Topograph: An efficient Graph-Based Framework for Strictly Topology Preserving Image Segmentation

Topological correctness plays a critical role in many image segmentation tasks, yet most networks are trained using pixel-wise loss functions, such as Dice, neglecting topological accuracy. Existing topology-aware methods often lack robust topological guarantees, are limited to specific use cases, or impose high computational costs. In this work, we propose a novel, graph-based framework for topologically accurate image segmentation that is both computationally efficient and generally applicable. Our method constructs a component graph that fully encodes the topological information of both the prediction and ground truth, allowing us to efficiently identify topologically critical regions and aggregate a loss based on local neighborhood information. Furthermore, we introduce a strict topological metric capturing the homotopy equivalence between the union and intersection of prediction-label pairs. We formally prove the topological guarantees of our approach and empirically validate its effectiveness on binary and multi-class datasets. Our loss demonstrates state-of-the-art performance with up to fivefold faster loss computation compared to persistent homology methods.

Topologically faithful multi-class segmentation in medical images

Topological accuracy in medical image segmentation is a highly important property for downstream applications such as network analysis and flow modeling in vessels or cell counting. Recently, significant methodological advancements have brought well-founded concepts from algebraic topology to binary segmentation. However, these approaches have been underexplored in multi-class segmentation scenarios, where topological errors are common. We propose a general loss function for topologically faithful multi-class segmentation extending the recent Betti matching concept, which is based on induced matchings of persistence barcodes. We project the N-class segmentation problem to N single-class segmentation tasks, which allows us to use 1-parameter persistent homology making training of neural networks computationally feasible. We validate our method on a comprehensive set of four medical datasets with highly variant topological characteristics. Our loss formulation significantly enhances topological correctness in cardiac, cell, artery-vein, and Circle of Willis segmentation.

Cross-domain and Cross-dimension Learning for Image-to-Graph Transformers

Direct image-to-graph transformation is a challenging task that solves object detection and relationship prediction in a single model. Due to the complexity of this task, large training datasets are rare in many domains, which makes the training of large networks challenging. This data sparsity necessitates the establishment of pre-training strategies akin to the state-of-the-art in computer vision. In this work, we introduce a set of methods enabling cross-domain and cross-dimension transfer learning for image-to-graph transformers. We propose (1) a regularized edge sampling loss for sampling the optimal number of object relationships (edges) across domains, (2) a domain adaptation framework for image-to-graph transformers that aligns features from different domains, and (3) a simple projection function that allows us to pretrain 3D transformers on 2D input data. We demonstrate our method's utility in cross-domain and cross-dimension experiments, where we pretrain our models on 2D satellite images before applying them to vastly different target domains in 2D and 3D. Our method consistently outperforms a series of baselines on challenging benchmarks, such as retinal or whole-brain vessel graph extraction.