1 Segmentation of Bruchs Membrane in retinal OCT with AMD using anatomical priors and

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Segmentation of Bruch’s Membrane in retinal

OCT with AMD using anatomical priors and

uncertainty quantiﬁcation

Botond Fazekas, Dmitrii Lachinov, Guilherme Aresta, Julia Mai, Ursula Schmidt-Erfurth,

and Hrvoje Bogunovi´

Christian Doppler Laboratory for Artiﬁcial Intelligence in Retina, Department of Ophthalmology and

Optometry, Medical University of Vienna, Austria

Abstract—Bruch’s membrane (BM) segmentation on op-

tical coherence tomography (OCT) is a pivotal step for the

diagnosis and follow-up of age-related macular degenera-

tion (AMD), one of the leading causes of blindness in the

developed world. Automated BM segmentation methods

exist, but they usually do not account for the anatomical

coherence of the results, neither provide feedback on the

conﬁdence of the prediction. These factors limit the applica-

bility of these systems in real-world scenarios. With this in

mind, we propose an end-to-end deep learning method for

automated BM segmentation in AMD patients. An Attention

U-Net is trained to output a probability density function

of the BM position, while taking into account the natural

curvature of the surface. Besides the surface position, the

method also estimates an A-scan wise uncertainty measure

of the segmentation output. Subsequently, the A-scans with

high uncertainty are interpolated using thin plate splines

(TPS). We tested our method with ablation studies on an

internal dataset with 138 patients covering all three AMD

stages, and achieved a mean absolute localization error of

4.10 µm. In addition, the proposed segmentation method

was compared against the state-of-the-art methods and

showed a superior performance on an external publicly

available dataset from a different patient cohort and OCT

device, demonstrating strong generalization ability.

I. INTRODUCTION

Age-related Macular Degeneration (AMD) is the leading

cause of blindness and irreversible loss of central vision in the

developed countries for people over age sixty [1]. The disease

stages are divided into early/intermediate (iAMD) and two late

ones. Early/intermediate stage AMD cases are characterized

by the deposition of metabolic products (drusen) in the macula

between the retinal pigment epithelium (RPE) and the Bruch’s

Membrane (BM). Late AMD appears as geographic atrophy

(GA or dry AMD) or neovascular AMD (nAMD or wet AMD),

although a mixture of both can occur in the same eye [2].

GA is characterized by the progressive loss of photoreceptors

and RPE in the macular region, resulting in the permanent

loss of the sharp vision. Neovascular AMD manifests in

the formation of abnormal blood vessels, typically in the

choroidal plexus below the RPE, leading to pigment epithelial

detachment (PED), and exudation into the retina. Thus, early

diagnosis and regular monitoring is crucial for the effective

treatment of the patients. Although AMD is usually detected

first by funduscopic examinations, other imaging modalities are

required to understand the full extent of the degeneration under

the macula [2]. The current state-of-the-art modality for AMD

monitoring and treatment is Optical Coherence Tomography.

Optical Coherence Tomography (OCT) is a non-invasive

3D imaging technique that can acquire high-resolution cross-

sectional images of human tissues, particularly suitable for the

retina [3], [4]. It is widely used in the diagnosis and monitoring

of patients with a large variety of retinal diseases, such as

diabetic retinopathy (DR) [5], retinal vein occlusion (RVO)

[6], glaucoma [7] and AMD [8], [9]. The segmentation of the

retinal layers in OCT scans is a crucial step in order to monitor

and quantify the progression of a disease. However, manual

layer annotation or correction is very time-consuming and

subjective, which has motivated the development of automated

accurate and objective methods [10]--[13].

Bruch’s Membrane is an elastic smooth and thin structure,

strategically located between the retina and the general cir-

culation, having a crucial role in retinal function, aging and

disease [14]. Automated segmentation of the BM is particularly

important in the context of AMD as, unlike other common

retinal diseases such as DR, RVO, or glaucoma, the BM

is distinguishable from the outer RPE boundary. In specific,

drusen in iAMD and PEDs in nAMD separate the RPE from

BM, requiring the segmentation of the region in-between them.

In addition, in case of GA, the RPE is completely lost in some

locations, exposing only the BM, thus imposing additional

difficulties for algorithms and calculations that depend on the

RPE position. Achieving correct automated identification of

the BM is challenging in many cases, mainly due to the small

thickness of this layer, the high reflectivity of the RPE that

shadows parts of the BM, and the noise being present in the

scans, which is often indistinguishable from the content of

drusen and PEDs (Fig. 1). Due to these difficulties, currently

many automated solutions either do not provide a segmentation

of the BM or its segmentation is often inaccurate in retinal

OCT with AMD, leaving this clinically relevant segmentation

task unaddressed or under-explored.

The state-of-the-art segmentation algorithms are based on

Deep Learning (DL), which depends on a large amount of

arXiv:2210.14799v2 [eess.IV] 30 Oct 2022

(a) iAMD (b) nAMD (c) GA

Fig. 1: The three stages of AMD, where the Bruch’s Membrane

is marked with a green line. As a reference, retina from the

Internal Limiting Membrane to the outer boundary of the RPE

is denoted with cyan lines.

annotated training data that is often difficult and expensive

to obtain. In addition, these models, when based only on

textural features of the OCT images, may fail where the

images contain artifacts due to the limitations in the scanning

process, e.g., shadowing, eye-movement or low-resolution

acquisition [15]. The introduction of prior knowledge about

the target domain imposes constraints on the possible solutions,

thus reducing the search space [16]. Such knowledge can

take several forms, including topology specification, distances

between regions [17], or shape models [16]. Utilizing prior

anatomical information for medical image segmentation has

already been proven useful in order to obtain more accurate

and plausible results, and with smaller training sets. They have

been successfully applied among others to improve cardiac

image segmentations [15], liver segmentation [18] and retinal

layer segmentation [17], [19], [20].

Quantifying uncertainty of DL models is crucial for clinical

applications in order to build trust in systems’ prediction

and at the same time for reducing the associated risks of

downstream tasks relying on uncertain or incorrect results. This

is particularly pertinent for image segmentation, where there is

an inherent ambiguity in the reference, due to the limitations

in the image acquisition processes and the subjectivity and

complexity of the annotation task, resulting in variations

between the manual annotations. However, DL segmentation

methods tend to provide unrealistic overconfident predictions

on these complex tasks, especially when they are applied on a

different patient cohort or pathologies not observed during the

training.

Having the above considerations in mind, in this paper,

we propose a new deep learning method for automated

segmentation of the BM. By using a probability distribution

function to infer its spatial coordinates, together with a loss

term incorporating anatomical priors which promotes smooth

predictions, the method accounts for local morphological

changes resulting from pathologies or acquisition artifacts,

and is capable of identifying regions of potential segmentation

failure. The acquired local uncertainty information is utilized

in a post-processing step to further improve the segmentation

in the areas of potentially erroneous segmentations. Large-

scale multi-dataset experiments show the robustness of the

developed model, which furthermore achieves the state-of-the-

art performance on an external public dataset.

A. Related works

The goal of layer segmentation is to obtain anatomically

coherent, smooth, and continuous retinal layer boundary

surfaces. The first widely-used approach was to extract image

features from the B-scans, which are then used by graph-based

methods to estimate the surface positions. For instance, the

IOWA Reference Algorithms [19], [21] represented the OCT

as a graph and the surface positioning was solved with dynamic

programming algorithms, while guaranteeing the correct topo-

logical ordering, satisfying prior layer thickness constraints,

and smoothing the results. The graph-based methods were later

further improved in several works [22]--[24]. Rathke et al. [25]

proposed a method using a probabilistic graphical model, which

incorporated anatomical shape priors for OCT segmentation,

including a post-processing fix for the BM. A drawback of

these methods is that they rely on hand-crafted image features

as the backbone for the graph construction and may perform

poor in the presence of noise or other imaging artifacts, as well

as severe pathologies. Several approaches attempted to improve

on this by incorporating machine learning-based methods to

estimate the cost function for the nodes of the graph [9], [26]-

-[28]. For these types of approaches, the performance of the

graph-search method is still tied to the quality of the initial

probability map, and subject to predefined hard morphological

constraints on layer thickness and smoothness variability.

With the advent of deep learning, U-Net [29] and its variants

became a dominant approach for medical image segmentation,

including retinal layer segmentation. In particular, ReLayNet

proposed in Roy et al. [11] presented a network architecture

similar to U-Net, which represented nine retinal layers and

possible fluid-filled pockets as distinct classes and predicted

their pixel-wise locations. A deficiency of this algorithm is

that it is not guaranteed to predict a single unique BM position

in an A-scan. Sousa et al. [13] uses a U-Net to create an initial

segmentation followed by a CNN based edge detection network

to further refine the results, while predicting one single location

per A-scan.

A major weakness of these two deep learning methods is that

they do not account for the natural ordering of the layers, and

consequently do not guarantee anatomically plausible results.

The framework presented by He et al. [10] improves on this by

predicting the surface positions using column-wise soft-argmax,

thus ensuring that only one position is inferred per A-scan. Also,

proper layer ordering is guaranteed with a topological module.

They further improved their method in [20] by removing the

fully-connected layers and hence requiring fewer parameters

than in their previous work, while also evaluating the model

performance on a BM segmentation task. Besides showing

improvement against the state of the art they also showed that

the surface connectivity is well constrained. However, they

did not include uncertainty estimation in their work and the

method was not validated on AMD patients.

An alternative, not machine learning based approach was

presented in Lou et al. [30], which uses a mathematical model

of the potential fluid energy in fluid mechanics. This method

inherently guarantees the correct topological ordering and the

smoothness of the predicted layers, however its performance

is significantly lower than of the CNN based method, possibly

because of the hard requirement of the algorithm, where the

gray values on both side of the boundaries must be different.

Other researchers have focused on including uncertainty

estimations coupled with the layer segmentation. The approach

proposed by Orlando et al. [31] predicts the photoreceptor

layer, and they perform Bayesian inference through Monte

Carlo sampling using the dropout in a modified U-Net architec-

ture. They investigated the correlation between the measured

uncertainty and the segmentation performance, although only

on a B-scan and volume level. In addition to using the same

approach to quantify uncertainty, the framework proposed by

Sedai et al. [32] uses a fully convolutional network that learns

to output the aleatoric uncertainty which it was observing.

The network performed comparably to the state of the art,

but the relation between the uncertainty and the segmentation

displacement, essential for the clinical applicability, was not

covered in the work.

A problem common to all the aforementioned methods is

that they lack one or more critical components for successful

clinical translation in AMD. Either they are not able to robustly

predict the BM, or they were not validated on all stages

of the AMD, with different acquisition settings, or they do

not provide an uncertainty estimation required for achieving

reliable, trustworthy segmentation methods.

B. Summary of contributions

In this paper, we propose a novel deep learning method

for segmentation of the BM layer from retinal OCT scans of

patients with AMD. The main contributions of this work are

the following:

•

A new curvature loss term to encode a shape anatomic

prior of the BM. This improves the model’s robustness

and the ability to detect the BM in low-contrast areas,

resulting in anatomically more plausible solutions.

•

Uncertainty quantification on A-scan, B-scan and OCT

volume level to detect possible mis-segmentations, which

can then be automatically corrected in a post-processing

step.

•

Large-scale evaluation of the proposed method, across all

three AMD stages and on images acquired with different

OCT devices from various patient cohorts reflecting a

real-world clinical setting, as well as on an external public

test set, proving the strong generalization capability of

the solution.

II. METHODS

The proposed deep learning method is designed to provide an

anatomically coherent segmentation of the BM. The input to the

network is a pre-processed B-scan and the single channel output

contains column-wise (A-scan-wise) a probability distribution

of the BM position. The BM positions are then regressed from

the expected values of the distributions. During the training,

curvature constraints are imposed to provide an inductive bias

on the correct shape of the surface even in the areas, where

it is hardly visible. During inference, volumetric predictions

are obtained by combining the B-scan-wise segmentations and

afterwards replacing uncertain regions with interpolated values.

A. Regressing BM position with anatomy-aware

probability distributions

All of the B-scans were resized regardless of the initial

resolution to

512 ×512

pixels using bilinear interpolation. The

backbone image segmentation network is an Attention U-Net

[33] with five downsampling and upsampling layers with 32,

64, 128, 256 and 512 channels, respectively. The input is a

512 ×512 ×1

image and and the output layer has a single

channel of the same size as the input. Every convolutional layer

is followed by a dropout layer with 0.2 drop probability. We

used LeakyReLU as activation function in the hidden layers.

The output of the network is a column-wise probability map,

in which each column represents a probability distribution,

where the value of each row corresponds to the probability of

the BM at this position. The target distribution is modeled to

be a Gaussian distribution to better accommodate for possible

pixel-wise imprecisions of the annotations. This allows the

network to identify several adjacent positions within a columns

as possible candidates.

We used a loss function consisting of three terms, each

focusing on a different aspect of the segmentation task: (i) a

term for regressing correct position of the BM, (ii) a term

providing a pixel-wise supervision per image columns to

weakly enforce a Gaussian distribution of the probability mass

function, used later for the uncertainty estimation, and (iii) a

curvature term which introduces the anatomical shape prior in

the training itself, and regularizes the curvature of the predicted

BM as well as enforcing its continuity.

1) Surface position regression with a probability mass function:

To regress the coordinates of the BM, the column-wise expected

value of the probability map is calculated, similarly to the

models proposed by He et al. [10], [20].

Let

be a random variable corresponding to the

coordinate (position) of the BM, and

is the position of

an A-scan. We aim to assess the expected BM position given

the A-scan x:

ˆµY|x=X

y·P(Y=y|X=x)(1)

The probability mass function (PMF)

P(Y|X)

is estimated

with the neural network. To ensure that

P(Y|X)

is a proper

PMF, we perform a column-wise softmax activation over the

network outputs.

The PMF, thus BM position, is learned with the help of

mean squared error (MSE) loss between the predicted BM

location ˆµand the reference standard µ:

L1=X

P(x)ˆµY|x−µY|x2(2)

We assume that all A-scans are equally important and

X∼U[1, N]

, where

is a number of A-scans in a single

B-scan.

2) Regularization of the distribution:As proposed in Ni-

bali et al. [34], we introduce a regularization term to guide

the model to match the output distribution to a target Gaussian

probability mass function for each column and thus introducing

a pixel-level supervision. We opted to use Kullback-Leibler

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1SegmentationofBruch'sMembraneinretinalOCTwithAMDusinganatomicalpriorsanduncertaintyquanticationBotondFazekas,DmitriiLachinov,GuilhermeAresta,JuliaMai,UrsulaSchmidt-Erfurth,andHrvojeBogunovi´cChristianDopplerLaboratoryforArticialIntelligenceinRetina,DepartmentofOphthalmologyandOptometry,MedicalUni...

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