed by coarse-to-fine
segmentation decoder transforms to reconstruct the output from fused features.
Karimi et al. [Karimi et al.(2021)Karimi, Vasylechko, and Gholipour] proposed
a convolution-free 3D network for medical image segmentation. The 3D image
block is divided into $n^{k}$ patches (k=3, or k=5), and computes a 1D
embedding for each patch. Their method predicts centre patch of the block
using self-attention between patch embeddings. MLP-Mixer [Tolstikhin et
al.(2021)Tolstikhin, Houlsby, Kolesnikov, Beyer, Zhai, Unterthiner, Yung,
Steiner, Keysers, Uszkoreit, et al.] proposed an alternative architecture for
image classification task built solely on multi-layer perceptrons (MLPs). The
channel- and token-mixing MLPs learn the per-location features and between
different spatial locations (tokens), respectively.

Although these most recent models attempt to overcome challenges posed by
CNNs, they are based on self-attention with quadratic computational complexity
and high memory issues. This paper introduces a convolution-free method to
mitigate the limitations of convolution-based architectures and a self-
attention-free approach with benefits that self-attention brings, i.e., the
global receptive field, dynamic weight mechanism, and long-range dependencies
at the expense of linear complexity. The contributions of this work are:

  1. 1.

To the best of our knowledge, we are the first to propose a convolution and
self-attention-free Mamba-based segmentation network, CAF-MambaSegNet.

  2. 2.

We propose a Linearly Interconnected Factorized Mamba (LIFM) Block to reduce
the trainable parameters of Mamba and enhance its non-linearity, and a weight-
sharing strategy for different scanning directions, specifically for the two
scanning direction strategies of vision Mamba to further reduce the
computational complexity whilst maintaining accuracy

  3. 3.

We introduce Mamba Channel Aggregation (MCA) and Mamba Spatial Aggregation
(MSA) and demonstrate how they can learn information along the channel and
spatial dimensions of the features, respectively.

  4. 4.

Extensive ablation studies are conducted to showcase the efficacy of each
component. Our proposed Mamba-based architecture is compared on the cardiac
image segmentation task against existing state-of-the-art segmentation
methods, including pure CNN, self-attention, and hybrid self-attention, as
well as methods using the original Mamba-based architecture combined with
CNNs.

##  3 Methodology

The proposed convolution and a self-attention-free segmentation network, CAF-
MambaSegNet, is shown in Fig. 1 (a). We removed the ‘Local convolution’ inside
the Mamba block to support our proposed _convolution-free_ approach,
demonstrated in Fig. 1 (b). The proposed architecture is built solely by
utilizing the SSMs and linear layers and performing on par with the existing
state-of-the-art methods at the expense of fewer parameters. This section will
explain the components of the CAF-MambaSegNet.

###  3.1 Factorized Mamba

Inspired by deep CNNs [Simonyan and Zisserman(2015)], where a stack of two
$3\times 3$ convolution filters have an effective receptive field of $5\times
5$, we propose the idea of factorized Mamba, which makes the decision function
more discriminative and also reduces the number of parameters. The ‘Mamba
block expansion factor’ _(E)_ and the ‘SSM state expansion factor’ _(D)_
control the overall complexity of the Mamba. More specifically, _E_ expands
the dimensions of the Mamba block using linear layers with learned weights
$\mathbf{W}_{1}$, and $\mathbf{W}_{2}$, while _D_ projects the dimension
within the SSM. We implemented the Mamba block with various _E_ and _D_
factors and analyzed their computational complexity, shown in Table 1
supplementary material. In the Mamba block, most of the parameters stem from
_E_ and with minimal increment from _D_. Most of the existing Mamba-based
networks use the default SSM and Mamba block extension, shown in Fig. 1 (c),
which is computationally expensive, and a single Mamba block brings 11,776
trainable parameters (for $c_{in}$=32 and $c_{out}$=64). Mathematically, it
can be represented as,

$x_{\text{out}}=\textbf{NC-
MambaBlock}(x_{\text{in}},D,E)=\mathbf{W}_{3}\Bigl{(}\sigma(\mathbf{W}_{2}x_{in})\odot\mathbf{SSM}(\sigma(\mathbf{W}_{1}x_{in}))\Bigr{)},$
(1)

where $\mathbf{W}_{1}$,$\mathbf{W}_{2}$,$\mathbf{W}_{3}$ are learnable weights
for linear layers shown in Fig. 1 (b) used for input $x_{in}$ projection,
$\odot$ represents element-wise multiplication and $\sigma$ SiLU activation
[Elfwing et al.(2018)Elfwing, Uchibe, and Doya].
Our factorized Mamba Block splits the extension parameters for SSM and Mamba,
shown in Fig. 1 (d). We also add a linear layer followed by SiLU activation
[Elfwing et al.(2018)Elfwing, Uchibe, and Doya] between two Mamba blocks to
add more non-linearity and named it the Linearly Interconnected Factorized
Mamba (LIFM) Block, used throughout our proposed architecture. A single
factorized Mamba block has 4,608 parameters (for $c_{in}$=32 and
$c_{out}$=64), and the proposed LIFM-Block requires only 9,184 trainable
parameters. For the first factorized Mamba block and linear layer, $C_{in}$ =
$C_{out}$ = 32, and for the second factorized Mamba block, $C_{out}$ = 64.
Mathematically, we can represent LIFM Block as,

$x_{\text{1}}=\textbf{NC-
MambaBlock}(x_{\text{in}},D_{1},E_{1}),\quad\quad\textrm{and}\quad\quad
x_{\text{2}}=\sigma(\mathbf{W}_{fm}x_{\text{1}}),$ (2)

and finally,

$x_{\text{out}}=\textbf{NC-MambaBlock}(x_{\text{2}},D_{2},E_{2}),$ (3)

where, $D_{1}$ = $D_{2}$ = 2 , and $E_{1}$ = $E_{2}$ = 1, $\mathbf{W}_{fm}$
represents the linear layer between factorized two Mamba blocks.

Empirically, we also found that a large Mamba block can easily overfit the
data and increase the overall computational burden of the network. So, we
factorized the larger Mamba blocks at each stage and used two consecutive
relatively smaller ones. This factorized approach reduces the number of
trainable parameters and helps the network to increase its non-linearity and
learn more complex patterns and representations in the data.

Figure 1: The proposed CAF-MambaSegNet Architecture (a), The Non-Convolutional
(NC) Mamba Block without local convolution (b), Comparison of proposed LIFM
Block with original Mamba, (b) and (c), Overview of proposed Mamba Channel
Aggregator (MCA), and Mamba Spatial Aggregator (MSA), shown in (e), and (g)
respectively, and the Channel-Spatial Information Fusion (CS-IF) Module (g).

###  3.2 Mamba Channel Aggregator

The Mamba channel aggregator (MCA) aims to learn cross-channel information, as
shown in Fig. 1 (e), learning the per-location features at different channels.
Similar to a CNN-based encoder-decoder structure, the number of channels is
increased as $\\{64,128,256,512,1024\\}$ at each encoder stage and decreased
as $\\{512,256,128,64\\}$ at each decoder stage. For the channel aggregator,
the incoming features $\mathbb{R}^{B\times C\times H\times W}$ are reshaped to
$\mathbb{R}^{B\times L\times C}$ where (B: Batch size, C: Number of channels,
H: Height, W: Width), and L = H$\times$W. Then, the input is divided into two
branches where, in one branch, the LIFM Block is applied, and the second
branch acts as a residual connection, where a linear layer is used, followed
by an element-wise addition operation with the features of the first branch.
Mathematically, it can be represented as,

$x_{\text{out}}=\overline{\mathbf{f_{1}}}\Bigl{(}\mathbf{LIFM\\_Block}\bigl{(}\mathbf{f_{1}}(x_{\text{in}}))\oplus\mathbf{W}_{c}(\mathbf{f_{1}}(x_{\text{in}}))\Bigl{)},$
(4)

where, $\mathbf{f}_{1}:\mathbb{R}^{B\times C\times H\times
W}\rightarrow\mathbb{R}^{B\times L\times C}$ represents a reshaping function
and $\overline{\mathbf{f_{1}}}:\mathbb{R}^{B\times L\times
C}\rightarrow\mathbb{R}^{B\times C\times H\times W}$ performs the inverse
operation, $\mathbf{W}_{c}$ is the residual linear layer of MCA, and $\oplus$
represents element-wise addition operation.

###  3.3 Mamba Spatial Aggregator

As shown in Fig. 1 (f), the Mamba spatial aggregator (MSA) aims to learn
information about different spatial locations and enables communication
amongst them. The spatial aggregator’s computational complexity depends on the
features’ spatial dimensions, so it is only used for the lower-dimensional
features of the U-shaped network. More specifically, it is used in the
bottleneck, one encoder’s stage before the bottleneck, and one decoder’s stage
after the bottleneck, shown in Fig. 1 (a). For the spatial aggregator, the
incoming features $\mathbb{R}^{B\times C\times H\times W}$ are reshaped to
$\mathbb{R}^{B\times C\times L}$, where L = H$\times$W. The features follow
the same protocol as that of MCA, and finally, a linear layer is used either
to expand (in the encoder) or to compress (in the decoder) the number of
channels. Mathematically, it can be represented as,

$x_{\text{out}}=\mathbf{W}_{ci}\overline{\mathbf{f_{2}}}\Bigl{(}\mathbf{LIFM\\_Block}\bigl{(}\mathbf{f_{2}}(x_{\text{in}})\bigl{)}\oplus\mathbf{W}_{s}\bigl{(}\mathbf{f_{2}}(x_{\text{in}})\bigl{)}\Bigl{)}.$
(5)

Here, $\mathbf{f}_{2}:\mathbb{R}^{B\times C\times H\times
W}\rightarrow\mathbb{R}^{B\times C\times L}$ represents a reshaping function
and $\overline{\mathbf{f_{2}}}:\mathbb{R}^{B\times C\times
L}\rightarrow\mathbb{R}^{B\times C\times H\times W}$ does the inverse,
$\mathbf{W}_{S}$ is the residual linear layer of MSA, and $\mathbf{W}_{ci}$ is
a linear layer that either increases or decreases the number of channels in
MSA, to match with MCA.

###  3.4 Bidirectional Information Learning

Inspired by Vision Mamba [Zhu et al.(2024)Zhu, Liao, Zhang, Wang, Liu, and
Wang], we implemented both MCA and MSA using a bidirectional scanning
arrangement scheme, shown in Figure 1 of supplementary material. We
incorporated the bidirectional SSMs to make the network spatially aware.
Unlike Vision Mamba, we found that sharing the weights for two-direction
schemes results in better performance and also lowers computational
complexity, as shown in the Table 1 of the ablation study. We also
experimented with a multi-directional scanning arrangement, such as a four-
directional [Liu et al.(2024)Liu, Tian, Zhao, Yu, Xie, Wang, Ye, and Liu] and
an eight-directional scheme [Hu et al.(2024)Hu, Baumann, Gui, Grebenkova, Ma,
Fischer, and Ommer]. However, the bidirectional scanning scheme augmented with
the proposed weight-sharing strategy is the best practice for the task at hand
due to its reduced complexity and smaller dataset.

###  3.5 Channel-Spatial Information Fusion Module

The Channel-Spatial Information Fusion (CS-IF) Module comprises the MCA and
MSA and merges the information extracted along channel and spatial dimensions,
depicted in Fig. 1 (g). The incoming features are passed to the MCA and MSA,
where each aggregation learns the features in both the forward pass and
backward pass using the same instance of the corresponding aggregation, making
it shareable in utilising the weights. An element-wise addition operation sums
up the output of both passes and to avoid overfitting, a dropout of 0.1 is
applied to the output of each aggregator.

###  3.6 Proposed CAF-MambaSegNet

The proposed CAF-MambaSegNet, shown in Fig. 1 (a), uses MCA in the first four
stages of the encoder to extract features from intensity images. It also
incorporates sinusoidal positional embeddings to encode spatial context
information, enabling the encoder to understand the relative positions of
different regions within the image. The features are also downsampled at each
encoder’s stage using a 2$\times$2 average pooling layer. In the next encoder
stage and bottleneck, we implemented the CS-IF module, allowing the model to
learn richer features along channel and spatial dimensions.

On the decoder side, the features are up-sampled at each stage using a
bilinear interpolation window of 2$\times$2 to match the output dimension,
followed by CS-IF module in the first stage after bottleneck and MCA in all
other decoder’s stages. The skip connections [Drozdzal et al.(2016)Drozdzal,
Vorontsov, Chartrand, Kadoury, and Pal] are also implemented at each encoder-
decoder stage. Finally, a five-class segmentation map (one for each class, LA,
RA, LV, RA and background) is generated, followed by a sigmoid activation.

##  4 Experimental Validation

Dataset Details: We used the segmentation data from the CMR×Recon MICCAI-2023
challenge [Wang et al.(2023)Wang, Lyu, Wang, Qin, Guo, Zhang, Yu, Li, Wang,
Jin, et al.]. The data has multi-contrast, multi-view, multi-slice, and multi-
coil Cardiac magnetic resonance imaging data from 300 subjects. The challenge
includes short-axis (SAX), two-chamber (2CH), three-chamber (3CH), four-
chamber (4CH) long-axis (LAX) views, and T1 mapping and T2 mappings. We used
the 4CH-LAX cine images and corresponding segmentation labels. An expert
radiologist performed the manual labeling, and annotations are provided for
four cardiac chambers: LA (label=1), RA (label=2), LV (label=3), and RV
(label=4).

Training Details: Comparative networks and the proposed framework were
implemented using PyTorch, and all experiments were performed using NVidia
A100 GPUs with 40GB RAM. AdamW [Loshchilov and Hutter(2018)] optimizer is used
with $\beta_{1}$, $\beta_{2}$ = [0.5,0.55]; training was performed for 500
training epochs using Dice Loss [Jadon(2020)] with an initial learning rate of
0.0001 which was halved after every 100 epochs. As a pre-processing step, each
input intensity image is normalized by its mean and standard deviation.
Various intensity and geometric data augmentation strategies are implemented,
including Gaussian noise, blur, brightness contrast, random ghosting,
rotation, scaling, random flipping, and random affine, to enhance the
diversity of the data. For a fair comparison, all the networks are trained
with the same protocols. The experiments use a five-fold cross-validation
split of CMR×Recon MICCAI-2023 challenge data.

###  4.1 Ablation Studies

The proposed CAF-MambaSegNet’s effectiveness is evaluated by comparing it with
different ablated versions, including/excluding the MCA/MSA, positional
embeddings, bidirectional scanning schemes, weight-sharing strategies, and
Mamba local convolution.

MCA and MSA: The MSA fosters intercommunication among spatial locations, and
its efficiency is evaluated by removing it from the CS-IF module. As the MSA
is only applied to the lower in-plane resolution features of the network, we
only utilised the CA throughout the network. The first two rows of Table 1
list the quantitative results of this ablation study, and we can observe that
utilizing the MSA improves all the evaluation metrics and brings an average
improvement of >3% in the Dice score.

Bidirectional scanning and weight sharing strategy: The bidirectional scanning
scheme incorporated at each encoder-decoder stage improves the results, shown
in row 3 of the Table 1. However, it costs extra parameters for each forward
and backward scanning scheme. The proposed bidirectional scanning, augmented
with a sharing strategy, overcomes this limitation by reducing the parameters
and improving the overall performance, incrementing the average Dice score by
$\sim$ 1 % as shown in row 4 of Table 1.

Positional embeddings: CAF-MambaSegNet also utilizes the sinusoidal positional
embeddings to encode spatial information about the position of each element
within the input image sequence [Vaswani et al.(2017)Vaswani, Shazeer, Parmar,
Uszkoreit, Jones, Gomez, Kaiser, and Polosukhin]. It can be seen that
positional embeddings help the network to improve its accuracy for all except
RV, row 6 of Table 1. Here, we speculate that the variability in the shape and
morphology of RV [Molnár et al.(2023)Molnár, Sánta, and Merkely] makes it
challenging for position embeddings to represent its spatial information
accurately compared to other structures.

Mamba Local convolution: We also included the Mamba local convolution in this
ablation. The proposed CAF-MambaSegNet does not significantly benefit from
convolutional operations, except for LA, shown in row 5 of Table 1. This
further advocates that convolution-free methods can be enough to capture
relevant features.

MCA |  MSA |  Bidirectional Scanning |  Sharing Weights |  Positional Embeddings |  Local Conv. | LA | RA | LV | RV | Avg
---|---|---|---|---|---|---|---|---|---|---
✓ | ✗ | ✗ | ✗ | ✗ | ✗ | 76.57 | 74.95 | 87.66 | 79.13 | 79.57
✓ | ✓ | ✗ | ✗ | ✗ | ✗ | 81.81 | 78.16 | 90.15 | 80.93 | 82.76
✓ | ✓ | ✓ | ✗ | ✗ | ✗ | 82.57 | 78.69 | 90.56 | 83.52 | 83.83
✓ | ✓ | ✓ | ✓ | ✗ | ✗ | 83.46 | 80.78 | 90.79 | 83.95 | 84.74
✓ | ✓ | ✓ | ✓ | ✓ | ✓ | 84.12 | 80.84 | 90.81 | 82.70 | 84.61
✓ | ✓ | ✓ | ✓ | ✓ | ✗ | 83.63 | 81.08 | 91.05 | 83.60 | 84.84

Table 1: Ablation studies (Dice score %) utilizing MCA, MSA, bidirectional
scanning augmented with weight sharing strategy, positional embeddings, and
local conv. of Mamba.

Methods | # Param (M)$\downarrow$ |  Dice-Scores($\%$) $\uparrow$ |  Hausdorff Distance- HD (mm) $\downarrow$
---|---|---|---
LA | RA | LV | RV | Avg | LA | RA | LV | RV | Avg
UNet[Ronneberger et al.(2015)Ronneberger, Fischer, and Brox] | 31.03 | 85.36 | 79.81 | 90.39 | 85.17 | 85.18 | 4.66 | 10.71 | 6.11 | 5.46 | 6.73
ResUNet[Diakogiannis et al.(2020)Diakogiannis, Waldner, Caccetta, and Wu] | 46.41 | 82.34 | 79.27 | 91.38 | 85.21 | 84.55 | 5.36 | 6.13 | 3.78 | 5.32 | 5.14
UNETR[Hatamizadeh et al.(2022)Hatamizadeh, Tang, Nath, Yang, Myronenko, Landman, Roth, and Xu] | 95.85 | 83.45 | 81.18 | 90.62 | 84.64 | 84.97 | 5.20 | 5.95 | 5.31 | 6.18 | 5.66
Swin-UNETR[Hatamizadeh et al.(2021)Hatamizadeh, Nath, Tang, Yang, Roth, and Xu] | 25.13 | 82.70 | 81.33 | 91.19 | 85.14 | 85.09 | 5.50 | 5.73 | 4.48 | 5.93 | 5.41
Swin-UNet[Cao et al.(2022)Cao, Wang, Chen, Jiang, Zhang, Tian, and Wang] | 41.35 | 83.48 | 81.91 | 90.60 | 84.54 | 85.13 | 4.51 | 6.28 | 4.48 | 6.10 | 5.34
VM-UNet[Ruan and Xiang(2024)] | 44.27 | 80.65 | 80.30 | 91.59 | 85.22 | 84.44 | 4.74 | 5.90 | 3.98 | 5.59 | 5.05
Mamba-UNet[Wang et al.(2024)Wang, Zheng, Zhang, Cui, and Li] | 35.85 | 82.27 | 81.06 | 91.58 | 85.33 | 85.05 | 4.95 | 6.29 | 4.02 | 5.73 | 5.24
CAF-MambaSegNet (proposed) | 22.41 | 83.63 | 81.08 | 91.05 | 83.60 | 84.84 | 5.02 | 6.46 | 4.89 | 6.51 | 5.72
Margin (Proposed Vs Best) | - | 1.73 | 0.83 | 0.54 | 1.73 | 0.34 | 0.51 | 0.73 | 1.10 | 1.19 | 0.67

Table 2: Comparison to state-of-the-art methods using a five-fold cross-
validation split. The best result is Bold, and the second best result is
Underlined. The number of parameters (# Param) is listed in millions (M). The
last row represents the performance difference between the proposed and the
best-performing method from comparative networks.
Figure 2: Qualitative comparison, row (a,b,c) depict the success cases and
(d,e,f) are examples of some failure cases from each comparison method.

##  5 Results and Discussion

We compared and performed experiments with many existing state-of-the-art
methods, including those based on CNNs like UNet[Ronneberger et
al.(2015)Ronneberger, Fischer, and Brox], ResUNet[Diakogiannis et
al.(2020)Diakogiannis, Waldner, Caccetta, and Wu], self-attention based Swin-
UNet[Cao et al.(2022)Cao, Wang, Chen, Jiang, Zhang, Tian, and Wang], hybrid-
architectures, UNETR[Hatamizadeh et al.(2022)Hatamizadeh, Tang, Nath, Yang,
Myronenko, Landman, Roth, and Xu], and Swin-UNETR[Hatamizadeh et
al.(2021)Hatamizadeh, Nath, Tang, Yang, Roth, and Xu], and those originated
from Mamba as well, VM-UNet[Ruan and Xiang(2024)] and Mamba-UNet[Wang et
al.(2024)Wang, Zheng, Zhang, Cui, and Li].

Table 2 lists the quantitative results of CMR×Recon segmentation data. The
proposed method marginally underperforms the existing methods at the expense
of fewer parameters. The last row of Table 2 shows the difference between the
best-performing method and the proposed CAF-MambaSegNet. Despite its
comparatively modest parameter count, our model competes against existing
state-of-the-art architectures and exhibits only a marginal difference in
performance (0.34 and 0.67 in average Dice and HD score), suggesting its
robustness and efficiency. Notably, no single network emerges as universally
superior among the comparative methods to precisely segment all four anatomies
(LA, RA, LV, RV); instead, different methods excel in segmenting specific
chambers. This highlights nuanced performance variations among the comparative
and proposed methods.

Our model’s efficiency in parameter utilization is noteworthy. With only 22.41
million trainable parameters compared to counterparts with parameter counts
ranging from 25.13 to 95.85 million. This efficiency is essential for real-
world deployment, where computational resources may be limited. We attribute
our model’s success to a combination of architectural innovations, including
the LIFM block, which factorizes the Mamba block; the CS-IF module, which
includes MCA and MSA capturing information along both channel and spatial
dimensions; and the proposed bidirectional scanning scheme augmented with the
proposed weight-sharing strategy.

Fig. 2 shows the visual results; for a fair comparison, we have shown both
_Success_ and _Failure_ results for each comparative network.We found that
both residual connection and incorporating long-range dependency can help
mitigate failure cases. For example, in rows (b,c) of Fig. 2, the proposed
method and ResUNet, with residual connection, perform better than other
methods. We also confirmed this effect by removing the residual connection in
the proposed method. From row (d), we can observe that the methods not
utilizing the self-attention or Mamba block lack non-local reasoning, leading
to over-segmentation (RV is segmented into RV and RA). Row (a) depicts results
where all the networks achieved accurate segmentation results, while for
row(f), none of the evaluated methods exhibit satisfactory performance. This
suggests the influence of image-specific characteristics and underscores the
importance of more robust and diverse segmentation methodologies.

##  6 Conclusion

We are the first to propose a Mamba-based segmentation network without
convolution operations and self-attention mechanisms to showcase the power of
SSM-based architectures. We introduced several innovative strategies to the
Mamba-based methods to increase their performance and reduce the computational
complexity, including a Linearly Interconnected Factorized Mamba (LIFM) Block
to reduce the number of trainable parameters and increase decision function,
Mamba-based spatial and channel aggregators to learn the information across
different spatial locations along with spatial aggregator, and a bidirectional
weight-sharing strategy scheme.

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