A skeletonization algorithm for gradient-based optimization

The skeleton of a digital image is a compact representation of its topology, geometry, and scale. It has utility in many computer vision applications, such as image description, segmentation, and registration. However, skeletonization has only seen limited use in contemporary deep learning solutions. Most existing skeletonization algorithms are not differentiable, making it impossible to integrate them with gradient-based optimization. Compatible algorithms based on morphological operations and neural networks have been proposed, but their results often deviate from the geometry and topology of the true medial axis. This work introduces the first three-dimensional skeletonization algorithm that is both compatible with gradient-based optimization and preserves an object's topology. Our method is exclusively based on matrix additions and multiplications, convolutional operations, basic non-linear functions, and sampling from a uniform probability distribution, allowing it to be easily implemented in any major deep learning library. In benchmarking experiments, we prove the advantages of our skeletonization algorithm compared to non-differentiable, morphological, and neural-network-based baselines. Finally, we demonstrate the utility of our algorithm by integrating it with two medical image processing applications that use gradient-based optimization: deep-learning-based blood vessel segmentation, and multimodal registration of the mandible in computed tomography and magnetic resonance images.

Self-pruning Graph Neural Network for Predicting Inflammatory Disease Activity in Multiple Sclerosis from Brain MR Images

Multiple Sclerosis (MS) is a severe neurological disease characterized by inflammatory lesions in the central nervous system. Hence, predicting inflammatory disease activity is crucial for disease assessment and treatment. However, MS lesions can occur throughout the brain and vary in shape, size and total count among patients. The high variance in lesion load and locations makes it challenging for machine learning methods to learn a globally effective representation of whole-brain MRI scans to assess and predict disease. Technically it is non-trivial to incorporate essential biomarkers such as lesion load or spatial proximity. Our work represents the first attempt to utilize graph neural networks (GNN) to aggregate these biomarkers for a novel global representation. We propose a two-stage MS inflammatory disease activity prediction approach. First, a 3D segmentation network detects lesions, and a self-supervised algorithm extracts their image features. Second, the detected lesions are used to build a patient graph. The lesions act as nodes in the graph and are initialized with image features extracted in the first stage. Finally, the lesions are connected based on their spatial proximity and the inflammatory disease activity prediction is formulated as a graph classification task. Furthermore, we propose a self-pruning strategy to auto-select the most critical lesions for prediction. Our proposed method outperforms the existing baseline by a large margin (AUCs of 0.67 vs. 0.61 and 0.66 vs. 0.60 for one-year and two-year inflammatory disease activity, respectively). Finally, our proposed method enjoys inherent explainability by assigning an importance score to each lesion for the overall prediction. Code is available at https://github.com/chinmay5/ms_ida.git

Detailed retinal vessel segmentation without human annotations using simulated optical coherence tomography angiographs

Optical coherence tomography angiography (OCTA) is a non-invasive imaging modality that can acquire high-resolution volumes of the retinal vasculature and aid the diagnosis of ocular, neurological and cardiac diseases. Segmentation of the visible blood vessels is a common first step when extracting quantitative biomarkers from these images. Classical segmentation algorithms based on thresholding are strongly affected by image artifacts and limited signal-to-noise ratio. The use of modern, deep learning-based segmentation methods has been inhibited by a lack of large datasets with detailed annotations of the blood vessels. To address this issue, recent work has employed transfer learning, where a segmentation network is trained on synthetic OCTA images and is then applied to real data. However, the previously proposed simulation models are incapable of faithfully modeling the retinal vasculature and do not provide effective domain adaptation. Because of this, current methods are not able to fully segment the retinal vasculature, in particular the smallest capillaries. In this work, we present a lightweight simulation of the retinal vascular network based on space colonization for faster and more realistic OCTA synthesis. Moreover, we introduce three contrast adaptation pipelines to decrease the domain gap between real and artificial images. We demonstrate the superior performance of our approach in extensive quantitative and qualitative experiments on three public datasets that compare our method to traditional computer vision algorithms and supervised training using human annotations. Finally, we make our entire pipeline publicly available, including the source code, pretrained models, and a large dataset of synthetic OCTA images.

FedPIDAvg: A PID controller inspired aggregation method for Federated Learning

This paper presents FedPIDAvg, the winning submission to the Federated Tumor Segmentation Challenge 2022 (FETS22). Inspired by FedCostWAvg, our winning contribution to FETS21, we contribute an improved aggregation strategy for federated and collaborative learning. FedCostWAvg is a weighted averaging method that not only considers the number of training samples of each cluster but also the size of the drop of the respective cost function in the last federated round. This can be interpreted as the derivative part of a PID controller (proportional-integral-derivative controller). In FedPIDAvg, we further add the missing integral term. Another key challenge was the vastly varying size of data samples per center. We addressed this by modeling the data center sizes as following a Poisson distribution and choosing the training iterations per center accordingly. Our method outperformed all other submissions.

Link Prediction for Flow-Driven Spatial Networks

Link prediction algorithms predict the existence of connections between nodes in network-structured data and are typically applied to refine the connectivity among nodes by proposing meaningful new links. In this work, we focus on link prediction for flow-driven spatial networks, which are embedded in a Euclidean space and relate to physical exchange and transportation processes (e.g., blood flow in vessels or traffic flow in road networks). To this end, we propose the Graph Attentive Vectors (GAV) link prediction framework. GAV models simplified dynamics of physical flow in spatial networks via an attentive, neighborhood-aware message-passing paradigm, updating vector embeddings in a constrained manner. We evaluate GAV on eight flow-driven spatial networks given by whole-brain vessel graphs and road networks. GAV demonstrates superior performances across all datasets and metrics and outperforms the current state-of-the-art on the ogbl-vessel benchmark by more than 18% (98.38 vs. 83.07 AUC).

Clustering disease trajectories in contrastive feature space for biomarker discovery in age-related macular degeneration

Age-related macular degeneration (AMD) is the leading cause of blindness in the elderly. Despite this, the exact dynamics of disease progression are poorly understood. There is a clear need for imaging biomarkers in retinal optical coherence tomography (OCT) that aid the diagnosis, prognosis and management of AMD. However, current grading systems, which coarsely group disease stage into broad categories describing early and intermediate AMD, have very limited prognostic value for the conversion to late AMD. In this paper, we are the first to analyse disease progression as clustered trajectories in a self-supervised feature space. Our method first pretrains an encoder with contrastive learning to project images from longitudinal time series to points in feature space. This enables the creation of disease trajectories, which are then denoised, partitioned and grouped into clusters. These clusters, found in two datasets containing time series of 7,912 patients imaged over eight years, were correlated with known OCT biomarkers. This reinforced efforts by four expert ophthalmologists to investigate clusters, during a clinical comparison and interpretation task, as candidates for time-dependent biomarkers that describe progression of AMD.

Topologically faithful image segmentation via induced matching of persistence barcodes

Image segmentation is a largely researched field where neural networks find vast applications in many facets of technology. Some of the most popular approaches to train segmentation networks employ loss functions optimizing pixel-overlap, an objective that is insufficient for many segmentation tasks. In recent years, their limitations fueled a growing interest in topology-aware methods, which aim to recover the correct topology of the segmented structures. However, so far, none of the existing approaches achieve a spatially correct matching between the topological features of ground truth and prediction. In this work, we propose the first topologically and feature-wise accurate metric and loss function for supervised image segmentation, which we term Betti matching. We show how induced matchings guarantee the spatially correct matching between barcodes in a segmentation setting. Furthermore, we propose an efficient algorithm to compute the Betti matching of images. We show that the Betti matching error is an interpretable metric to evaluate the topological correctness of segmentations, which is more sensitive than the well-established Betti number error. Moreover, the differentiability of the Betti matching loss enables its use as a loss function. It improves the topological performance of segmentation networks across six diverse datasets while preserving the volumetric performance. Our code is available in https://github.com/nstucki/Betti-matching.

Automated analysis of diabetic retinopathy using vessel segmentation maps as inductive bias

Recent studies suggest that early stages of diabetic retinopathy (DR) can be diagnosed by monitoring vascular changes in the deep vascular complex. In this work, we investigate a novel method for automated DR grading based on optical coherence tomography angiography (OCTA) images. Our work combines OCTA scans with their vessel segmentations, which then serve as inputs to task specific networks for lesion segmentation, image quality assessment and DR grading. For this, we generate synthetic OCTA images to train a segmentation network that can be directly applied on real OCTA data. We test our approach on MICCAI 2022's DR analysis challenge (DRAC). In our experiments, the proposed method performs equally well as the baseline model.

Physiology-based simulation of the retinal vasculature enables annotation-free segmentation of OCT angiographs

Optical coherence tomography angiography (OCTA) can non-invasively image the eye's circulatory system. In order to reliably characterize the retinal vasculature, there is a need to automatically extract quantitative metrics from these images. The calculation of such biomarkers requires a precise semantic segmentation of the blood vessels. However, deep-learning-based methods for segmentation mostly rely on supervised training with voxel-level annotations, which are costly to obtain. In this work, we present a pipeline to synthesize large amounts of realistic OCTA images with intrinsically matching ground truth labels; thereby obviating the need for manual annotation of training data. Our proposed method is based on two novel components: 1) a physiology-based simulation that models the various retinal vascular plexuses and 2) a suite of physics-based image augmentations that emulate the OCTA image acquisition process including typical artifacts. In extensive benchmarking experiments, we demonstrate the utility of our synthetic data by successfully training retinal vessel segmentation algorithms. Encouraged by our method's competitive quantitative and superior qualitative performance, we believe that it constitutes a versatile tool to advance the quantitative analysis of OCTA images.

SoK: Differential Privacy on Graph-Structured Data

In this work, we study the applications of differential privacy (DP) in the context of graph-structured data. We discuss the formulations of DP applicable to the publication of graphs and their associated statistics as well as machine learning on graph-based data, including graph neural networks (GNNs). The formulation of DP in the context of graph-structured data is difficult, as individual data points are interconnected (often non-linearly or sparsely). This connectivity complicates the computation of individual privacy loss in differentially private learning. The problem is exacerbated by an absence of a single, well-established formulation of DP in graph settings. This issue extends to the domain of GNNs, rendering private machine learning on graph-structured data a challenging task. A lack of prior systematisation work motivated us to study graph-based learning from a privacy perspective. In this work, we systematise different formulations of DP on graphs, discuss challenges and promising applications, including the GNN domain. We compare and separate works into graph analysis tasks and graph learning tasks with GNNs. Finally, we conclude our work with a discussion of open questions and potential directions for further research in this area.