GraphMorph: Tubular Structure Extraction by Morphing Predicted Graphs

TL;DR

GraphMorph reframes tubular structure extraction from pixel-level classification to explicit graph-based topology learning. A Graph Decoder predicts a graph $G=(V,E)$ for image ROIs and a Morph Module, via SkeletonDijkstra, morphs this graph into topologically accurate centerline masks; a post-processing step then refines segmentation by leveraging these centerlines. Training employs a Deformable DETR-inspired node prediction with dynamic adjacency and a combination of pixel, Hungarian, and adjacency losses, while inference assembles patch-level results into full-image centerlines. Across four datasets (medical and road) and multiple backbones, GraphMorph achieves notable improvements in topological metrics (e.g., $\beta_0$, $\beta_1$, $\chi$) and overall segmentation performance, demonstrating the value of branch-level features and graph-guided morphology for tubular structures.

Abstract

Accurately restoring topology is both challenging and crucial in tubular structure extraction tasks, such as blood vessel segmentation and road network extraction. Diverging from traditional approaches based on pixel-level classification, our proposed method, named GraphMorph, focuses on branch-level features of tubular structures to achieve more topologically accurate predictions. GraphMorph comprises two main components: a Graph Decoder and a Morph Module. Utilizing multi-scale features extracted from an image patch by the segmentation network, the Graph Decoder facilitates the learning of branch-level features and generates a graph that accurately represents the tubular structure in this patch. The Morph Module processes two primary inputs: the graph and the centerline probability map, provided by the Graph Decoder and the segmentation network, respectively. Employing a novel SkeletonDijkstra algorithm, the Morph Module produces a centerline mask that aligns with the predicted graph. Furthermore, we observe that employing centerline masks predicted by GraphMorph significantly reduces false positives in the segmentation task, which is achieved by a simple yet effective post-processing strategy. The efficacy of our method in the centerline extraction and segmentation tasks has been substantiated through experimental evaluations across various datasets. Source code will be released soon.

Figures (9)

• Figure 1: Illustrating the impact of topological feature utilization on segmentation accuracy. (a) An input neuron image. Column (b) Ground truth with segmented membranes (white) and its centerline (blue lines); the constructed graph (nodes in red, edges in green). Column (c) and (d) Predictions of two methods milletari2016vshit2021cldice without explicit topological learning, highlighting broken branches (false negatives in yellow), redundant branches (false positives in green), and topological errors (in red). Column (e) Our GraphMorph guarantees topological accuracy by learning explicit branch-level features. Details of skeletonization and graph construction are given in Appendix \ref{['ssec:graph_construction']}. Evaluation metrics: Dice and clDice (higher is better), $\beta_0$ error and $\chi$ error (lower is better).
• Figure 2: Overview of the training process. Given an image, the segmentation network outputs a probability map of the centerline or segmentation and produces multi-scale feature maps. Then, $R$ regions of interest (ROIs) are randomly sampled from the image, and their corresponding features are fed into the Graph Decoder, which predicts the nodes within these ROIs using a modified Deformable DETR and outputs the adjacency matrices utilizing the proposed link prediction module.
• Figure 3: Inference process of centerline extraction. First, the segmentation network generates a centerline probability map $P_m$ along with multi-scale image features. Subsequently, the Graph Decoder utilizes the image features to predict graphs $G$ via sliding window inference. Finally, the Morph Module employs $P_m$ to find the optimal path between each pair of connected nodes in $G$, resulting in a final centerline mask. This approach achieves higher topological accuracy compared to direct thresholding of $P_m$.
• Figure 4: Effect of ROI size $H$ on two tasks.
• Figure 4: Visual comparison for our GraphMorph with other methods (zoom for details). Areas indicated by yellow arrows show false negatives (FNs), areas pointed by green arrows demonstrate false positives (FPs), and regions highlighted by red arrows are topological errors (TEs) identifiable in other methods but are accurately resolved by our approach.