Learning shape distributions from large databases of healthy organs applications to zero-shot and few-shot abnormal pancreas detection

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Learning shape distributions from large databases

of healthy organs: applications to zero-shot and

few-shot abnormal pancreas detection

Rebeca Vétil1,2,∗, Clément Abi-Nader2, Alexandre Bône2, Marie-Pierre

Vullierme3, Marc-Michel Rohé2, Pietro Gori1, and Isabelle Bloch1,4

1LTCI, Télécom Paris, Institut Polytechnique de Paris, France

2Guerbet Research, Villepinte, France

3Department of Radiology, Hospital of Annecy-Genevois, Université de Paris, France

4Sorbonne Université, CNRS, LIP6, Paris, France

rebeca.vetil@guerbet.com

Abstract. We propose a scalable and data-driven approach to learn

shape distributions from large databases of healthy organs. To do so, vol-

umetric segmentation masks are embedded into a common probabilistic

shape space that is learned with a variational auto-encoding network.

The resulting latent shape representations are leveraged to derive zero-

shot and few-shot methods for abnormal shape detection. The proposed

distribution learning approach is illustrated on a large database of 1200

healthy pancreas shapes. Downstream qualitative and quantitative ex-

periments are conducted on a separate test set of 224 pancreas from

patients with mixed conditions. The abnormal pancreas detection AUC

reached up to 65.41% in the zero-shot conﬁguration, and 78.97% in the

few-shot conﬁguration with as few as 15 abnormal examples, outperform-

ing a baseline approach based on the sole volume.

Keywords: Shape Analysis ·Anomaly Detection ·Pancreas

1 Introduction

Anatomical alterations of organs such as the brain or the pancreas may be infor-

mative of functional impairments. For instance, hippocampal atrophy and duct

dilatation are well-known markers of Alzheimer’s disease and pancreatic ductal

adenocarcinoma, respectively [9,15]. In these examples, quantifying anatomical

diﬀerences bears therefore a great potential for determining the patient’s clini-

cal status, anticipating its future progression or regression, and supporting the

treatment planning.

Since the seminal work of Thompson [19], the computational anatomy lit-

erature proposed several Statistical Shape Modeling (SSM) approaches, which

embed geometrical shapes into metric spaces where notions of distance and diﬀer-

ence can be deﬁned and quantiﬁed [2,5,12]. Taking advantage of these represen-

tations, statistical shape models were then proposed to perform group analyses

*Corresponding author: rebeca.vetil@guerbet.com

arXiv:2210.12095v1 [cs.CV] 21 Oct 2022

2 Vétil at al.

of shape collections. In particular, atlas models [16] learn geometrical distribu-

tions in terms of an “average” representative shape and associated variability,

generalizing the Euclidean mean-variance analysis. In medical imaging, learning

atlases from healthy examples allows for the deﬁnition of normative models for

anatomical structures or organs, such as brain MRIs or subcortical regions seg-

mented from neuroimaging data [10,22], thus providing a natural framework for

the detection of abnormal anatomies.

In practice, leveraging an atlas model to compute the likelihood of a given

shape to belong to the underlying distribution either requires to identify land-

marks [6], or to solve a registration problem [3]. To circumvent the computational

cost of this shape embedding operation, the authors in [21] proposed to train an

encoder network to predict registration parameters from image pairs. In [7, 14],

the authors built on this idea and used the variational autoencoder (VAE) of [13]

to learn the embedding space jointly with the atlas model, instead of relying on

pre-determined parametrization strategies. However, the structure of the decod-

ing network remained constrained by hyperparameter-rich topological assump-

tions, enforced via costly smoothing and numerical integration operators from a

computational point of view.

Alternative approaches proposed to drop topological hypotheses by relying

on variations of the AE or its variational counterparts [13] to learn normative

models that are subsequently used to perform Anomaly Detection (AD). These

methods compress and reconstruct images of healthy subjects to capture a nor-

mative model of organs [1,23]. Yet, they are usually applied on the raw imaging

data, thus they entail the risk of extracting features related to the intensity dis-

tribution of a dataset which are not necessarily speciﬁc to the organ anatomy.

Therefore, regularization constraints [1, 4] are introduced to improve the detec-

tion performances compared to the vanilla AE. To further reduce the overﬁtting

risk, these methods artiﬁcially increase the dataset size by working on 2D slices.

Given this context, we propose a VAE-based method to learn a normative

model of organ shape that can subsequently be used to detect anomalies, thus

bridging the gap between SSM and AD models. Although SSM methods with

explicit modeling constraints proved eﬀective to learn relevant shape spaces from

relatively small collections of high-dimensional data, we propose to further re-

duce the set of underlying hypotheses and leave the decoding network uncon-

strained in its architecture. With the objective to learn normative shape models

from collections of healthy organs, we argue that suﬃciently large databases of

relevant medical images can be constructed by pooling together diﬀerent data

sources, see [8] for instance. To reduce the risk of overﬁtting and focus on the

anatomy of organs, the VAE is learned from 3D binary segmentation masks

and is coupled with a shape-preserving data augmentation strategy consisting of

translations, rotations and scalings. An approach to study and visualize group

diﬀerences is also proposed.

Section 2 details the proposed method, which is then illustrated on a pancreas

shape problem in Section 3. Section 4 discusses the results and concludes.

Learning shape distributions from large databases of healthy organs 3

2 Methods

Modeling organ shape. We consider an image acquired via a standard imaging

technique. For a given organ in the image, its anatomy can be represented by a

binary segmentation mask X={xi, i = 1...d}with xi∈ {0,1}and dthe number

of voxels in the image. We are interested in studying the shape of this organ,

and assume that it is characterized by a set of underlying properties that can be

extracted from the segmentation mask. Therefore, we hypothesize the following

generative process for the segmentation mask:

pθ(X|z) =

i=1

fθ(z)xi

i(1 −fθ(z)i)1−xi(1)

where 00= 1 by convention, and zis a latent variable generated from a prior

distribution p(z). This latent variable provides a low-dimensional representation

of the segmentation mask embedding its main shape features. The function fθis

a non-linear function mapping zto a predicted probabilistic segmentation mask.

We are interested in inferring the parameters θof the generative process, as

well as approximating the posterior distribution of the latent variable zgiven

a segmentation mask X. We rely on the VAE framework [13] to estimate the

model parameters. Hence, we assume that p(z)is a multivariate Gaussian with

zero mean and identity covariance. We also introduce the approximate posterior

distribution qφ(z|X)parameterized by φ, and optimize a lower bound Lof the

marginal log-likelihood, which can be written for the segmentation mask Xpof

a subject pas:

L=Eqφ(z|Xp)[log pθ(Xp|z)] −KL[qφ(z|Xp)|p(z)],(2)

where qφ(z|Xp)follows a Gaussian distribution N(µφ(Xp), σ2

φ(Xp)I)with I

the identity matrix, and KL is the Kullback-Leibler divergence.

To capture shape features, we rely on a convolutional network and adopt the

U-Net [17] encoder-decoder architecture without skip connections∗. In practice,

the number of convolutional layers and the convolutional blocks are automati-

cally inferred thanks to the nnU-Net self-conﬁguring procedure [11] (see Section

A in the supplementary material for details). Due to this encoder-decoder ar-

chitecture, the segmentation masks are progressively down-sampled to obtain

low-resolution feature maps which are mapped through a linear transformation

to the latent variable z. The latent code is subsequently decoded by a symmetric

path to reconstruct the original masks.

Anomaly detection. We propose to learn a normative model of organ

shapes by applying the VAE framework previously presented on the segmen-

tation masks of a large cohort of Nhealthy patients, allowing the model to

capture a low-dimensional embedding characteristic of a normal organ anatomy.

In addition, we use a data augmentation procedure consisting of random trans-

lations, rotations and scalings, in order to be invariant to these transformations

∗Code available at https://github.com/rebeca-vetil/HealthyShapeVAE.

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Learningshapedistributionsfromlargedatabasesofhealthyorgans:applicationstozero-shotandfew-shotabnormalpancreasdetectionRebecaVétil1;2;,ClémentAbi-Nader2,AlexandreBône2,Marie-PierreVullierme3,Marc-MichelRohé2,PietroGori1,andIsabelleBloch1;41LTCI,TélécomParis,InstitutPolytechniquedeParis,France2Guerb...

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Learning shape distributions from large databases of healthy organs applications to zero-shot and few-shot abnormal pancreas detection

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