Enhancing Boundary Segmentation for Topological Accuracy with Skeleton-based Methods

TL;DR

The paper tackles topology-driven errors in boundary segmentation of reticular images by introducing the Skea-Topo Aware loss, a two-component framework combining Skeleton Aware Weighted loss (Skeaw) and Boundary Rectified Term (BoRT). Skeaw leverages object skeletons to produce geometry- and topology-aware weights, while BoRT rapidly identifies topology-critical pixels and applies a rectified penalty, with the total objective $L_{total} = L_{skeaw} + \lambda L_{bort_topo}$. The approach demonstrates consistent improvements across three diverse datasets (neural EM, material grains, and aerial roads), achieving up to a 7-point reduction in Variation of Information and showing robustness in both quantitative metrics and qualitative segmentation quality. The work also shows BoRT’s plug-in versatility, efficiency, and potential for extension to multi-class and 3D settings, underscoring its practical impact for topology-sensitive downstream analyses.

Abstract

Topological consistency plays a crucial role in the task of boundary segmentation for reticular images, such as cell membrane segmentation in neuron electron microscopic images, grain boundary segmentation in material microscopic images and road segmentation in aerial images. In these fields, topological changes in segmentation results have a serious impact on the downstream tasks, which can even exceed the misalignment of the boundary itself. To enhance the topology accuracy in segmentation results, we propose the Skea-Topo Aware loss, which is a novel loss function that takes into account the shape of each object and topological significance of the pixels. It consists of two components. First, a skeleton-aware weighted loss improves the segmentation accuracy by better modeling the object geometry with skeletons. Second, a boundary rectified term effectively identifies and emphasizes topological critical pixels in the prediction errors using both foreground and background skeletons in the ground truth and predictions. Experiments prove that our method improves topological consistency by up to 7 points in VI compared to 13 state-of-art methods, based on objective and subjective assessments across three different boundary segmentation datasets. The code is available at https://github.com/clovermini/Skea_topo.

Figures (6)

• Figure 1: Examples of four types of errors that cause topological changes in boundary segmentation results: Incorrect Closure, Object Disappearance, Incorrect Fracture, and Object Appearance. (a) Foreground and background weighted maps calculated by Skeaw. The background weight accurately models the geometric features of each object. (b) Illustration of the topological critical pixels identified by BoRT. UNet Prediction is the prediction result of the UNet model trained with the cross-entropy loss. The blue areas represent the discrepancies between prediction and ground truth, which signify errors. The red areas highlight the topological critical pixels, which constitute only a small portion of these errors.
• Figure 2: (a) Illustration of the proposed Skea-Topo Aware Loss. (b) Flowchart of the process to calculate topological false negatives. Our method utilizes both foreground and background skeletons from the ground truth and predicted results, which complement each other to precisely identify the critical pixels. (c) Results of Skeleton-Based Weighting versus Traditional Distance-Based Weighting and calculations for $d^1(x)$, $d^2(x)$, $d^{nsp}(x)$ and $\widetilde{d}_0^{nsp}(x)$. Compared to traditional weighted methods, the skeleton-based approach assigns higher weights to the narrow regions in irregular objects.
• Figure 3: Qualitative results of different losses on the SNEMI3D dataset. The red arrows and blue rectangles indicate topological false positive and false negative errors, respectively.
• Figure 4: Qualitative results of different losses on the IRON dataset.
• Figure 5: Qualitative results of different losses on the MASS. ROAD dataset.