# Dynamic Coarse-to-Fine Learning for Oriented Tiny Object Detection

Chang Xu1, Jian Ding2, Jinwang Wang1, Wen Yang1, Huai Yu1, Lei
Yu111footnotemark: 1, Gui-Song Xia2
1 School of Electronic Information, Wuhan University
2 School of Computer Science, Wuhan University
<EMAIL_ADDRESS>Corresponding Authors

###### Abstract

Detecting arbitrarily oriented tiny objects poses intense challenges to
existing detectors, especially for label assignment. Despite the exploration
of adaptive label assignment in recent oriented object detectors, the extreme
geometry shape and limited feature of oriented tiny objects still induce
severe mismatch and imbalance issues. Specifically, the position prior,
positive sample feature, and instance are mismatched, and the learning of
extreme-shaped objects is biased and unbalanced due to little proper feature
supervision. To tackle these issues, we propose a dynamic prior along with the
coarse-to-fine assigner, dubbed DCFL. For one thing, we model the prior, label
assignment, and object representation all in a dynamic manner to alleviate the
mismatch issue. For another, we leverage the coarse prior matching and finer
posterior constraint to dynamically assign labels, providing appropriate and
relatively balanced supervision for diverse instances. Extensive experiments
on six datasets show substantial improvements to the baseline. Notably, we
obtain the state-of-the-art performance for one-stage detectors on the
DOTA-v1.5, DOTA-v2.0, and DIOR-R datasets under single-scale training and
testing. Codes are available at https://github.com/Chasel-Tsui/mmrotate-dcfl.

##  1 Introduction

The oriented bounding box is a finer representation for object detection since
the object’s background region is greatly eradicated by introducing the
rotation angle [55]. This advantage is pronounced in aerial images, where
objects are in arbitrary orientations, resulting in the prosperity of
corresponding object detection datasets [55, 11, 7, 35] and customized
oriented object detectors [10, 18, 62, 60, 17]. Nevertheless, one unignorable
fact is that there exist numerous tiny objects in aerial images. When oriented
objects are tiny-sized, the challenges posed to existing object detectors are
quite remarkable. Especially, the extreme geometry characteristics of oriented
tiny objects hamper the accurate label assignment.

Figure 1: Comparisons of different learning paradigms for oriented object
detection. M* means the matching function. Each box in the $2^{nd}$ row
denotes a prior location. The $3^{rd}$ row are predictions of the RetinaNet
and DCFL, where green, blue, and red boxes denote true positive, false
positive, and false negative predictions. (a) RetinaNet, FCOS, and Rotated RPN
statically assign labels between fixed priors and fixed gts. (b) Our proposed
DCFL dynamically updates priors and gts, and dynamically assigns labels.

Label assignment is a fundamental and crucial process in object detection
[68], in which priors (box for anchor-based [30] and point for anchor-free
detectors [50]) need to be assigned with appropriate labels to supervise the
network training. In fact, there have been some works that lay a foundation
for the effective label assignment of oriented objects, as shown in Fig. 1.
Early works additionally preset anchors of different angles (e.g. Rotated RPN
[36]) or refine high-quality anchors (e.g. $\rm S^{2}A$-Net [17]) based on the
generic object detector, then a static rule (e.g. MaxIoU strategy [44]) is
used to separate positive and negative (pos/neg) training samples. The derived
prior boxes can thus cover more ground truth (gt) boxes and a considerable
accuracy improvement can be expected. However, the static assignment cannot
adaptively divide pos/neg samples according to the gt’s shape and filter out
low-quality samples, usually leading to sub-optimal performance.

Recently, the exploration of adaptive label assignment [68] brings new insight
to the community. For oriented object detection, DAL [38] defines a
prediction-aware matching degree and utilizes it to reweight anchors,
achieving dynamic sample learning. Besides, several studies [21, 23, 26]
incorporate the shape information into detectors and propose shape-aware
sampling and measurement.

Figure 2: The mismatch and imbalance issues. Each point in the left image
denotes a prior location. The number in the pie-shaped bar chart denotes the
mean number of positive samples assigned to each instance in a specific angle
range.

Despite the progress, the arbitrary orientation and extreme size of oriented
tiny objects still pose a dilemma to the detector. As shown in Fig. 2, the
mismatch and imbalance issues are particularly pronounced. For one thing,
there is a mutual mismatch issue between the position prior, feature, and
instance. Although some adaptive label assignment schemes may explore a better
pos/neg division of the prior boxes or points, the sampled feature location
behind the prior is still fixed and the derived prior is still static and
uniformly located, most priors deviate from the tiny object’s main body. The
prior and feature themselves cannot well-match the extreme shapes of oriented
tiny objects, no matter how we divide pos/neg samples. For another, the
existing detectors tend to introduce bias and imbalance for oriented and tiny
objects. More precisely, for anchor-based detectors, gt with shapes different
from anchor boxes will yield low IoU[38, 59], leading to the lack of positive
samples. In Fig. 2, we calculate the mean number of positive samples assigned
to different gts with the RetinaNet and observe that there is an extreme lack
of positive samples for gts with angles and scales far from predefined
anchors. For anchor-free detectors, the static prior and its fixed stride
limit the upper number of high-quality positive samples. Tiny objects only
cover a limited number of feature points, and most of these points are away
from the object’s main body.

This motivates us to design a more dynamic and balanced learning pipeline for
oriented tiny object detection. As shown in Fig. 1, we alleviate the mismatch
issue by reformulating the prior, label assignment, and gt representation all
in a dynamic manner, which can be updated by the Deep Neural Network (DNN).
Simultaneously, we dynamically and progressively assign labels in a coarse-to-
fine manner to seek balanced supervision for various instances.

Specifically, we introduce a dynamic Prior Capturing Block (PCB) to learn the
prior, which adaptively adjusts the prior location while retaining the
physical meaning of prior [54]. The PCB is inspired by the paradigm of
learnable proposals in the DETR [4] and Sparse R-CNN [48] which naturally
avoids the mismatch issue between the predefined prior and feature. Compared
to this paradigm, we introduce its flexibility for prior updates while keeping
the fast-convergence ability of dense detectors [54, 32]. Based on the dynamic
prior, we then select Cross-FPN-layer Coarse Positive Sample (CPS) candidates
for further label assignment, and the CPS is realized by the Generalized
Jensen-Shannon Divergence [39] (GJSD) between the gt and the dynamic prior.
The GJSD is able to enlarge the CPS to the object’s nearby spatial locations
and adjacent FPN layers, ensuring more candidates for extreme-shaped objects.
After obtaining the CPS, we re-rank these candidates with predictions
(posterior) and represent the gt with a finer Dynamic Gaussian Mixture Model
(DGMM), filtering out low-quality samples. All designs are incorporated into
an end-to-end one-stage detector without additional branches.

In short, our contributions are listed as follows: (1) We identify that there
exist severe mismatch and imbalance issues in the current learning pipeline
for oriented tiny object detection. (2) We design a Dynamic Coarse-to-Fine
Learning (DCFL) scheme for oriented tiny object detection, which is the first
to model the prior, label assignment, and gt representation all in a dynamic
manner. In the DCFL, we propose to use the GJSD to construct Coarse Positive
Samples (CPS) and represent objects with a finer Dynamic Gaussian Mixture
Model (DGMM), obtaining coarse-to-fine label assignment. (3) Extensive
experiments on six datasets show promising results.

##  2 Related Work

###  2.1 Oriented Object Detection

Prior for Oriented Objects. Anchor, as a classic design in generic object
detectors (e.g. Faster R-CNN [44], RetinaNet [30]), has facilitated object
detection for a long time. Similarly, oriented object detection also benefits
from the anchor design. Initially, rotated RPN [36] extends the RPN to the
field of oriented object detection by tiling 54 anchors each location with
preset angles and scales. Indeed, enumerating potential gt shapes can notably
improve the recall, apart from the sacks of additional computational cost. RoI
Transformer [10] utilizes horizontal anchors and transforms the RPN-generated
horizontal proposals to oriented proposals, reducing the number of rotated
anchors. To save computation, the Oriented R-CNN [56] introduces an oriented
RPN that directly predicts oriented proposals based on horizontal anchors.
Recently, one-stage oriented object detectors gradually emerged, including
anchor-based detectors [60, 17] with box prior and anchor-free detectors [28,
26] with point prior. Most of them retain the fixed prior design, except for
the $\rm{S^{2}A}$-Net [17] which proposes to generate high-quality anchors.

Label Assignment. ATSS [68] reveals that label assignment plays a pivotal role
in the detectors’ performance [24, 14, 37]. In the field of oriented object
detection, DAL [38] observes inconsistency between the input prior IoU and the
output predicted IoU, then defines a matching degree as the soft label that
dynamically reweights anchors. Recently, SASM [21] introduces a shape-adaptive
sample selection and measurement strategy to improve detection performance.
Similarly, GGHL [23] proposes to fit the main body of the instance by a single
2-D Gaussian heatmap, then it divides and reweights samples in a dynamic
manner. In addition, Oriented Reppoints [26] improves the RepPoints [65] by
assessing the quality of points for more effective label assignment.

###  2.2 Tiny Object Detection

Multi-scale Learning. Basically, one can use a multi-resolution image pyramid
to obtain multi-scale learning. However, the vanilla image pyramid will bring
much computation cost. Thus, some works [34, 29, 69, 33, 49, 42] reduce
computation with the efficient Feature Pyramid Network (FPN). Unlike the FPN,
TridentNet [27] introduces multi-branch detection heads of various receptive
fields for multi-scale prediction. Moreover, one can normalize the scale of
objects for scale-invariant object detection, for example, SNIP [46] and
SNIPER [47] resize images and train objects within a certain scale range.

Label Assignment. Tiny objects usually have low IoU with anchors or cover a
limited number of feature points, thus suffering from the lack of positive
samples. ATSS [68] slightly reconciles the number of positive samples for
objects of different scales. NWD [57] designs a new metric to replace IoU,
which can sample more positive samples for tiny objects. Recently, the RFLA
[58] utilizes outliers to detect tiny objects for scale-balanced learning.

Context Information. Tiny object lacks discriminative features, but objects
are closely related to the surrounding context. Therefore, we can leverage the
context information to enhance small object detection. Muti-Region CNN (MRCNN)
[15] and Inside-Outside Network (ION) [3] are two representative works that
exploit local and global context information. Recently, the Relation Network
[22] and transformer-based detectors [4, 54, 72] reason about the association
between instances via the attention mechanism.

Feature Enhancement. The feature representation of small objects can be
enhanced by super-resolution or GAN. PGAN [25] first applies GAN to small
object detection. Besides, Bai et al. [1] introduce the MT-GAN which trains an
image-level super-resolution model to improve the RoI features of small
objects. In addition, there are some other methods based on super-resolution
including [40, 8, 2, 43].

By contrast, our method simultaneously handles the prior mismatch and
unbalanced learning via dynamically modeling the prior, label assignment, and
gt representation. Meanwhile, unlike the two-stage RoI-Transformer [10] or
one-stage $\rm{S^{2}A}$-Net [17], we embed the dynamic prior inside the end-
to-end one-stage detector without introducing any auxiliary branch.

##  3 Method

Overview. Given a set of dense prior $P\in\mathbb{R}^{W\times H\times C}$
($W\times H$ is the feature map size, $C$ is the shape information number,
each feature point has one prior for simplicity), object detectors remap the
set $P$ into final detection results $D$ through the Deep Neural Network
(DNN), which can be simplified as:

$D=\mathrm{DNN}_{h}(P),$ (1)

where $\mathrm{DNN}_{h}$ denotes the detection head. Detection results $D$
contain two parts: classification scores $D_{cls}\in\mathbb{R}^{W\times
H\times A}$ ($A$ is the class number) and box locations
$D_{reg}\in\mathbb{R}^{W\times H\times B}$ ($B$ is the box parameter number).

To train the $\mathrm{DNN}_{h}$, we need to find a proper matching between the
prior set $P$ and the gt set $GT$, and assign pos/neg labels to $P$ to
supervise the network learning. For static assigners (e.g. RetinaNet [30]),
the set of pos labels $G$ can be obtained via hand-crafted matching function
$\mathcal{M}_{s}$:

$G=\mathcal{M}_{s}(P,GT).$ (2)

For dynamic assigners [24, 14, 38], they tend to simultaneously leverage the
prior information $P$ and posterior information (predictions) $D$, and then
apply a prediction-aware mapping $\mathcal{M}_{d}$ to get the set $G$:

$G=\mathcal{M}_{d}(P,D,GT).$ (3)

After the pos/neg label separation, the loss function can be summarized into
two parts:

$\mathcal{L}=\sum_{i=1}^{N_{pos}}\mathcal{L}_{pos}(D_{i},G_{i})+\sum_{j=1}^{N_{neg}}\mathcal{L}_{neg}(D_{j},y_{j}),$
(4)

where $N_{pos}$, $N_{neg}$ are the number of positive and negative samples
respectively, $y_{j}$ denotes the negative label.

While in this work, we model the prior, label assignment, and gt
representation all in a dynamic manner to alleviate the mismatch issue. To
begin with, the dynamic prior is reformulated to ( $\tilde{}$ denotes the
dynamic item):

$\tilde{D}=\mathrm{DNN}_{h}(\underbrace{\mathrm{DNN}_{p}(P)}_{\text{Dynamic
Prior}~{}\tilde{P}}),$ (5)

$\mathrm{DNN}_{p}$ is a learnable block incorporated within the detection head
to update the prior. Then, the matching function is reformulated to a coarse-
to-fine paradigm:

$\tilde{G}=\mathcal{M}_{d}(\mathcal{M}_{s}(\tilde{P},GT),\tilde{GT}),$ (6)

the $\tilde{GT}$ is a finer representation of an object with the Dynamic
Gaussian Mixture Model (DGMM). In a nutshell, our final loss is modeled as:

$\mathcal{L}=\sum_{i=1}^{\tilde{N}_{pos}}\mathcal{L}_{pos}(\tilde{D}_{i},\tilde{G}_{i})+\sum_{j=1}^{\tilde{N}_{neg}}\mathcal{L}_{neg}(\tilde{D}_{j},y_{j}).$
(7)

Figure 3: The process of feature extraction and dynamic coarse-to-fine
learning. PCB denotes the prior capturing block.

###  3.1 Dynamic Prior

Inspired by the purely learnable paradigm of proposal updation in the DETR [4]
and Sparse R-CNN [48], we propose to introduce more flexibility into the prior
to mitigate the mismatch issue. Moreover, we retain the physical meaning of
prior where each individual prior stands for a feature point, inheriting the
fast convergence ability of dense detectors. The structure of the proposed
Prior Capturing Block (PCB) is shown in Fig. 3, in which a dilated convolution
is deployed to take the surrounding information into account, and then the
Deformable Convolution Network (DCN) [9] is leveraged to capture the dynamic
prior. Besides, we utilize the learned offsets from the regression branch to
guide the feature extraction of the classification branch, leading to better
alignment between the two tasks.

The dynamic prior capturing process is as follows. First of all, we initialize
each prior location $\mathbf{p}(x,y)$ by each feature point’s spatial location
$\mathbf{s}$ (which is remapped to the image). In each iteration, we forward
the network to capture the offset sets of each prior location
$\Delta\mathbf{o}$. Hence, the prior spatial location can be updated by:

$\tilde{\mathbf{s}}=\mathbf{s}+st\sum_{i=1}^{n}\Delta\mathbf{o}_{i}/2n,$ (8)

where $st$ is the feature map’s stride, $n$ is the number of offsets. Finally,
we utilize the 2-D Gaussian distribution
$\mathcal{N}_{p}(\boldsymbol{\mu}_{p},\boldsymbol{\Sigma}_{p})$ which is
demonstrated conducive to small objects [58, 61] and oriented objects [61, 63]
to fit the prior spatial location. Concretely, the dynamic
$\tilde{\mathbf{s}}$ serves as the Gaussian’s mean vector
$\boldsymbol{\mu}_{p}$. We preset one prior which is square-shaped
$(w,h,\theta)$ as that in RetinaNet [30] on each feature point, then compute
the co-variance matrix $\boldsymbol{\Sigma}_{p}$ by [64]:

$\small\mathbf{\Sigma}_{p}=\begin{bmatrix}\cos{\theta}&-\sin{\theta}\\\
\sin{\theta}&\cos{\theta}\end{bmatrix}\begin{bmatrix}\frac{w^{2}}{4}&0\\\
0&\frac{h^{2}}{4}\end{bmatrix}\begin{bmatrix}\cos{\theta}&\sin{\theta}\\\
-\sin{\theta}&\cos{\theta}\end{bmatrix}.$ (9)

###  3.2 Coarse Prior Matching

Given a set of prior, one basic assignment rule is to specify a range of
candidate true prediction samples for a specific gt. Some adaptive strategies
restrict the candidates of a given gt inside a single FPN layer [68, 23, 14],
while some works release all layers as candidates [67, 71]. However, for
oriented tiny objects, the former strict heuristic rule may lead to a sub-
optimal layer selection and the latter loose one will induce the slow
convergence issue [32].

Hence, we propose Cross-FPN-layer Coarse Positive Sample (CPS) candidates,
which narrows down the sample range compared to the all-FPN-layer manner while
discarding the single-layer heuristic. In the CPS, we slightly expand the
range of candidates to the gt’s nearby spatial location and adjacent FPN
layers, which warrants relatively diverse and sufficient candidates compared
to the single-layer heuristic and alleviates the quantity imbalance issue.

Specifically, the similarity measurement in constructing the CPS is realized
with the Jensen-Shannon Divergence (JSD) [13], which inherits the scale
invariance property of the Kullback–Leibler Divergence (KLD) [63] and can
measure the gt’s similarity with nearby non-overlapping priors [63, 58].
Moreover, it conquers KLD’s drawback of asymmetry. However, the closed-form
solution of the JSD between Gaussian distributions is unavailable [39], thus,
we utilize the Generalized Jensen-Shannon Divergence (GJSD) [39] which yields
a closed-form solution, as the substitute.

For example, the GJSD between two Gaussian distributions
$\mathcal{N}_{p}(\boldsymbol{\mu}_{p},\boldsymbol{\Sigma}_{p})$ and
$\mathcal{N}_{g}(\boldsymbol{\mu}_{g},\boldsymbol{\Sigma}_{g})$ is defined by:

$\displaystyle\mathrm{GJSD}(\mathcal{N}_{p},\mathcal{N}_{g})$
$\displaystyle=(1-\alpha)\mathrm{KL}(\mathcal{N}_{\alpha},\mathcal{N}_{p})+\alpha\mathrm{KL}(\mathcal{N}_{\alpha},\mathcal{N}_{g}),$
(10)

where $\mathrm{KL}$ denotes the KLD, and
$\mathcal{N}_{\alpha}(\boldsymbol{\mu}_{\alpha},\boldsymbol{\Sigma}_{\alpha})$
is given by:

$\boldsymbol{\Sigma}_{\alpha}=\left(\boldsymbol{\Sigma}_{p}\boldsymbol{\Sigma}_{g}\right)_{\alpha}^{\boldsymbol{\Sigma}}=\left((1-\alpha)\boldsymbol{\Sigma}_{p}^{-1}+\alpha\boldsymbol{\Sigma}_{g}^{-1}\right)^{-1},$
(11)

and

$\displaystyle\boldsymbol{\mu}_{\alpha}$
$\displaystyle=\left(\boldsymbol{\mu}_{p}\boldsymbol{\mu}_{g}\right)_{\alpha}^{\boldsymbol{\mu}}$
(12)
$\displaystyle=\boldsymbol{\Sigma}_{\alpha}\left((1-\alpha)\boldsymbol{\Sigma}_{p}^{-1}\boldsymbol{\mu}_{p}+\alpha\boldsymbol{\Sigma}_{g}^{-1}\boldsymbol{\mu}_{g}\right).$

Note that $\alpha$ is a parameter that controls the weight of two
distributions [39] in similarity measurement. In our work, the
$\mathcal{N}_{p}$ and $\mathcal{N}_{g}$ contribute equally, thus $\alpha$ is
set to 0.5.

Ultimately, for each gt, we select $K$ priors which hold the top $K$ GJSD
score with this gt as the Coarse Positive Samples (CPS) and regard the
remaining priors as negative samples, this coarse matching serves as the
$\mathcal{M}_{s}$ in Eq. 6. The ranking manner works together with the GJSD
measurement to construct the Cross-FPN-layer CPS, eliminating the imbalance
issue raised by the MaxIoU matching for outlier angles and scales, which will
be analyzed in Sec. 5.

###  3.3 Finer Dynamic Posterior Matching

Based on Coarse Positive Sample (CPS) candidates, we design a dynamic
posterior (prediction) matching rule $\mathcal{M}_{d}$ to filter out low-
quality samples. The $\mathcal{M}_{d}$ consists of two key components, namely
a posterior re-ranking strategy and a Dynamic Gaussian Mixture Model (DGMM)
constraint.

We re-rank the sample candidates in the CPS according to their predicted
scores. In other words, we further refine the positive samples by their
Possibility of becoming True predictions ($PT$) [14], which is a linear
combination of the predicted classification score and the location score with
the gt. We define the $PT$ of the $i^{th}$ sample $D_{i}$ as:

$PT_{i}=\frac{1}{2}Cls(D_{i})+\frac{1}{2}IoU(D_{i},gt_{i}),$ (13)

where $Cls$ is the predicted classification confidence and $IoU$ is the
rotated IoU between the predicted location and its corresponding gt location.
We select candidates with $Q$ highest $PT$ as Medium Positive Sample (MPS)
candidates.

Following this, we filter out those samples too far away from the gts with a
finer instance representation, getting the Finer Positive Samples (FPS).
Different from previous works which utilize the center probability map [53] or
the single-Gaussian [64, 23] for instance representation, we represent the
instance by a finer DGMM. It consists of two components: one is centered on
the geometry center and the other is centered on the semantic center of the
object. Concretely, for a specific instance $gt_{i}$, the geometry center
$(cx_{i},cy_{i})$ serves as the mean vector $\boldsymbol{\mu}_{i,1}$ of the
first Gaussian, and the semantic center $(sx_{i},sy_{i})$, which is deduced by
averaging the location of the samples in the MPS, serves as the
$\boldsymbol{\mu}_{i,2}$. That is to say, we parameterize the instance as:

$\mathit{DGMM}_{i}(s|x,y)=\sum_{m=1}^{2}w_{i,m}\sqrt{2\pi|\boldsymbol{\Sigma}_{i,m}|}\mathcal{N}_{i,m}(\boldsymbol{\mu}_{i,m},\boldsymbol{\Sigma}_{i,m}),$
(14)

where $w_{i,m}$ is the weight of each Gaussian with a summation of 1,
$\boldsymbol{\Sigma}_{i,m}$ equals to the gt’s $\boldsymbol{\Sigma}_{g}$. Each
sample in MPS has a DGMM score $\mathit{DGMM}(s|MPS)$, we set negative masks
to samples which have $\mathit{DGMM}(s|MPS)<e^{-g}$ with any gt, the $g$ is
adjustable.

##  4 Experiments

###  4.1 Datasets

Experiments are done on six datasets, i.e., DOTA-v1.0 [55]/v1.5/v2.0 [11],
DIOR-R [7], VisDrone [12], and MS COCO [31]. In ablation studies and analyses,
we choose the large-scale DOTA-v2.0 train set for training and val set for
evaluation, which contains a large number of tiny objects. To compare with
other methods, we use trainval sets of DOTA-v1.0, DOTA-v1.5, DOTA-v2.0, and
DIOR-R for training and their test sets for testing, we choose the
VisDrone2019, MS COCO train set, val set for training and testing.

Method | Backbone | Plane | BD | Bridge | GTF | SV | LV | Ship | TC | BC | ST | SBF | RA | Harbor | SP | HC | CC | Air | Heli | mAP
---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---
multi-stage: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
FR OBB [44] | R50 | 71.61 | 47.20 | 39.28 | 58.70 | 35.55 | 48.88 | 51.51 | 78.97 | 58.36 | 58.55 | 36.11 | 51.73 | 43.57 | 55.33 | 57.07 | 3.51 | 52.94 | 2.79 | 47.31
FR OBB + Dp | R50 | 71.55 | 49.74 | 40.34 | 60.40 | 40.74 | 50.67 | 56.58 | 79.03 | 58.22 | 58.24 | 34.73 | 51.95 | 44.33 | 55.10 | 53.14 | 7.21 | 59.53 | 6.38 | 48.77
MR [19] | R50 | 76.20 | 49.91 | 41.61 | 60.00 | 41.08 | 50.77 | 56.24 | 78.01 | 55.85 | 57.48 | 36.62 | 51.67 | 47.39 | 55.79 | 59.06 | 3.64 | 60.26 | 8.95 | 49.47
HTC* [5] | R50 | 77.69 | 47.25 | 41.15 | 60.71 | 41.77 | 52.79 | 58.87 | 78.74 | 55.22 | 58.49 | 38.57 | 52.48 | 49.58 | 56.18 | 54.09 | 4.20 | 66.38 | 11.92 | 50.34
RT [10] | R50 | 71.81 | 48.39 | 45.88 | 64.02 | 42.09 | 54.39 | 59.92 | 82.70 | 63.29 | 58.71 | 41.04 | 52.82 | 53.32 | 56.18 | 57.94 | 25.71 | 63.72 | 8.70 | 52.81
Oriented R-CNN [56] | R50 | 77.95 | 50.29 | 46.73 | 65.24 | 42.61 | 54.56 | 60.02 | 79.08 | 61.69 | 59.42 | 42.26 | 56.89 | 51.11 | 56.16 | 59.33 | 25.81 | 60.67 | 9.17 | 53.28
one-stage: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
DAL [38] | R50 | 71.23 | 38.36 | 38.60 | 45.24 | 35.42 | 43.75 | 56.04 | 70.84 | 50.87 | 56.63 | 20.28 | 46.53 | 33.49 | 47.29 | 12.15 | 0.81 | 25.77 | 0.00 | 38.52
SASM [21] | R50 | 70.30 | 40.62 | 37.01 | 59.03 | 40.21 | 45.46 | 44.60 | 78.58 | 49.34 | 60.73 | 29.89 | 46.57 | 42.95 | 48.31 | 28.13 | 1.82 | 76.37 | 0.74 | 44.53
RetinaNet-O [30] | R50 | 70.63 | 47.26 | 39.12 | 55.02 | 38.10 | 40.52 | 47.16 | 77.74 | 56.86 | 52.12 | 37.22 | 51.75 | 44.15 | 53.19 | 51.06 | 6.58 | 64.28 | 7.45 | 46.68
$\rm{R^{3}Det}$ w/ KLD [63] | R50 | 75.44 | 50.95 | 41.16 | 61.61 | 41.11 | 45.76 | 49.65 | 78.52 | 54.97 | 60.79 | 42.07 | 53.20 | 43.08 | 49.55 | 34.09 | 36.26 | 68.65 | 0.06 | 47.26
FCOS-O [51] | R50 | 74.84 | 47.53 | 40.83 | 57.41 | 43.89 | 47.72 | 55.66 | 78.61 | 57.86 | 63.00 | 38.02 | 52.38 | 41.91 | 53.24 | 40.22 | 7.15 | 65.51 | 7.42 | 48.51
Oriented Rep [26] | R50 | 73.02 | 46.68 | 42.37 | 63.05 | 47.06 | 50.28 | 58.64 | 78.84 | 57.12 | 66.77 | 35.21 | 50.76 | 48.77 | 51.62 | 34.23 | 6.17 | 64.66 | 5.87 | 48.95
ATSS-O [68] | R50 | 77.46 | 49.55 | 42.12 | 62.61 | 45.15 | 48.40 | 51.70 | 78.43 | 59.33 | 62.65 | 39.18 | 52.43 | 42.92 | 53.98 | 42.70 | 5.91 | 67.09 | 10.68 | 49.57
$\rm{S^{2}A}$-Net [17] | R50 | 77.84 | 51.31 | 43.72 | 62.59 | 47.51 | 50.58 | 57.86 | 80.73 | 59.11 | 65.32 | 36.43 | 52.60 | 45.36 | 52.46 | 40.12 | 0.00 | 62.81 | 11.11 | 49.86
one-stage: |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |
DCFL | R50 | 75.71 | 49.40 | 44.69 | 63.23 | 46.48 | 51.55 | 55.50 | 79.30 | 59.96 | 65.39 | 41.86 | 54.42 | 47.03 | 55.72 | 50.49 | 11.75 | 69.01 | 7.75 | 51.57
$\rm{S^{2}A}$-Net w/ DCFL | R50 | 74.79 | 53.25 | 45.81 | 65.46 | 46.49 | 53.23 | 58.10 | 81.51 | 60.13 | 66.42 | 43.24 | 55.09 | 50.52 | 55.58 | 54.53 | 5.23 | 68.73 | 13.06 | 52.84
DCFL† | R50 | 78.30 | 53.03 | 44.24 | 60.17 | 48.56 | 55.42 | 58.66 | 78.29 | 60.89 | 65.93 | 43.54 | 55.82 | 53.33 | 60.00 | 54.76 | 30.90 | 74.01 | 15.60 | 55.08
DCFL† | ReR101 | 79.49 | 55.97 | 50.15 | 61.59 | 49.00 | 55.33 | 59.31 | 81.18 | 66.52 | 60.06 | 52.87 | 56.71 | 57.83 | 58.13 | 60.35 | 35.66 | 78.65 | 13.03 | 57.66

Table 1: Main results on the DOTA-v2.0 OBB Task. We follow the official class
abbreviations as the DOTA-v2.0 benchmark[11]. † denotes training for 40
epochs. Note that this paper [63] reports 50.90% mAP for $\rm{R^{3}Det}$ w/
KLD under 20 epochs, the ReR101 backbone is proposed by the ReDet [18]. The
results in red and blue denote the best and second-best performance of each
column.

Method | CFA [16] | RetinaNet-O [30] |  $\rm{R^{3}Det}$ [60] | Oriented Rep [26] | ATSS-O [68]
---|---|---|---|---|---
mAP | 69.63 | 69.79 | 70.18 | 71.94 | 72.29
Method | KLD [63] |  $\rm{S^{2}A}$-Net [17] | GGHL [23](3x) | DCFL | DCFL(3x)
mAP | 72.76 | 73.91 | 73.98 | 74.26 | 75.35

Table 2: Comparison with one-stage detectors on the DOTA-v1.0 OBB Task. All
results are based on the MMRotate [70] with 12 epochs except for GGHL [23]. 3x
means training for 36 epochs.

Method | Backbone | SV | Ship | ST | mAP
---|---|---|---|---|---
RetinaNet-O [30] | R50 | 44.53 | 73.31 | 59.96 | 59.16
FR OBB [19] | R50 | 51.28 | 79.37 | 67.50 | 62.00
CMR [19] | R50 | 51.64 | 79.99 | 67.58 | 63.41
RT [10] | R50 | 52.05 | 80.72 | 68.26 | 65.03
ReDet [18] | ReR50 | 52.38 | 80.92 | 68.64 | 66.86
DCFL | R50 |  56.72 (+12.19) |  80.87 (+7.56) |  75.65 (+15.69) |  67.37 (+8.21)
DCFL | ReR101 |  57.31 (+12.78) |  86.60 (+13.29) |  76.55 (+16.59) |  70.24 (+11.08)

Table 3: Main results on the DOTA-v1.5 OBB Task.

Method | RetinaNet-O [30] | FR-OBB [44] | RT [10] | AOPG [7]
---|---|---|---|---
mAP | 57.55 | 59.54 | 63.87 | 64.41
Method | GGHL [23] | Oriented Rep [26] | DCFL | DCFL (ReR101)
mAP | 66.48 | 66.71 | 66.80 | 71.03

Table 4: Performance comparisons on the DIOR-R dataset.

Method | Backbone | VE | BR | WM
---|---|---|---|---
RetinaNet-O [30] | R50 | 38.0 | 24.0 | 60.2
Oriented Rep [26] | R50 | 50.4 | 38.8 | 64.7
DCFL | R50 |  50.9 (+12.9) |  42.1 (+18.1) |  70.9 (+10.7)

Table 5: Detection results of typical tiny objects on the DIOR-R dataset. VE,
BR, and WM denote vehicle, bridge, and wind-mill.

Dataset | VisDrone | MS COCO | DOTA-v2.0 HBB
---|---|---|---
Method |  RetinaNet [30] | DCFL | RetinaNet | DCFL |  FCOS [58] | DCFL
$\rm{AP}_{0.5}$ | 29.2 | 32.1 | 55.4 | 57.3 | 55.4 | 57.4

Table 6: Results of one-stage object detectors on HBB datasets.

###  4.2 Implementation Details

We conduct all the experiments on the computer with a single NVIDIA RTX 3090
GPU, and the batch size is set to 4. Models are built based on MMDetection [6]
and MMRotate [70] with PyTorch [41]. The ImageNet [45] pre-trained models are
used as the backbone. The Stochastic Gradient Descent (SGD) optimizer is used
for training with a learning rate of 0.005, a momentum of 0.9, and a weight
decay of 0.0001. The ResNet-50 [20] with FPN [29] is the default backbone if
not specified. We use Focal loss [30] for classification and IoU loss [66] for
regression. We only use random flipping as data augmentation for all
experiments.

For experiments on the DOTA-v1.0 and DOTA-v2.0, we follow the official
settings of the DOTA-v2.0 benchmark [11], i.e., we crop images into patches of
$\rm{1024\times 1024}$ with overlaps of 200 and train the model for 12 epochs.
For DOTA-v2.0, we reproduce one-stage state-of-the-art methods [50, 68, 26,
60, 63, 38, 21, 17] with the same settings.

For experiments on other datasets, we set the input size to $1024\times 1024$
(overlap 200), $800\times 800$, $1333\times 800$, and $1333\times 800$ for
DOTA-v1.5, DIOR-R, VisDrone, and COCO respectively. We train the models for
40, 40, 12, and 12 epochs on the DOTA-v1.5, DIOR-R, COCO, and VisDrone as
previous works do [16, 26]. The above settings are fixed unless otherwise
specified.

###  4.3 Main Results

Results on DOTA series. As shown in Tab. 1, our proposed method achieves the
state-of-the-art performance of 57.66% mAP on the DOTA-v2.0 OBB benchmark
under single-scale training and testing. Besides, our model achieves 51.57%
mAP without bells and whistles, surpassing all one-stage object detectors
tested. The results on the DOTA-v1.0 [55] and DOTA-v1.5 are listed in Tab. 2,
Tab. 3. Results also indicate that our DCFL is very effective for detecting
tiny oriented objects on the tested datasets, such as small vehicles, ships,
and storage tanks, where a boost of about 10 points can be expected compared
to the baseline.

Results on DIOR-R. DIOR-R contains some tiny oriented objects, such as the
vehicle, bridge, and windmill. The mAP and class-wise AP of tiny objects are
in Tab. 4 and Tab. 5, we also achieve the state-of-the-art performance of
71.03% mAP and notable improvements on tiny objects.

Results on HBB Datasets. Moreover, we discard the angle to verify the
versatility of the DCFL on the generic small object detection datasets
VisDrone [12], MS COCO [31], and DOTA-v2.0 HBB [11]. In Tab. 6, our method
gets a notable $\rm{AP}_{0.5}$ boost compared to the baseline.

Figure 4: Different ways of constructing the CPS. Yellow and orange denote the
possible regions of CPS and MPS respectively.

Method | CPS | MPS | DGMM | mAP
---|---|---|---|---
baseline [30] |  |  |  | 51.70
| ✓ | ✓ |  | 53.41
DCFL | ✓ |  | ✓ | 57.20
| ✓ | ✓ | ✓ | 59.15
(a)

Strategy | Measurement | mAP
---|---|---
All-FPN-layer | Gaussian | 50.12
Single-FPN-layer | Gaussian | 56.72
Cross-FPN-layer |  KLD [63] | 57.82
Cross-FPN-layer |  GWD [61] | 58.55
Cross-FPN-layer | GJSD | 59.15
(b)

DCN | Dilated Conv | DP | mAP
---|---|---|---
|  |  | 58.07
✓ |  |  | 58.41
✓ | ✓ |  | 58.65
Separate | ✓ | ✓ | 58.71
Guiding | ✓ | ✓ | 59.15
(c)

$K$ | 24 | 20
---|---|---
$Q$ | 20 | 16 | 12 | 8 | 16 | 12 | 10 | 8
mAP | 58.31 | 58.11 | 58.95 | 59.06 | 58.66 | 58.71 | 58.92 | 58.28
$K$ | 16 | 12
$Q$ | 12 | 10 | 8 | 6 | 10 | 8 | 6 | 4
mAP | 59.15 | 58.57 | 58.97 | 57.84 | 58.79 | 58.25 | 57.01 | 57.37
(d)

$g$ | 1.2 | 1.0
---|---|---
mAP | 57.91 | 58.20
$g$ | 0.8 | 0.4
mAP | 59.15 | 58.95
(e)

Table 7: Ablations. We train on DOTA-v2.0 train set, test on val set, and
report mAP under IoU threshold 0.5.

###  4.4 Ablation Study

Effects of Individual Strategy. We check the effectiveness of each proposed
strategy in the proposed method. In all ablation experiments, we employ one
prior for each feature point for fair comparisons. As seen in Tab.
LABEL:tab:ablation:individual, the baseline detector RetinaNet-OBB yields a
result of 51.70% mAP. When we gradually apply the posterior re-ranked MPS and
DGMM into the detector based on the CPS, the mAP improves progressively,
verifying each design’s effectiveness. Note that the CPS cannot be
independently used since the samples in it are too coarse to serve as the
final positive samples. Nevertheless, we compare some different ways of
constructing the CPS to verify its superiority.

Comparisons of Different CPS. The design of the CPS matters in the training
pipeline. We show several paradigms of designing the CPS as shown in Fig.
LABEL:tab:ablation:cps, including limiting the CPS for a specific gt within a
single layer, releasing all FPN layers as the CPS, like Objectbox [67]. We
compare their performance in Tab. LABEL:tab:ablation:cps. For fair
comparisons, the number of samples in CPS is fixed at 16, and all other
components are kept the same. For the Single-FPN-layer way, we group gt onto
different layers according to the scale division strategy in FCOS, then assign
labels within each layer. For the All-FPN-layer way, we do not group gt onto
different layers, instead, we discard the prior scale information and directly
measure the distance between Gaussian gt and prior points. The results are
shown in Tab. LABEL:tab:ablation:cps, we can observe that neither of the above
two ways will yield the best performance. By contrast, the distribution
distances (KLD, GWD, GJSD) are able to construct the Cross-FPN-layer CPS,
where the candidates are extended to adjacent layers besides the main layer.
We can also see the GJSD gets the best performance of 59.15% mAP, mainly
resulting from its property of scale-invariance [63, 39], symmetry [39], and
ability to measure non-overlapping boxes [39] compared to other counterparts.

Fixed Prior and Dynamic Prior. We conduct a finer group of ablation studies to
verify the necessity of introducing the dynamic prior. As shown in Tab.
LABEL:tab:ablation:pcb, if we disable the dynamic prior by fixing the location
of samples, a slight performance drop will be introduced. Hence, the prior
should be adjusted accordingly when leveraging the dynamic sampling strategy
to better capture the shape of objects.

Detailed Design in PCB. For the PCB, it is made up of a dilated convolution
and a guiding DCN, we slightly enlarge the receptive field with a dilation
rate of 3. After that, we take advantage of the DCN to generate dynamic priors
in a guiding manner. As shown in Tab. LABEL:tab:ablation:pcb, we can observe
that the DCN can bring an improvement of 0.34 mAP points and the dilated
convolution can slightly enhance the mAP. We find that the application of the
DCN [9] to the single regression branch will slightly deteriorate the accuracy
(noted by Separate in Tab. LABEL:tab:ablation:pcb), which may cause mismatch
issues between the two branches. Thus we utilize the offsets from the
regression head to guide the offsets classification head for better alignment
(noted by Guiding).

Effects of Parameters. The introduced three parameters are robust in a certain
range. From Tab. LABEL:tab:ablation:kq, we can see that a combination of
$K=16$ and $Q=12$ gets the best performance. In Tab. LABEL:tab:ablation:g, we
verify the threshold $e^{-g}$ in the DGMM, we empirically set $w_{i,1}$ to
0.7, then a threshold of $g=0.8$ yields the highest mAP. Although making the
CPS/MPS/FPS coarser and stricter will weaken the performance, the mAP only
waves marginally. In other words, the coarse-to-fine assignment manner
somewhat warrants the parameter selection’s robustness since multiple
parameters can attenuate the effects of an under-tuned one.

Figure 5: Visualization analysis of the predicted results. The first row is
the result of the RetinaNet-OBB while the second row is the result of the
DCFL. TP, FN, and FP predictions are marked in green, red, and blue
respectively.  Figure 6: Statistical analysis of imbalance issues. The first
and second columns show quality and quantity imbalance respectively. Figure 7:
Visualization of sampled dynamic priors.

##  5 Analysis

For a clearer dissection of why the proposed scheme works, we perform more
meticulous analyses as follows.

Reconciliation of imbalance problems. To delve into the imbalance issue, we
calculate the mean predicted IoU and the mean positive sample number of gt
holding different angles and different scales (absolute size). Results are
shown in Fig. 6, which are from the models’ last training epoch. Here we
summarize two kinds of imbalance issues (quantity and quality imbalance) for
RetinaNet: (1) The positive sample number assigned to each instance changes
periodically w.r.t. its angle and scale, whereas objects with shapes (scale,
angle) different from predefined priors will hold much fewer positive samples.
(2) The predicted IoU changes periodically w.r.t. gt’s scale while remaining
invariant w.r.t. gt’s angle. By contrast, DCFL remarkably reconciles the
imbalance: (1) more positive samples are compensated to previously outlier
angles and scales. (2) the samples’ quality (predicted IoU) can also be
improved and balanced across all angles and scales. The above results are the
desired behavior of dynamic coarse-to-fine learning.

Method |  $\rm{R^{3}Det}$ [60] |  $\rm{S^{2}A}$-Net [17] | GA-RetinaNet [52] | RetinaNet [30] | DCFL
---|---|---|---|---|---
Params, GFLOPs | 42.0M, 337.3 | 38.6M, 197.9 | 37.4M, 206.9 | 36.5M, 217.3 | 36.1M, 157.8

Table 8: Comparison of params, GFLOPs with $1024\times 1024$ input.

Visualization. We visualize the predicted results and positive samples in Fig.
5 and Fig. 7. We can see that the DCFL remarkably eliminates the False
Negative and False Positive predictions, especially for the extreme-shaped
oriented tiny objects. Fig. 7 shows that the proposed strategy is able to
dynamically generate and sample priors that better fit the instance’s main
body, verifying the claims of dynamic modeling and mismatch alleviation in
this work.

Speed. We test the inference speed on DOTA-v2.0 val set with a single RTX3090
GPU, the FPS of the $\rm{R^{3}Det}$, $\rm{S^{2}A}$-Net, RetinaNet, and DCFL is
16.2, 18.9, 20.8, and 20.9. It indicates that our method is of high
efficiency. Moreover, we provide the parameters and GLOPs in Tab. 8, where we
can see that the DCFL is lighter.

##  6 Conclusion

In this paper, we propose a novel DCFL scheme for detecting oriented tiny
objects. We identify that the mismatched feature prior and unbalanced positive
samples are two obstacles hampering the label assignment for oriented tiny
objects. To address these, we propose a dynamic prior to alleviate the
mismatch issue and a coarse-to-fine assigner to mitigate the imbalance issue,
where the prior, label assignment, and gt representation are all reformulated
in a dynamic manner. Extensive experiments and analyses show the convincing
improvements brought by the DCFL.

## Acknowledgement

We thank the reviewers for their comments. This work was supported in parts by
NSFC (62271355, 62271354) and the Fundamental Research Funds for the Central
Universities (2042022kf1010).

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# Measuring Sources of Bias in Diving Competitions

Monnie McGee<EMAIL_ADDRESS>Department of Statistics and Data Science,
Southern Methodist University  Gabe Downey<EMAIL_ADDRESS>Achievement and
Assessment Institute, University of Kansas  Zachary Berg
<EMAIL_ADDRESS>Pembroke Hill School, Kansas City, MO

## Abstract

We examine bias in diving scores from high school meets. Usually, examination
of bias in sports where judges assign subjective scores has been examined in
terms of nationalistic bias, where judges award favorable scores to athletes
from their own home countries. In this work, bias is defined as difference
between the judge’s scores for a given meet and the ability of the diver. As a
measure of the ability of a diver, we calculate a mean score for all dives and
all meets in which the diver has participated. We call this mean score a
diver’s competency score. We use the difference between judges’ scores within
a given meet and the diver’s competency to define a discrepancy: the
difference between a judge’s estimation of a diver’s ability and their true
ability. We examine this discrepancy with respect to age, gender, direction of
dive, position of dive, round of competition, and dive difficulty.

Key Words: scoring bias, subjective scores, springboard diving competitions

## Introduction

Sports analytics usually bring to mind analysis of outcomes associated with
football, soccer, basketball, hockey, and baseball. While it might not
generate as much revenue as the “big 5”, diving is a beautiful sport and is
one of the most watched Olympic sports, along with gymnastics and track &
field. It is also in the top 3 sports searched on the Internet during the
Olympics, and has the second most newspaper articles published during the
Olympics [12]. Diving, swimming, synchronized diving, and water polo are often
lumped together as “aquatics”. Diving is also a popular high school sport and
collegiate sport, and aquatics as a whole is ranked as the 5th easiest
scholarship to get for both men and women, just behind football and baseball
for men and soccer and field hockey for women [8]. Generally, 85% of the 14
total D1 scholarships are allocated to the swim team and 15% to the dive team
[2]. For its popularity, scores in diving have not been well studied.

Diving, like gymnastics, ice skating and ski-jumping, is scored by a panel of
judges; therefore, there is a subjective element to a diving score. Regardless
of competition level, dives are scored on a scale of 0 to 10 in increments of
0.5, with 0 being a failed dive, and 10 being a perfect dive. Most high school
scores are in the range of 4-7. A panel of an odd number of judges, usually 5
although sometimes 3, 7, or 9, gives their scores independently for each diver
for each round of a competition. The exception to independent scoring is a
failed dive. To fail a dive and give the diver a score of 0, the entire panel
of judges must agree to do so. The net score for each diver in each round is
the sum of the three judges’ scores in the middle of the sorted scores per
round, and the award for the round is the net score multiplied by the degree
of difficulty (DD) of the dive. The DD is determined by the Fédération
Internationale de Natation (FINA, the international governing body for aquatic
sports), and is not up for discussion. The meet score for each diver is the
sum of their awards for each round. The diver with the largest sum is the
winner of the meet.

More prestigious competitions typically have 11 rounds, in which a diver must
perform 2 dives in each direction (forward, backward, reverse, inward, or
twist) and an $11^{th}$ dive of the diver’s choice [6]. More precisely, the
diver performs a series of voluntary dives and optional dives. The voluntary
dives consist of one dive from each of the 5 diving directions. The sum of the
DDs for the voluntary dives must be $\leq 9.0$. The six optional dives consist
of one dive from each of the 5 diving directions with one direction
represented twice. The DD when added for the optional dives must be a minimum
of 11.5 for girls and 12.0 for boys. In addition, all five groups must be
represented in the first 8 rounds of diving and all 11 dives must be totally
different dives [6]. For example, performing a 1.5 forward somersault in a
pike position is the same as performing a 1.5 forward somersault in the tuck
position; thus this combination would not be permissible. However, a backward
1.5 somersault in the tuck position and a forward 1.5 somersault in the tuck
position are different dives.

## Measuring Bias in Judges’ Scores

When considering bias in judging, the mind goes to thoughts of national bias
in the Olympics or other world championships - where a judge favors a diver
from his or her own country. There are plenty of recent scandals in ice
skating [3] and gymnastics [13] to feed the imagination. There has been
previous work showing evidence of nationalistic bias in diving in the 2000
Olympics [5, 4]. The data considered for this paper are from high school
competitions, and there is no information on the judge affiliation; therefore,
it is not possible to spin juicy tales about bias between rival high schools.
However, nationalistic bias is not the only type of bias. FINA warns against
reputation bias, round bias, dive-order bias, difficulty bias, seeding bias,
and conformity bias [1]. This paper focuses on difficulty bias, which is
typically defined as awarding a diver more points for a more difficult dive,
and round bias, where a diver’s scores systematically do not reflect the
diver’s ability as a competition wears on.

Difficulty bias and round bias are defined in terms of a judges’ mark that
does not reflect a diver’s ability. In other words, the definition of
statistical bias applies, as given by $E(\theta-\hat{\theta})$, where $\theta$
represents a diver’s true ability and $\hat{\theta}$ represents an estimate of
a diver’s ability. Ideally, the expected value of the difference of the
diver’s ability and the estimate of that ability is 0. In order to estimate
the score bias, we need a reasonable estimate for a diver’s true ability,
$\theta$.

Measuring overall diver ability is a tricky thing. Diving, especially high
school diving, does not have a technical judging panel, as in ice skating or
gymnastics, to assure that the athletes do the jumps and flips that a routine
demands. In high school competitions, there are no announcers examining every
frame of an instant replay. There is research using videos from a diving
competition to measure characteristics of dives that typically differentiate a
good dive from a bad one, such as height of splash, distance of entry from the
end of the board, and angle of entry [9]. That work showed that the judges’
scores are closely aligned with quantitative values measured from the video
evidence, and only in one instance of multiple dives would the ordinal
standing of the divers have been affected in a way that mattered by a
difference between scores using only the video evidence and versus scores
given by the judges. In other words, trained diving judges are generally quite
accurate when it comes to judging dive quality within a diving competition.
The same work also showed that untrained diving judges are unreliable when it
comes to qualitative scores matching quantitative measurements [9].

For the current study, there is no video evidence or panel of technical
judges. To define diver ability, the mean net score for every dive of each
diver over all competitions in which that diver has competed is computed.
There is a precedent in several previous papers on diving, ice skating, and
gymnastics for using the median score as a measure of ability [5, 4, 10];
however, we use the mean score for this work as the there is generally little
variability in scores for each round. We call this average measure per diver
the “competency” score, $C_{d}$, for that diver. Mathematically,

$C_{d}=\frac{1}{mr}\sum_{all\ meets\ and\ rounds}Net\ Score_{d,m,r}$ (1)

where $m$ is the number of meets in which a diver, denoted by $d$,
participates between 2017 and 2022, which is the time span of the data. $r$ is
the number of rounds in the dive meet. Usually $r=11$. The data set from
divemeets.com contains information on 39105 dives from 261 unique meets, 1911
unique athletes, and 86 unique dives. All divers are high school divers. As a
measure of bias, we measure the discrepancy,

$D_{dmr}=Net\ Score_{dmr}-C_{d}$ (2)

where $C_{d}$ is defined in Equation 1 and the net score is the sum of the
middle three scores given by judges for a particular diver (d) in a particular
meet (m) during a particular round (r).

The goal of this study is to determine whether discrepancy is independent of
age, gender, round, and difficulty. These items are those over which a diver
has little or no control. A positive discrepancy indicates that the judges’
net score is greater than the diver’s ability, which indicates lenient
judging. A negative discrepancy indicates that the judges’ score is less than
the ability of the diver, which indicates strict judging. For unbiased
judging, discrepancy is independent of any characteristic that the diver
cannot control.

## Results

Potential explanatory variables for discrepancy were gender, age, degree of
difficulty, dive direction, and dive position. For all meets, divers, and
dives, ridgeline plots are used to show the distribution of the discrepancy
according to gender, age, dive position, dive direction, and DD (Figures 1(a)
\- 3). The y axis for each plot gives different categories for an explanatory
variable. The x-axis is the discrepancy, which is typically in a range of -25
to 15. The black line in the middle of each curve is the median discrepancy,
the red area marks the $2.5^{th}$ percentile for the discrepancies, and the
blue area marks the $97.5^{th}$ percentile for the discrepancies. For all
ridgeline plots, the categories are ordered by the median discrepancy. For
each category, the total number of dives is given under the category name on
the vertical axis.

(a) Discrepancy by gender

(b) Discrepancy by age at dive

Figure 1(a) shows a plot of the distribution of the discrepancy for male and
female divers. The black lines in the middle of each curve correspond to the
median discrepancy. The medians are aligned at 0 for both genders; therefore,
there is no evidence of gender bias as a main effect. Figure 1(b) shows the
discrepancy plotted for each age. There is a slight shift to the right as the
divers age. For younger divers, the scores are unbiased. The shift might
indicate improvement in diver ability with experience in diving as much as it
would indicate favoritism for older divers.

(a) Discrepancy by Dive Direction

(b) Discrepancy by Dive Position

Figures 2(a) and 2(b) show the distribution of discrepancy scores for dive
directions and dive positions, respectively. The five directions are forward,
backward, inward, reverse, and twist. To perform a forward dive, the diver
faces the pool on take off and rotates forward. For a reverse dive, the diver
faces the pool on take off and rotates backward toward the board (the opposite
direction of a forward dive). To perform a backward dive, the diver turns his
or her back to the pool and rotates backward. An inward dive is performed by
turning one’s back to the pool and rotating toward the board on take off.
Generally, reverse and inward dives are considered more difficult than forward
and backward dives in the sense that a dive in a forward direction will have a
lower degree of difficulty than that same dive in a reverse direction. The
median discrepancy (bias) for all directions is close to 0, with a slightly
negative discrepancy for twisting dives and a slightly positive discrepancy
for reverse dives.

The positions are tuck, straight, pike, and free. Free is most often reserved
for twisting dives, where the diver is free to twist in any position.
Generally, the pike and straight positions are considered more difficult. For
example, a 1.5 forward somersault in a tuck position has a DD of 1.5, while a
1.5 forward somersault in a pike position has a DD of 1.7. Again, there is
little deviation from 0 for any position, except for the tuck position. There
is evidence of judges scoring dives in the tuck position more leniently.

Figure 3: Discrepancy plotted against the degree of difficulty assigned by
FINA for a given dive. The number of dives performed at this difficulty is on
the vertical axis under each assigned DD.

### Difficulty Bias

Dive position and dive direction are associated with degree of difficulty
(DD). FINA assigns DD for each direction and position of dive. The lowest DD
is 1.0 (for a straight forward jump into the pool) and the highest in the
divemeets.com data set is a 3.4 (a reverse dive with 2.5 somersaults in a tuck
position). For further examination of DD, the values of the DD assigned by
FINA were plotted on the vertical axis with the discrepancy on the horizontal
axis (Figure 3). Because few dives at this level have DD greater than 2.7, any
dive with a DD between of 2.7 to 2.9 was assigned to a DD of 2.8, and any dive
with DD of 3.0 or greater was assigned a DD of 3.0. Easier dives, with degrees
of difficulty between 1.2 and 1.6, are more leniently judged, while more
difficult dives, with DD of 2.1 or greater are more harshly judged. It is not
strictly true that more difficult dives are more harshly judged, as dives with
DD of 1.8, for example, are judged more harshly than dives with a DD or 2.3 or
2.6. Therefore, there is evidence of difficulty bias, but not in the direction
originally assumed. It is presumed that more difficult dives are judged more
leniently, but this does not seem to be the case. In other words, from these
data, it appears that it is better to do a less difficult dive well than it is
to attempt a difficult dive and do it poorly.

### Round Bias

Figure 4: Discrepancies (vertical axis) plotted as a line for each diver in 10
randomly selected meets. The horizontal axis is the round for the meet from 1
to 11. The blue line is a loess smoother. Each meet shows evidence of harsher
judging (negative discrepancies) as the meet wears on.

We have visual evidence for a difficulty bias in the opposite direction for
which difficulty bias is usually seen. Another potential bias to examine is
“round bias” to determine whether dives in the beginning of meet are judged
more harshly (or leniently) than dives at the end of a meet. Recall that each
meet is 11 rounds, and, depending on the number of divers in a meet, the
judges could be judging for several hours.

Figure 4 shows discrepancies for all divers in ten randomly selected meets.
Each frame represents a single meet, and each dark gray or black line
represents the discrepancies for a different diver. The discrepancy is plotted
on the vertical axis and the round in which a dive was performed on the
horizontal axes for all frames. The number within the left-hand strip for each
frame is the unique meet ID. Some of the meets had only one or two divers. The
blue curve within each frame is a loess smoothed line. We can see a definite
trend toward harsher scores as the meet wears on, regardless of the meet or
number of divers, although the effect is less for meets with a large number of
divers, which we would expect by the law of large numbers. Interestingly, the
effect is there regardless of the meet, which is confounded with the judging
panel. In other words, it seems that judges in different meets behave
similarly, regardless of the particular judge or the number of divers within a
meet.

There is a bit of confounding with round and dive. Divers are free to perform
dives in almost any order for a given meet, with respect to the stipulations
on voluntary vs. optional dives mentioned in the introduction. Unfortunately,
we do not have access to sequential diver order; that is, the data do not have
an indicator for which diver went first, which went second, etc. We have
access to the round in which each dive was performed for each diver; however,
the data does not designate which dives are voluntary and which are optional.
It is possible to determine voluntary from optional dives in a reasonable
fashion and examine the discrepancies between voluntary vs. optional dives,
but this is left for future research.

### Mixed Effects Model

The figures show discrepancies for each variable separately. We wish to model
them simultaneously in order to control for the fixed effects. We use a mixed
effects model with a random intercept for diver. Round, Age, and DD are fixed
effects. Girls and boys were modeled separately.

Table 1 shows the parameter estimates, standard error, and t-statistics for
each of the fixed effects. The coefficients on the round are small; however,
the t-statistic is large. The round effect is similar for boys and girls. For
every round that passes, the discrepancy decreases by approximately 0.08,
indicating that the judges tend to judge more harshly (net scores are less
than the diver’s competency) as a competition continues, adjusted for age and
DD. This finding matches the visual evidence seen in Figure 4. The coefficient
for age is 0.28 for girls and 0.30 for boys, which indicates that judges tend
to judge more favorably for each year increase in age of the diver. This
finding is commensurate with Figure 1(b). These coefficients for age are
small, but they are large enough to make a difference in the outcome of a
competition because the net score changes during a meet while the diver
ability remains constant. An increase (or decrease) of a fraction of a point
per round could change ordinal standings for a given meet.

| Girls, $n=1045$, ICC = 4% | Boys, $n=866$, ICC = 2%
---|---|---
Effect | Estimate | SE | t-statistic | Estimate | SE | t-statistic
Intercept | 1.8 | 0.33 | 5.47 | -0.33 | 0.37 | -0.91
Round | -0.09 | 0.0006 | -14.79 | -0.08 | 0.007 | -11.56
Age | 0.28 | 0.019 | 14.63 | 0.30 | 0.021 | 14.26
DD | -3.26 | 0.065 | -50.04 | -2.20 | 0.063 | -34.84
Table 1: Coefficients for a Mixed Effects Model with a random intercept for
Diver and Discrepancy as the response

The largest coefficient belongs to degree of difficulty (DD), and the
coefficients for boys and girls are one point apart. Girls seem to get
penalized more for more difficult dives than do boys. Perhaps this is a
reflection of the fact that boys are expected to engage in riskier behavior
(trying dives that are beyond their ability) than girls are; therefore, they
are less penalized, on average, for those difficult dives. This assertion
needs to be further tested with a more careful data analysis.

Note that the adjusted intraclass coefficients (ICC) for the girls and boys
are small (0.04 and 0.02, respectively). We report the adjusted ICC because it
gives proportion of variability associated with the random effects without
accounting for the fixed effects in the model [11]. The ICC can be interpreted
as the proportion of variance that is attributable to the “grouping structure”
in the population [7]. Here, the random intercept, which represents a
different starting discrepancy for each diver, defines the “grouping
structure”. Therefore, only 4% of the variability in discrepancy for girls and
2% of the variability in discrepancy for boys is accounted for by different
starting discrepancies for each diver. In plain language, any effect of
discrepancy that an individual diver contributes is completely overshadowed by
the fixed effects.

## Discussion and Conclusion

To sum up, there seems to be a bias for the round of competition, difficulty
of the dive, and age of the diver. While we did not see a bias for gender of
the diver when visually examining discrepancies by gender, there is some
evidence from the coefficients of the mixed model in Table 1 that girls and
boys are scored differently with respect to DD, when controlling for age and
round. We have the data to examine the specific order of the dives performed;
however, we did not attempt an analysis with dive order for this study. Dive
order is confounded with round, because each diver can choose his or her own
dive order within certain parameters. Finally, we did not have information on
sequential order, which would be the order of divers within a competition. We
had only the dive order in which a particular diver performed a particular
dive. In later studies, we hope to obtain information on the order of the
divers within a meet and to examine sequential bias and conformity bias.

We also leave a statistical model for future work. Clearly we have a random
effect for diver and repeated measurements for each diver. We also have divers
nested within meet, and each meet has a different panel of judges; therefore
we can use meet as a surrogate for a panel of judges. There are fixed effects
for DD, gender, age, direction, and position, and a correlation between
direction, position, and DD. In future work, we will use a more sophisticated
model accounting for repeated measures and nesting effects.

Some caveats: like all observational data, confounding factors exist in the
diving data, and we do not have information in these data to account for
several of these factors within a statistical model. However, given our
measure of diver competency, the results showed that biases exist for degree
of difficulty and round of the meet.

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