# Estimating Egocentric 3D Human Pose in the Wild with External Weak
Supervision

Jian Wang1,2 Lingjie Liu1,2 Weipeng Xu3 Kripasindhu Sarkar1,2
Diogo Luvizon1,2 Christian Theobalt1,2
1MPI Informatics 2Saarland Informatics Campus 3Facebook Reality Labs
<EMAIL_ADDRESS><EMAIL_ADDRESS>
###### Abstract

Egocentric 3D human pose estimation with a single fisheye camera has drawn a
significant amount of attention recently. However, existing methods struggle
with pose estimation from in-the-wild images, because they can only be trained
on synthetic data due to the unavailability of large-scale in-the-wild
egocentric datasets. Furthermore, these methods easily fail when the body
parts are occluded by or interacting with the surrounding scene. To address
the shortage of in-the-wild data, we collect a large-scale in-the-wild
egocentric dataset called _Egocentric Poses in the Wild (EgoPW)_. This dataset
is captured by a head-mounted fisheye camera and an auxiliary external camera,
which provides an additional observation of the human body from a third-person
perspective during training. We present a new egocentric pose estimation
method, which can be trained on the new dataset with weak external
supervision. Specifically, we first generate pseudo labels for the EgoPW
dataset with a spatio-temporal optimization method by incorporating the
external-view supervision. The pseudo labels are then used to train an
egocentric pose estimation network. To facilitate the network training, we
propose a novel learning strategy to supervise the egocentric features with
the high-quality features extracted by a pretrained external-view pose
estimation model. The experiments show that our method predicts accurate 3D
poses from a single in-the-wild egocentric image and outperforms the state-of-
the-art methods both quantitatively and qualitatively.

##  1 Introduction

Egocentric motion capture using head- or body-mounted cameras has recently
become popular because traditional motion capture systems with outside-in
cameras have limitations when the person is moving around in a large space and
thus restrict the scope of applications. Different from traditional systems,
the egocentric motion capture system is mobile, flexible, and has no
requirements on recording space, which enables capturing a wide range of human
activities for many applications, such as wearable medical monitoring, sports
analysis, and $x$R.

Figure 1: Compared with Mo2Cap2, our method gets a more accurate egocentric
pose from a single in-the-wild image, especially when the body parts are
occluded. Note that the external images are only used for visualization, not
the inputs to our method.

In this work, we focus on estimating the full 3D body pose from a single head-
mounted fisheye camera. The most related works are Mo2Cap2 [44] and
$x$R-egopose [35]. While these methods have produced compelling results, they
are only trained on synthetic images as limited real data exists and,
therefore, suffer from significant performance drop on real-world scenarios.
Furthermore, these methods often struggle with the cases when parts of the
human body are occluded by or interacting with the surrounding scene (see the
Mo2Cap2 results in Fig. 1). This is due to the domain gap between synthetic
and real data, but also due to their limited capability of handling
occlusions.

To address the issue of the limited real egocentric data, we capture a large-
scale in-the-wild egocentric dataset called _Egocentric Poses in the Wild
(EgoPW)_. This is currently the largest egocentric in-the-wild dataset,
containing more than 312k frames and covering 20 different daily activities in
8 everyday scenes. To obtain the supervision for the network training, one
possibility is using a multi-view camera setup to capture training data with
ground truth 3D body poses or apply multi-view weak supervision. However, this
setup is impractical for recording in an environment with limited space (e.g.
in the small kitchen shown in Fig. 3), which is a common recording scenario.
Therefore, considering a trade-off between flexibility and 3D accuracy, we use
a new device setup consisting of an egocentric camera and a single auxiliary
external camera. We demonstrate that the external view can provide additional
supervision during training, especially for the highly occluded regions in the
egocentric view (e.g. the lower body part).

To handle occlusions and estimate accurate poses, we propose a new egocentric
pose estimation method for training on the EgoPW dataset in a weakly
supervised way. Specifically, we propose a spatio-temporal optimization method
to generate accurate 3D poses for each frame in the EgoPW dataset. The
generated poses are further used as pseudo labels for training an egocentric
pose estimation network [44]. To improve the network performance, we
facilitate the training of the egocentric pose estimation network with the
extracted features from the external pose estimation network which has been
trained on a large in-the-wild body pose dataset. Specifically, we enforce the
feature extracted from these two views to be similar by fooling a
discriminator not being able to detect which view the features are from. To
further improve the performance of the pose estimation network, besides the
EgoPW dataset, we also use a synthetic dataset [44] to train the network and
adopt a domain adaptation strategy to minimize the domain gap between
synthetic and real data.

We evaluate our method on the test data provided by Wang  _et al_. [42] and Xu
_et al_. [44]. Our method significantly outperforms the state-of-the-art
methods both quantitatively and qualitatively. We also show qualitative
results on various in-the-wild images, demonstrating that our method can
predict accurate 3D poses on very challenging scenes, especially when the body
joints are seriously occluded (see our results in Fig. 1). To summarize, our
contributions are presented as follows:

  * •

A new method to estimate egocentric human pose with weak supervision from an
external view, which significantly outperforms existing methods on in-the-wild
data, especially when severe occlusions exist;

  * •

A large in-the-wild egocentric dataset (EgoPW) captured with a head-mounted
fisheye camera and an external camera. We will make it publicly available;

  * •

A new optimization method to generating pseudo labels for the in-the-wild
egocentric dataset by incorporating the supervision from an external view;

  * •

An adversarial method for training the network by learning the feature
representation of egocentric images with external feature representation.

##  2 Related Work

##### Egocentric 3D full body pose estimation.

Rhodin _et al_. [30] developed the first method to estimate the full-body pose
from a helmet-mounted stereo fisheye camera. Cha  _et al_. [4] presented an
RNN-based method to estimate body pose with two pinhole cameras mounted on the
head. Xu  _et al_. [44] introduced a single wide-view fisheye camera setup and
proposed a single-frame based egocentric motion capture system. With the same
setup, Tome _et al_. [35] captured the egocentric pose with an auto-encoder
network which captures the uncertainty in the predicted heatmaps. In order to
further mitigate the effect of image distortions, Zhang  _et al_. [46]
proposed an automatic calibration module. Hwang _et al_. [14] put an ultra-
wide fisheye camera on the user’s chest and estimate body pose, camera
rotation and head pose simultaneously. Jiang  _et al_. [16] mounted a front-
looking fisheye camera on the user’s head and estimated the body and head pose
by leveraging the motion of the environment and extremity of the human body.
Wang  _et al_. [42] proposed an optimization algorithm to obtain temporally
stable egocentric poses with motion prior learned from Mocap datasets.
However, these methods are all trained on synthetic datasets, thus suffering
from the performance drop on the real images due to the domain gap and lack of
external supervision. Our method, on the contrary, achieves better performance
on the in-the-wild scenes.

Figure 2: Overview of our method. We first collected the new EgoPW dataset
(Sec. 3.1), where pseudo labels are generated by a multi-view based
optimization method (Sec. 3.2). We then train our model with the proposed
framework (Sec. 3.3), where the network is simultaneously trained with EgoPW
datasets and synthetic data from Mo2Cap2. We enforce the egocentric network to
learn a better feature representation from the external view (Sec. 3.3.2) and
bridge the gap between synthetic and real data with a domain classifier (Sec.
3.3.1).

##### Pseudo label generation.

The task of pseudo-labeling [20, 34, 45] is a semi-supervised learning
technique that generates pseudo labels for unlabeled data and uses the
generated labels to train a new model. This has been applied in the areas of
segmentation [22, 48, 47, 8], pose estimation [2, 21, 25, 23] and image
classification [13, 29, 1]. Since the pseudo labels may be inaccurate, some
methods have been proposed to filter inaccurate labels to increase the
labeling stability. Shi  _et al_. [34] set confidence levels on unlabeled
samples by measuring the sample density. Chen  _et al_. [5] enforced the
stability of pseudo labels by adopting an easy-to-hard transfer strategy. Wang
and Wu [41] introduced a repetitive re-prediction strategy to update the
pseudo labels, while Rizve  _et al_. [32] proposed an uncertainty-aware
pseudo-label selection framework that selects pseudo labels. Morerio  _et al_.
[24] used a conditional GAN to filter the noise in the pseudo labels.
Different from previous pseudo-labeling works which generate the labels from
network predictions or clustering, we design an optimization framework to
generate labels with supervision from egocentric and external views
simultaneously.

##### Weakly Supervised 3D Human Pose Estimation.

Recently, there is a growing interest in developing weakly-supervised 3D pose
estimation methods. Weakly-supervised methods do not require datasets with
paired images and 3D annotations. Some works [40, 27] leverages the non-rigid
SFM to get 3D joint positions from 2D keypoint annotations in unconstrained
images. Some works [10, 6, 38, 28, 7] present an unsupervised learning
approach to train the 3D pose estimation network with the supervision from 2D
reprojections. The closest to our work are the approaches of [15, 31, 39, 19]
in that they leverage the weak supervision from multi-view images for
training. Iqbal  _et al_. [15] and Rhodin  _et al_. [31] supervise the network
training process by calculating the differences between Procrustes-aligned 3D
poses from different views. Wandt  _et al_. [39] predict the camera poses and
3D body poses in a canonical form, and then supervise the training with the
multi-view consistency. Kocabas  _et al_. [19] obtain the pseudo labels with
epipolar geometry between different views and use the pseudo labels to train
the 3D pose lifting network. Different from previous works [15, 31, 39, 19],
our method uses spatio-temporal optimization framework that takes egocentric
and external view as input to obtain robust 3D pseudo labels for training the
network. This optimization method ensures the stability of the network
training process when the 2D pose estimations are inaccurate.

##  3 Method

We propose a new approach to train a neural network on the in-the-wild dataset
with weak supervision from egocentric and external views. The overview of our
approach is illustrated in Fig. 2. We first capture a large-scale egocentric
in-the-wild dataset, called _EgoPW_ , which contains synchronized egocentric
and external image sequences (Sec. 3.1). Next, we generate pseudo labels for
the EgoPW dataset with an optimization-based framework. This framework takes
as input a sequence in a time window with $B$ frames of egocentric images
$\mathcal{I}^{ego}_{seq}=\\{\mathcal{I}^{ego}_{1},\dots,\mathcal{I}^{ego}_{B}\\}$
and external images
$\mathcal{I}^{ext}_{seq}=\\{\mathcal{I}^{ext}_{1},\dots,\mathcal{I}^{ext}_{B}\\}$
and outputs egocentric 3D poses
$\mathcal{P}^{ego}_{seq}=\\{\mathcal{P}^{ego}_{1},\dots,\mathcal{P}^{ego}_{B}\\}$
as the pseudo labels (Sec. 3.2). Next, we train the egocentric pose estimation
network on the synthetic data from Mo2Cap2 [44] and on the EgoPW dataset with
pseudo labels $\mathcal{P}^{ego}_{seq}$. In the training process, we leverage
the feature representation from an on-the-shelf external pose estimation
network [43] to enforce our egocentric network to learn a better feature
representation in an adversarial way (Sec. 3.3.2). We also use an adversarial
domain adaptation strategy to mitigate the domain gap between synthetic and
real datasets (Sec. 3.3.1).

###  3.1 EgoPW Dataset

We first describe the newly collected _EgoPW_ dataset, which is the first
large-scale in-the-wild human performance dataset captured by an egocentric
camera and an external camera (Sony RX0), both synchronized. EgoPW contains a
total of 318k frames, which are divided into 97 sequences of 10 actors in 20
clothing styles performing 20 different actions, including reading
magazine/newspaper, playing board games, doing a presentation, walking,
sitting down, using a computer, calling on the phone, drinking water, writing
on the paper, writing on the whiteboard, making tea, cutting vegetables,
stretching, running, playing table tennis, playing baseball, climbing floors,
dancing, opening the door, and waving hands. All personal data is collected
with an IRB approval. We generate 3D poses as pseudo labels using the
egocentric and external images, which will be elaborated later. In terms of
size, our EgoPW dataset is larger than existing in-the-wild 3D pose estimation
datasets, like 3DPW [37], and has similar scale to the existing synthetic
egocentric datasets, including the Mo2Cap2 [44] and the $x$R-egopose [35]
datasets.

###  3.2 Optimization for Generating Pseudo Labels

In this section, we present an optimization method based on [42] to generate
pseudo labels for EgoPW. Given a sequence, we split it into segments
containing $B$ consecutive frames. For the egocentric frames $I^{ego}_{seq}$,
we estimate the 3D poses represented by 15 joint locations in the coordinate
system of the egocentric camera (called “egocentric poses”)
$\widetilde{\mathcal{P}}^{ego}_{seq}=\\{\widetilde{\mathcal{P}}^{ego}_{1},\dots,\widetilde{\mathcal{P}}^{ego}_{B}\\}$,
$\widetilde{\mathcal{P}}^{ego}_{i}\in\mathbb{R}^{15{\times}3}$, and 2D
heatmaps $H^{ego}_{seq}=\\{H^{ego}_{1},\dots,H^{ego}_{B}\\}$ using the Mo2Cap2
method [44]. Aside from egocentric poses, we also estimate the transformation
matrix between the egocentric camera poses of two adjacent frames
$[R_{seq}^{SLAM}\mid t_{seq}^{SLAM}]=\\{[R_{1}^{2}\mid
t_{1}^{2}],\dots,[R_{B-1}^{B}\mid t_{B-1}^{B}]\\}$ using ORB-SLAM2 [26]. For
the external frames $I^{ext}_{seq}$, we estimate the 3D poses (called
“external poses”)
$\mathcal{P}^{ext}_{seq}=\\{\mathcal{P}^{ext}_{1},\dots,\mathcal{P}^{ext}_{B}\\}$,
$\mathcal{P}^{ext}_{i}\in\mathbb{R}^{15\times 3}$ using VIBE [18] and 2D
joints
$\mathcal{J}^{ext}_{seq}=\\{\mathcal{J}^{ext}_{1},\dots,\mathcal{J}^{ext}_{B}\\}$,
$\mathcal{J}^{ext}_{i}\in\mathbb{R}^{15\times 2}$ using openpose [3].

Next, following [42], we learn a latent space to encode an egocentric motion
prior with a sequential VAE which consists of a CNN-based encoder $f_{enc}$
and decoder $f_{dec}$. We then optimize the egocentric pose by finding a
latent vector $z$ such that the corresponding pose sequence
$P^{ego}_{seq}=f_{dec}(z)$ minimizes the objective function:

$\displaystyle E(\mathcal{P}_{seq}^{ego},R_{seq},t_{seq})$
$\displaystyle=\lambda_{R}^{ego}E_{R}^{ego}+\lambda_{R}^{ext}E_{R}^{ext}+\lambda_{J}^{ego}E_{J}^{ego}$
(1)
$\displaystyle+\lambda_{J}^{ext}E_{J}^{ext}+\lambda_{T}E_{T}+\lambda_{B}E_{B}$
$\displaystyle+\lambda_{C}E_{C}+\lambda_{M}E_{M}.$

In this objective function, $E_{R}^{ego}$, $E_{J}^{ego}$,$E_{T}$, and $E_{B}$
are egocentric reprojection term, egocentric pose regularization term, motion
smoothness regularization term and bone length regularization term, which are
the same as those defined in [42]. $E_{R}^{ext}$, $E_{J}^{ext}$, $E_{C}$, and
$E_{M}$ are the external reprojection term, external 3D body pose
regularization term, camera pose consistency term, and camera matrix
regularization term, which will be described later. Please see the
supplemental material for a detailed definition of each term.

Note that since the relative pose between external camera and egocentric
camera is unknown, we also need to optimize the relative egocentric camera
pose with respect to the external camera pose for each frame, i.e. the
rotations $R_{seq}={R_{1},\dots,R_{B}}$ and translations
$t_{seq}={t_{1},\dots,t_{B}}$.

##### External Reprojection Term.

In order to supervise the optimization process with the external 2D pose, we
designed the external reprojection term which minimizes the difference between
the projected 3D pose with the external 2D joints. The energy term is defined
as:

$E_{R}^{ext}(\mathcal{P}_{seq}^{ego},R_{seq},t_{seq})=\sum_{i=1}^{B}\left\|\mathcal{J}_{i}^{ext}-K\left[R_{i}\mid
t_{i}\right]\mathcal{P}_{i}^{ego}\right\|_{2}^{2},$ (2)

where $K$ is the intrinsic matrix of the external camera; $\left[R_{i}\mid
t_{i}\right]$ is the pose of the egocentric camera in the $i$ th frame w.r.t
the external camera position. In Eq. 2, we first project the egocentric body
pose $\mathcal{P}_{i}^{ego}$ to the 2D body pose in the external view with the
egocentric camera pose $\left[R_{i}\mid t_{i}\right]$ and the intrinsic matrix
$K$, and then compare the projected body pose with the 2D joints estimated by
the openpose [3]. Since the relative pose between the external camera and
egocentric camera are unknown at the beginning of the optimization, we
optimize the egocentric camera pose $\left[R_{i}\mid t_{i}\right]$
simultaneously while optimizing the egocentric body pose
$\mathcal{P}_{seq}^{ego}$. In order to make the optimization process converge
faster, we initialize the egocentric camera pose $\left[R_{i}\mid
t_{i}\right]$ with the Perspective-n-Point algorithm [11].

##### Camera Pose Consistency.

We cannot get the accurate 3D pose only with the external reprojection term
because the egocentric camera pose and the optimized body pose can be
arbitrarily changed without violating the external reprojection constraint. To
alleviate this ambiguity, we introduce the camera consistency term $E_{C}$ as
follows:

$\displaystyle E_{C}(R_{seq},t_{seq})$
$\displaystyle=\sum_{i=1}^{B-1}\left\|\begin{bmatrix}R_{i}&t_{i}\\\
0&1\end{bmatrix}\begin{bmatrix}R^{i+1}_{i}&t^{i+1}_{i}\\\
0&1\end{bmatrix}\right.$ (3)
$\displaystyle-\left.\begin{bmatrix}R_{i+1}&t_{i+1}\\\
0&1\end{bmatrix}\right\|_{2},$

It enforces the egocentric camera pose at $(i+1)$ th frame $[R_{i+1}\mid
t_{i+1}]$ to be consistent with the pose obtained by transforming the
egocentric camera pose at the $i$ th frame $[R_{i}\mid t_{i}]$ with the
relative pose between the $i$ th and $(i+1)$ th frame.

##### External 3D Body Pose Regularization.

Besides the external reprojection term, we also use the external 3D body poses
to supervise the optimization of the egocentric 3D body pose. We define the
external 3D pose term which measures the difference between the external and
the egocentric body poses after a rigid alignment:

$E_{J}(\mathcal{P}_{seq}^{ego},\mathcal{P}_{seq}^{ext})=\sum_{i=1}^{B}\left\|\mathcal{P}_{i}^{ext}-\left[R_{i}^{pa}\mid
t_{i}^{pa}\right]\mathcal{P}_{i}^{ego}\right\|_{2}^{2},$ (4)

where $\left[R_{i}^{pa}\mid t_{i}^{pa}\right]$ is the transformation matrix
calculated with Procrustes analysis, which rigidly aligns the external 3D pose
estimation $\mathcal{P}_{i}^{ext}$ and the egocentric 3D pose
$\mathcal{P}_{i}^{ego}$.

By combining the body poses estimated from the egocentric view and external
view, we can reconstruct more accurate pseudo labels. As shown in Fig. 3, the
hands of the person are occluded in the external view, resulting in the
tracking of the hands failing in the external view (Fig. 3, b), however, the
hands can be clearly seen and tracked in the egocentric view (Fig. 3, d); on
the other hand, the feet cannot be observed in the egocentric view and thus
fail to be tracked in this view (Fig. 3, b), but can be easily viewed and
tracked in the external view (Fig. 3, d). By joining the information from both
views, we can successfully predict accurate 3D poses as the pseudo labels
(Fig. 3, c). We note that the external camera is only used for generating the
pseudo labels but at test time, only the egocentric camera is used.

Figure 3: Our pseudo label generation method combines the information from
both the egocentric view and external view, therefore leading to more accurate
pseudo labels (c). Only with the egocentric camera, the feet cannot be
observed and well-tracked (b). Only with the external camera, the hands are
occluded and result in the wrong result on the hand part (d).

##### Camera Matrix Regularization.

We constrain the camera rotation matrix $R_{i}$ to be orthogonal:

$E_{J}(R_{seq})=\sum_{i=1}^{B}\left\|R_{i}^{T}R_{i}-I\right\|_{2}^{2}.$ (5)

Different from previous single-view pose estimation methods which leverages
the weak supervision from multiple views [15, 31, 39, 19], our spatio-temporal
optimization method generates the pseudo labels under the guidance of learned
motion prior, making it robust to noisy and inaccurate 2D pose estimations
which is common for the 2D pose estimation results from the egocentric view.

###  3.3 Training Egocentric Pose Estimation Network

Through the optimization framework in Sec. 3.2, we can get accurate 3D pose
pseudo labels $\mathcal{P}_{seq}^{ego}$ for each egocentric frame in the EgoPW
dataset, which is further processed into the 2D heatmap $H_{E}$ and the
distance between joints and egocentric camera $D_{E}$ with the fisheye camera
model [33] described in supplementary materials.

Afterward, we train a single-image based egocentric pose estimation network on
both the synthetic dataset from Mo2Cap2 and the EgoPW dataset, as shown in the
right part of Fig. 2. The pose estimation network contains a feature extractor
$\Theta$ which encodes an image into a feature vector and a pose estimator
$\Psi$ which decodes the feature vector to 2D heatmaps and a distance vector.
The 3D pose can be reconstructed from them with the fisheye camera model.
Here, we note the synthetic dataset $S=\\{I_{S},H_{S},D_{S}\\}$ including
synthetic images $I_{S}$ along with their corresponding heatmaps $H_{S}$ and
distance labels $D_{S}$ from Mo2Cap2 dataset, and the EgoPW dataset
$E=\\{I_{E}^{ego},H_{E},D_{E},I_{E}^{ext}\\}$ including egocentric in-the-wild
images $I_{E}^{ego}$ along with pseudo heatmaps $H_{E}$, distance labels
$D_{E}$ and corresponding external images $I_{E}^{ext}$. During the training
process, we train the egocentric pose estimation network with two
reconstruction loss terms and two adversarial loss terms. The reconstruction
losses are defined as the mean squared error (MSE) between the predicted
heatmaps/distances and heatmaps/distances from labels:

$\displaystyle L_{S}$
$\displaystyle=\text{mse}(\hat{H}_{S},H_{S})+\text{mse}(\hat{D}_{S},D_{S})$
(6) $\displaystyle L_{E}$
$\displaystyle=\text{mse}(\hat{H}_{E},H_{E})+\text{mse}(\hat{D}_{E},D_{E}),$

where

$\displaystyle\hat{H}_{S},\hat{D}_{S}=\Psi(F_{S}),$ $\displaystyle
F_{S}=\Theta(I_{S});$ (7)
$\displaystyle\hat{H}_{E},\hat{D}_{E}=\Psi(F_{E}^{ego}),$ $\displaystyle
F_{E}^{ego}=\Theta(I_{E}^{ego}).$

Two adversarial losses are separately designed for learning egocentric feature
representation and bridging the domain gap between synthetic and real
datasets. These two losses are described as follows.

####  3.3.1 Adversarial Domain Adaptation

To bridge the domain gap between the synthetic and real data domains,
following Tzeng  _et al_. [36], we introduce an adversarial discriminator
$\Gamma$ which takes as input the feature vectors extracted from a synthetic
image and an in-the-wild image, and determines if the feature is extracted
from an in-the-wild image. The adversarial discriminator $\Gamma$ is trained
with a cross-entropy loss:

$\mathcal{L}_{D}=-E[\log(\Gamma(\mathcal{F_{S}}))]-E[\log(1-\Gamma(\mathcal{F_{T}}))].$
(8)

Once the discriminator $\Gamma$ has been trained, the feature extractor
$\Theta$ maps the images from different domains to the same feature space such
that the classifier $\Gamma$ cannot tell if the features are extracted from
synthetic images or real images. Therefore, the pose estimator $\Psi$ can
predict more accurate poses for the in-the-wild data.

####  3.3.2 Supervising Egocentric Feature Representation with External View

Although our new training dataset is large, the variation of identities in the
dataset is still relatively limited (20 identities) compared with the existing
large-scale external-view human datasets (thousands of identities). Generally
speaking, the representations learned with these external-view datasets are of
higher quality due to the large diversity of the datasets. To further improve
the generalizability of our network and prevent overfitting to the training
identities, we propose to supervise our egocentric representation by
leveraging the high-quality third-person-view features. From a transfer
learning perspective, although following Mo2Cap2 [44], our egocentric network
is pretrained on the third-person-view datasets, it can easily “forget” the
learned knowledge while being finetuned on the synthetic dataset. The
supervision from third-person-view features can prevent the egocentric
features from deviating too much from those learned from large-scale real
human images.

However, directly minimizing the distance between egocentric features
$F_{E}^{ego}$ and external features $F_{E}^{ext}$ will not enhance the
performance since the intermediate features of the egocentric and external
view should be different from each other due to significant difference on the
view direction and camera distortions. To tackle this issue, we use the
adversarial training strategy to align the feature representation from
egocentric and external networks. Specifically, we use an adversarial
discriminator $\Lambda$ which takes the feature vectors extracted from an
egocentric image and the corresponding in-the-wild images and predicts if the
feature is from egocentric or external images. The adversarial discriminator
$\Lambda$ is trained with a cross-entropy loss:

$L_{V}=-E[\log(\Lambda(F_{E}^{ego}))]-E[\log(1-\Lambda(F_{E}^{ext}))],$ (9)

where $F_{E}^{ext}=\Theta^{ext}(I_{E}^{ext})$ and $\Theta^{ext}$ is the
feature extractor of external pose estimation network that shares exactly the
same architecture as the egocentric pose estimation network. The parameters of
the features extractor $\Theta^{ext}$ and the pose estimator $\Psi^{ext}$ of
the external pose estimation network are obtained from the pretrained model in
Xiao  _et al_.’s work [43] and keep fixed during the training process.

Note that the deep layers of the pose estimation network usually represent the
global semantic information of the human body [9], we use the output feature
of the 4th res-block of ResNet-50 network [12] as the input to the
discriminator $\Lambda$. Furthermore, the spatial position of the joints is
quite different in the egocentric view and the external view, which will make
the discriminator $\Lambda$ easily learn the difference between egocentric and
external features. To solve this, we use an average pooling layer in the
discriminator $\Lambda$ to spatially aggregate features, thus further
eliminating the influence of spatial distribution between egocentric and
external images. Please refer to the suppl. mat. for further details.

During the training process, the egocentric pose estimation network is trained
to produce the features $F_{E}^{ego}$ to fool the domain classifier $\Lambda$
such that it cannot distinguish whether the feature is from an egocentric or
external image. To achieve this, the egocentric network learns to pay more
attention to the relevant parts of the input image,  _i.e_., the human body,
which is demonstrated in Fig. 4.

Figure 4: The visualization of features with (b) or without (c) the
adversarial supervision from external features. By supervising the training of
the egocentric network with the feature representation from an external view,
the egocentric network is able to focus on extracting the semantic features of
the human body.

##  4 Experiments

###  4.1 Datasets

We quantitatively evaluate our finetuned network on the real-world dataset
from Mo2Cap2 [44] and Wang _et al_. [42]. The real-world dataset in Mo2Cap2
[44] contains 2.7k frames of two people captured in indoor and outdoor scenes,
and that in Wang _et al_. [42] contains 12k frames of two people captured in
the studio. To measure the accuracy of our pseudo labels, we evaluate our
optimization method (Sec. 3.2) only on the dataset from Wang _et al_. [42]
since the Mo2Cap2 dataset does not include the external view.

To evaluate our method on the in-the-wild data, we also conduct a qualitative
evaluation on the test set of the EgoPW dataset. The EgoPW dataset will be
made publicly available, and more details and comparisons to other datasets
are included in the supplementary materials.

###  4.2 Evaluation Metrics

We measure the results of our method as well as other baseline methods with
two metrics, PA-MPJPE and BA-MPJPE, which estimate the accuracy of a single
body pose. For PA-MPJPE, we rigidly align the estimated pose
$\mathcal{\hat{P}}$ of each frame to the ground truth pose $\mathcal{P}$ using
Procrustes analysis [17]. In order to eliminate the influence of the body
scale, we also report the BA-MPJPE scores. In this metric, we first resize the
bone length of each predicted body pose $\mathcal{\hat{P}}$ and ground truth
body pose $\mathcal{P}$ to the bone length of a standard skeleton. Then, we
calculate the PA-MPJPE between the two resulting poses.

Figure 5: Qualitative comparison between our method and the state-of-the-art
methods. From left to right: input image, Mo2Cap2 result, $x$R-egopose result,
our result, and external image. The ground truth pose is shown in red. Note
that the external images are not used during inference.

###  4.3 Pseudo Label Generation

2.5 Method |  PA-MPJPE |  BA-MPJPE
---|---|---
Mo2Cap2 |  102.3 |  74.46
$x$R-egopose |  112.0 |  87.20
Wang _et al_. [42] |  83.40 |  63.88
VIBE [18] |  68.13 |  52.99
Our Optimizer |  57.19 |  46.14
2.5 |  |
Table 1: The performance of our optimization framework on Wang _et al_.’s
dataset. Our optimization method outperforms all previous egocentric pose
estimation methods and the state-of-the-art pose estimation method of the
external view.

In this paper, we first generate the pseudo labels with the optimization
framework (Sec. 3.2) and use them to train our network. Thus, pseudo labels
with higher accuracy generally lead to better network performance. In this
experiment, we evaluate the accuracy of pseudo labels on Wang  _et al_.’s
dataset and show the results in Table 1. This table shows that our method
outperforms all the baseline methods by leveraging both the egocentric view
and external view during optimization. Note that though compared in Table 1,
we cannot use any external-view based pose estimation method, _e.g_. VIBE [18]
and 3DPW [37], for training the egocentric pose estimation network. This is
because the relative pose between the external and egocentric camera is
unknown, making it impossible to obtain the egocentric body pose only from the
external view. Compared with our optimization approach, the method in [42]
performs worse due to the lack of external-view supervision.

###  4.4 Comparisons on 3D Pose Estimation

2.5 Method |  PA-MPJPE |  BA-MPJPE
---|---|---
Wang _et al_.’s test dataset |
Rhodin _et al_. [31] |  89.67 |  73.56
Mo2Cap2 [44] |  102.3 |  74.46
$x$R-egopose [35] |  112.0 |  87.20
Ours |  81.71 |  64.87
2.5 Mo2Cap2 test dataset |  |
Rhodin _et al_. [31] |  97.69 |  76.92
Mo2Cap2 [44] |  91.16 |  70.75
$x$R-egopose [35] |  86.85 |  66.54
Ours |  83.17 |  64.33
2.5 |  |
Table 2: The experimental results on Wang  _et al_.’s test dataset and Mo2Cap2
test dataset [44]. Our method outperforms the state-of-the-art methods, i.e.
Mo2Cap2 [44] and $x$R-egopose [35] on both of the metrics. Our method also
outperforms a video-based method [42] in terms of PA-MPJPE.

We compare our approach with previous single-frame-based methods on the test
dataset from [42] under the “Wang  _et al_.’s test dataset” in Table 4.4.
Since the code or the predictions of $x$R-egopose are not publicly available,
we use our reimplementation of $x$R-egopose instead. On this dataset, our
method outperforms Mo2Cap2 by 20.1% and $x$R-egopose by 27.0% respectively. We
also compared with previous methods on the Mo2Cap2 test dataset and show the
results under the “Mo2Cap2 test dataset” in Table 4.4. On the Mo2Cap2 test
dataset, our method performs better than Mo2Cap2 and $x$R-egopose by 8.8% and
4.2%, respectively.

From the results in Table 4.4, we can see that our approach outperforms all
previous methods on the single-frame egocentric pose estimation task. More
quantitative results on each type of motion are available in the supplementary
material. For the qualitative comparison, we show the results of our method on
the studio dataset and in-the-wild dataset in Fig. 5. Our method performs much
better compared with Mo2Cap2 and $x$R-egopose, especially for the in-the-wild
cases where the body parts are occluded. Please refer to the supplementary
materials for more qualitative results.

We also compared our method with Rhodin  _et al_.’s method [31], which
leverages the weak supervision from multiple views to supervise the training
of a single view pose estimation network. In our EgoPW dataset, we only have
one egocentric and one external view. Thus, we fix the 3D pose estimation
network for the external view and only train the egocentric pose estimation
network. Following Rhodin  _et al_. [31], we align the prediction from the
egocentric and external view with Procrustes analysis and calculate the loss
proposed by Rhodin  _et al_. Our result in Table 4.4 shows that the
performance of our method is better. This is mainly because our spatio-
temporal optimization method predicts accurate and temporally stable 3D poses
as pseudo labels, while other methods suffer seriously from inaccurate
egocentric pose estimations.

###  4.5 Ablation Study

2.5 Method |  PA-MPJPE |  BA-MPJPE
---|---|---
w/o external view |  90.05 |  68.99
w/o learning representation |  85.46 |  67.01
w/o domain adaptation |  84.22 |  66.48
Unsupervised DA |  91.56 |  69.17
Ours |  81.71 |  64.87
2.5 |  |
Table 3: The quantitative results of ablation study.

##### Supervision from the external view.

In our work, we introduce the external view as supervision for training the
network on the real EgoPW dataset. The external view enables generating
accurate pseudo labels, especially when the human body parts are occluded in
the egocentric view but can be observed in the external view. Without the
external view, the obtained pseudo labels are less accurate and will further
affect the network performance. In order to demonstrate this, we firstly
generate the 3D poses as pseudo labels with Wang  _et al_.’s method, _i.e_.
without any external supervision, and then train the pose estimation network
on these new pseudo labels. The result is shown in the “w/o external view” row
of Table 3. We also show the qualitative results with and without external-
view supervision in Fig. 6. Both the qualitative and quantitative results
demonstrate that with the external supervision, the performance of our pose
estimation network is significantly better especially on occluded cases.

Figure 6: The results of our method with (c) and without external view (b).
The network cannot predict accurate poses for the occluded cases without the
external view supervision. The external view is only for visualization and not
used for predicting the pose.

##### Learning egocentric feature representation and bridging the domain gap
with adversarial training.

In our work, we train the pose estimation network with two adversarial
components in order to learn the feature representation of the egocentric
human body (Sec. 3.3.2) and bridge the domain gap between synthetic and real
images (Sec. 3.3.1). In order to demonstrate the effectiveness of both
modules, we removed the domain classifier $\Lambda$ in our training process
and show the results in the row of “w/o learning representation” in Table 3.
We also removed the domain classifier $\Gamma$, train the network without
$L_{D}$ and show the quantitative results in the row of “w/o domain
adaptation” in Table 3. After moving any of the two components, our method
suffers from the performance drop, which demonstrates the effectiveness of
both the feature representation learning module and the domain adaptation
module.

##### Comparison with only using unsupervised domain adaptation.

In this experiment, we compare our approach with the unsupervised adversarial
domain adaptation method [36] which is commonly used for transfer learning
tasks. We train the network only with the $L_{S}$ and $L_{D}$ in the
adversarial domain adaptation module (Sec. 3.3.1) and show the results in the
“Unsupervised DA” of the Table 3. Our approach outperforms the unsupervised
domain adaptation method due to our high-quality pseudo labels.

##  5 Conclusions

In this paper, we have proposed a new approach to egocentric human pose
estimation with a single head-mounted fisheye camera. We collected a new in-
the-wild egocentric dataset (EgoPW) and designed a new optimization method to
generate accurate egocentric poses as pseudo labels. Next, we supervise the
egocentric pose estimation network with the pseudo labels and the features
from the external network. The experiments show that our method outperforms
all of the state-of-the-art methods both qualitatively and quantitatively and
our method also works well under severe occlusion. As future work, we would
like to develop a video-based method for estimating temporally-consistent
egocentric poses from an in-the-wild video.

Limitations. The accuracy of pseudo labels in our method is constrained by our
in-the-wild capture system, which only contains one egocentric view and one
external view, and further constrains the performance of our method. To solve
this, we can fuse different sensors, including IMUs and depth cameras, for
capturing the in-the-wild dataset, which can be explored in our follow-up
work.

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11institutetext: School of Biomedical Engineering and Imaging Sciences, King’s
College London, UK 22institutetext: School of Cancer and Pharmaceutical
Sciences, King’s College London, UK

# An Investigation Into Race Bias in Random Forest Models Based on Breast DCE-
MRI Derived Radiomics Features

Mohamed Huti 11 Tiarna Lee 11 Elinor Sawyer 22 Andrew P. King 11

###### Abstract

Recent research has shown that artificial intelligence (AI) models can exhibit
bias in performance when trained using data that are imbalanced by protected
attribute(s). Most work to date has focused on deep learning models, but
classical AI techniques that make use of hand-crafted features may also be
susceptible to such bias. In this paper we investigate the potential for race
bias in random forest (RF) models trained using radiomics features. Our
application is prediction of tumour molecular subtype from dynamic contrast
enhanced magnetic resonance imaging (DCE-MRI) of breast cancer patients. Our
results show that radiomics features derived from DCE-MRI data do contain
race-identifiable information, and that RF models can be trained to predict
White and Black race from these data with 60-70% accuracy, depending on the
subset of features used. Furthermore, RF models trained to predict tumour
molecular subtype using race-imbalanced data seem to produce biased behaviour,
exhibiting better performance on test data from the race on which they were
trained.

###### Keywords:

Bias AI Fairness Radiomics Breast DCE-MRI.

##  1 Introduction

The potential for artificial intelligence (AI) models to exhibit bias, or
disparate performance for different protected groups, has been demonstrated in
a range of computer vision and more recently medical imaging applications. For
example, biased performance has been reported in AI models for diagnostic
tasks from chest X-rays [9, 21], cardiac magnetic resonance (MR) image
segmentation [19, 18, 10], brain MR image analysis [7, 16, 24, 22] and
dermatology image analysis [1, 6]. In response, the field of _Fair AI_ has
emerged to address the challenge of making AI more trustworthy and equitable
in its performance for protected groups [14].

A common cause of bias in AI model performance is the combination of a
distributional shift between the data of different protected groups and
demographic imbalance in the training set. For example, in chest X-rays there
is a distributional shift between sexes due to the presence of breast tissue
lowering the signal-to-noise ratio of images acquired from female subjects
[9]. However, more subtle distributional shifts can also exist which cannot be
perceived by human experts, and recent work has shown that race-based
distributional shifts are present in a range of medical imaging modalities,
including breast mammography [5]. This raises the possibility of race bias in
AI models trained using imbalanced data from these modalities.

Most work on AI bias to date has focused on deep learning techniques, in which
the features used for the target task are optimised as part of the training
process. In the presence of distributional shift and training set imbalance
this learning process can lead to bias in the features and potentially in
model performance. Classical AI approaches are trained using fixed hand-
crafted features such as radiomics, and so might be considered to be less
susceptible to bias. However, despite these approaches still being widely
applied, little experimental work has been performed to assess the potential
for, and presence of, bias in these features and the resulting models.

In this paper, we investigate the potential for bias in a classical AI model
(Random Forest) based on radiomics features. Our chosen application is
potential race bias in Random Forest models trained using radiomics features
derived from dynamic contrast enhanced magnetic resonance imaging (DCE-MRI) of
breast cancer patients. This application is of interest because there have
been reported differences in breast density and composition between races [12,
15], as well as tumour biology [11], indicating a possible distributional
shift in (imaging) data acquired from different races, and hence the
possibility of bias in AI models trained using these data. Our target task is
the prediction of tumour molecular subtype from the radiomics features. This
is a clinically useful task because different types of tumour are commonly
treated in different ways (e.g. surgery, chemotherapy), and tumour molecular
subtype is normally determined through an invasive biopsy. Therefore,
development and validation of an AI model to perform this task from imaging
data would obviate the need for such biopsies.

This paper makes two key contributions to the field of Fair AI. First, we
present the first thorough investigation into possible bias in AI models based
on radiomics features. Second, we perform the first investigation of bias in
AI models based on features derived from breast DCE-MRI imaging.

##  2 Materials

In our experiments we employ the dataset described in [20]111The dataset is
publicly available at: https://doi.org/10.7937/TCIA.e3sv-re93., which features
pre-operative DCE-MRI images acquired from 922 female patients with invasive
breast cancer at Duke Hospital, USA, together with demographic, clinical,
pathology, genomic, treatment, outcome and other data. From the DCE-MRI
images, 529 radiomics features have been derived which are split into three
(partially overlapping) categories: whole breast, fibroglandular tissue (FGT)
only and tumour only. The full dataset consists of approximately 70% White
subjects, 22% Black subjects and 8% other races. We refer the reader to [20]
for a full summary of patient characteristics and the data provided.

##  3 Methods

For all experiments we employed a Random Forest (RF) classifier as our AI
model, similar to the work described in [20]. For each model, we performed a
grid search hyperparameter optimisation using a 5-fold cross validation on the
training set. Following this, the final model was trained with the selected
hyperparameter values using all training data and applied to the test set. The
hyperparameters optimised were the number of trees (50, 100, 200, 250), the
maximum depth of the trees (10, 15, 30, 45) and the splitting criterion
(entropy, Gini). Our model training differed from that described in [20] in
three important ways:

  1. 1.

We used only Black and White subjects to enable us to analyse bias in a
controlled environment. Data from all other races were excluded from both the
training and test sets. This meant that our dataset comprised 854 subjects
(651 White and 203 Black).

  2. 2.

To simplify our analysis, we focused on just one of the binary classification
problems reported in [20]: prediction of _Luminal A_ vs _non-Luminal A_ tumour
molecular subtype. Based on these labels, the numbers of positive (_Luminal
A_) and negative (_non-Luminal A_) subjects for each race are summarised in
Table 1. As can be seen, there is a higher proportion of _non-Luminal A_
tumours in the Black patients, which is consistent with prior studies on
relative incidence of tumour subtypes by race [2, 8].

  3. 3.

We did not perform feature selection prior to training and evaluating the RF
classifiers. We chose to omit this step because one of our objectives was to
analyse which specific radiomics features (if any) could lead to bias in the
trained models, so we did not want to exclude any features prior to this
analysis.

Label | White | Black |  All
---|---|---|---
Positive (_Luminal A_) | 442 | 107 | 549
Negative (_non-Luminal A_) | 209 | 96 | 305
Table 1: Summary of positive (_Luminal A_) and negative (_non-Luminal A_)
labels in the dataset overall and broken down by race.

##  4 Experiments and Results

###  4.1 Race Classification

In the first experiment, our aim was to determine if the radiomics features
contain race-identifiable information. The presence of such information is a
known potential cause of bias in trained models as it would be indicative of a
distributional shift in the data between races, not just in the imaging data
but in the derived (hand-crafted) radiomics features. To investigate this, we
trained RF classifiers to predict race (White or Black) from the entire
radiomics feature set, and also for the whole breast, FGT and tumour features
individually. For these experiments, to eliminate the effect of class (i.e.
race) imbalance, we randomly sampled from the dataset to create race-balanced
training and test sets, each consisting of 100/100 White/Black subjects.

Results are reported as percentage classification accuracy in Table 2 for all
subjects in the test set and also separately for each race. We can see that it
is possible to predict race from radiomics features with around 60-70%
accuracy. The results are similar for both White and Black subjects and do not
differ significantly for the category of radiomics features used. It should be
noted that the whole breast, FGT and tumour categories are partially
overlapping, hence the similar performance for the different radiomics
categories. Specifically, a set of features related to breast and FGT volume
is included in both the whole breast and FGT categories, and another set
related to FGT and tumour enhancement is present in both the FGT and tumour
categories [20].

Radiomics features | Whole test set | White subjects only | Black subjects only
---|---|---|---
All | 63% | 64% | 66%
Whole breast only | 62% | 70% | 57%
FGT only | 61% | 65% | 60%
Tumour only | 62% | 62% | 66%
Table 2: Race classification accuracy from radiomics features derived from
breast DCE-MRI. Results are presented as percentage classification accuracy
and reported for whole test set as well as broken down by race. Classification
was performed from all radiomics features as well as just those derived from
the whole breast, fibroglandular tissue (FGT) and tumour only.

###  4.2 Bias Analysis

Having established one of the key conditions for the presence of bias in AI
models, i.e. a distributional shift between the data of different protected
groups, we next investigated whether training with highly imbalanced training
sets can lead to bias in performance.

For these experiments we split the dataset into a training set of 426 subjects
and a test set of 428 subjects. The split was random under the constraints
that the White and Black subjects and the _Luminal A_ and _non-Luminal A_
subjects were evenly distributed between train and test sets. The training set
consisted of 325/101 White/Black subjects and 274/152 _Luminal A_ /_non-
Luminal A_ subjects, and the test set consisted of 326/102 White/Black
subjects and 275/153 _Luminal A_ /_non-Luminal A_ subjects.

In addition, we curated two additional training sets consisting of only the
White subjects and only the Black subjects from the combined training set
described above. Due to the racial imbalance in the database, these training
sets consisted of 325/101 subjects for White/Black subjects. Using all three
training sets (i.e. all, White-only and Black-only), we trained RF models for
the task of classifying _Luminal A_ vs _non-Luminal A_ tumour molecular
subtype and evaluated their performance for the entire test set as well as for
the White subjects and the Black subjects in the test set individually. Class
(i.e. molecular subtype) imbalance was addressed by applying a weighting to
training samples that was inversely proportional to the class frequency.

Results are presented in Table 3, in which performance is quantified using the
percentage classification accuracy. We performed this experiment using all
radiomics features, just the whole breast features, just the FGT features and
just the tumour features. We can see that in terms of overall performance, the
models trained using all data and the White-only data had higher accuracy than
the models trained using Black-only data, reflecting the impact of different
training set sizes. Regarding race-specific performance, the models trained
using all training data (i.e. 325/101 White/Black subjects) performed slightly
better on White subjects, likely reflecting the effect of training set
imbalance. The difference in performance in favour of White subjects varied
from 3-11% (mean 6.25%), depending on the subset of features used. The models
trained using White-only data had a larger performance disparity in favour of
White subjects, varying between 6-11% (mean 9%). The models trained using
Black-only data showed generally better performance on Black subjects (mean
3.5% difference), although the model trained using all radiomics features was
1% better for White subjects. In contrast, the model trained using whole
breast radiomics features performed 10% better for Black subjects. With the
exception of this last result, in general there was not a noticeable
difference in bias between the models trained using all radiomics features,
just whole breast features, just FGT features and just tumour features, which
is consistent with the similar race classification results reported in Section
4.1.

ALL FEATURES |  Train
---|---
Test |  |  All |  White |  Black
All | 65% | 65% | 60%
White | 68% | 67% | 60%
Black | 57% | 58% | 59%

WHOLE BREAST |  Train
---|---
Test |  |  All |  White |  Black
All | 61% | 62% | 53%
White | 62% | 63% | 51%
Black | 57% | 57% | 61%

FGT |  Train
---|---
Test |  |  All |  White |  Black
All | 67% | 64% | 61%
White | 68% | 67% | 60%
Black | 62% | 56% | 62%

TUMOUR |  Train
---|---
Test |  |  All |  White |  Black
All | 67% | 65% | 59%
White | 68% | 67% | 58%
Black | 65% | 57% | 61%

Table 3: Tumour molecular subtype classification accuracy for _Luminal A_ vs.
_non-Luminal A_ task. Results presented as percentage accuracy and reported
for training/testing using all subjects, White subjects only and Black
subjects only. From top-to-bottom: results computed using all radiomics
features, just whole breast features, just fibroglandular tissue (FGT)
features and just tumour features.

###  4.3 Covariate Analysis

Next we investigated a range of covariates to test for the presence of
confounding variable(s) that could be leading to the observed bias. From the
full set of patient data available within the dataset we selected those
variables that could most plausibly have associations with both race and model
performance. These variables are summarised in Table 4. For the continuous
variable (i.e. age), the table shows the median and lower/upper quartiles for
White and Black patients separately. For categorical variables (i.e. all other
variables), counts and percentages are provided. The $p$-values were computed
using a Mann-Whitney U test for age and Chi-square tests for independence for
all other variables. We can see that three of the covariates showed
significant differences (at 0.05 significance) in their distributions between
White and Black subjects: age, estrogen receptor status and neoadjuvant
chemotherapy.

As stated earlier, non-luminal breast cancer, which is generally estrogen
receptor negative, is more commonly seen in Black subjects than White subjects
[2, 8]. In addition, this cancer is more commonly treated with neoadjuvant
chemotherapy, whereas luminal breast cancer is treated with surgery, followed
by endocrine therapy and chemotherapy [23] [4]. This may contribute to the
statistically significant differences seen in the covariates.

Covariate | White | Black |  $p$-value
---|---|---|---
Age at diagnosis (years, M(L,U)) | $53.3(45.9,61.8)$ | $50.5(44.0,58.5)$ | $0.012$
Scanner (N / %): | GE | 451 / 69.3% | 134/ 66.0% | 0.430
| Siemens | 200 / 30.7% | 69 / 34.0%
Field strength (N / %): | 1.5T | 315 / 48.4% | 111 / 54.7% | 0.258
| 2.89T | 1 / 0.1% | 0 / 0.0%
| 3T | 335/ 51.5% | 92 / 45.3%
Menopause at diagnosis | Pre | 276 / 42.4% | 94 / 46.3% | 0.574
(N / %): | Post | 364 / 55.9% | 105 / 51.7%
| N/A | 11 / 1.7% | 4 / 2.0%
Estrogen receptor status | Positive | 510/ 78.3% | 123 / 60.6% | 7.430e-07
(N / %): | Negative | 141 / 21.7% | 80 / 39.4%
Human epidermal growth | Positive | 111 / 17.1% | 36 / 17.7% | 0.906
factor 2 receptor status (N / %): | Negative | 540 / 82.9% | 167 / 82.3%
Adjuvant radiation | Yes | 434 / 67.7% | 144 / 71.0% | 0.341
therapy (N / %): | No | 210 / 32.3% | 58 / 29.0%
Neoadjuvant radiation | Yes | 13 / 2.0% | 7/ 3.4% | 0.358
therapy (N / %): | No | 632 / 98.0% | 7 / 96.6%
Adjuvant chemotherapy | Yes | 391/ 63.1% | 108 / 57.1% | 0.167
(N / %): | No | 229 / 36.9% | 81 / 42.9%
Neoadjuvant chemotherapy | Yes | 178/ 28.1% | 91 / 46.9% | 1.593e-06
(N / %): | No | 455 /71.9 % | 103 / 53.1%
Table 4: Distributions of covariates in the dataset by race (White and Black
subjects only). Continuous variables are reported as median (M), lower (L) and
upper (U) quartiles. Categorical variables are reported as count (N) and
percentage (%). $p$-values calculated using Mann Whitney U tests for
continuous variables and Chi Square tests for independence for categorical
variables.

##  5 Discussion and Conclusions

The main contribution of this paper has been to present the first
investigation focused on potential bias in AI models trained using radiomics
features. The work described in [20] also reported performance of their AI
models based on radiomics features broken down by race. However, in our work
we have performed a more controlled analysis to investigate the potential for
bias and its possible causes. As a second key contribution, our paper
represents the first investigation into bias in AI models based on breast DCE-
MRI imaging.

Our key findings are that: (i) radiomics features derived from breast DCE-MRI
data contain race-identifiable information, leading to the potential for bias
in AI models trained using such data, and (ii) RF models trained to predict
tumour molecular subtype seem to exhibit biased behaviour when trained using
race-imbalanced training data.

These findings show that the process of producing hand-crafted features such
as radiomics features does not _remove_ the potential for bias from the
imaging data, and so further investigation of the performances of other
similar models is warranted. However, an unanswered question is whether the
production of hand-crafted features _reduces_ the potential for bias. To
investigate this, in future work we will compare bias in radiomics-based AI
models to similar image-based AI models.

Our analysis of covariates did highlight several possible confounders, so we
emphasise that the cause of the bias we have observed remains to be
established. In future work we will perform further analysis of these
potential confounders, including of interactions between multiple variables,
to help determine this cause.

Interestingly, the work described in [20], which included the same _Luminal A_
vs. _non-Luminal A_ classification task using the same dataset did not find a
statistically significant difference in performance between races. However,
there are a number of differences between our work and [20]. First, [20] used
all training data (half of the full dataset) when training their RF models,
i.e. they did not create deliberately imbalanced training sets as we did.
Therefore, their race distribution was presumably similar to that of the full
dataset (i.e. 70% White, 22% Black, 8% other races). It may be that this was
not a sufficient level of imbalance to result in biased performances, and/or
that the presence of other races (apart from White and Black) in the training
and test sets reduced the bias effect. Second, we also note that the
comparison performed in [20] was between White and other races, whereas we
compared White and Black races. Third, in [20] a feature selection step was
employed to optimise performance of their models. It is possible that this
reduced the potential for bias by removing features that contained race-
specific information, although our race classification results (see Section
4.1) suggest that this information is present across all categories of
feature.

In this work we have focused on distributional shift in imaging data (and
derived features) as a cause of bias, but bias can also arise from other
sources, such as bias in data acquisition, annotations, and use of the models
after deployment [13, 3]. We emphasise that by focusing on this specific cause
of bias we do not believe that others should be neglected, and we argue for
the importance of considering possible bias in all parts of the healthcare AI
pipeline.

Finally, this paper has focused on highlighting the _presence_ of bias, and we
have not addressed the important issue of what should be _done_ about it. Bias
mitigation techniques have been proposed and investigated in a range of
medical imaging problems [19, 25, 26], and approaches such as these may have a
role to play in addressing the bias we have uncovered in this work. However,
when attempting to mitigate bias one should bear in mind that the
classification tasks of different protected groups may have different levels
of difficulty, making it challenging to eliminate bias completely.
Furthermore, one should take care to ensure that the performances of the
protected groups are ‘levelled up’ rather than ‘levelled down’ [17] to avoid
causing harm to some protected groups.

####  5.0.1 Acknowledgements

This work was supported by the National Institute for Health Research (NIHR)
Biomedical Research Centre at Guy’s and St Thomas’ NHS Foundation Trust and
King’s College London, United Kingdom. Additionally this research was funded
in whole, or in part, by the Wellcome Trust, United Kingdom WT203148/Z/16/Z.
The views expressed in this paper are those of the authors and not necessarily
those of the NHS, the NIHR or the Department of Health and Social Care.

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