Dynamic Exploration on Segment-Proposal Graphs for Tubular Centerline Tracking

TL;DR

This paper tackles tubular centerline tracking by addressing the deficiencies of both point-wise and static segment-wise methods, notably shortcut risk and the need for a complete pre-built graph. It introduces DSG-RL, a reinforcement learning framework that constructs and weights a segment-based graph on demand, using Q-Learning to find an optimal path through dynamically discovered edges in an orientation-lifted space with curvature-aware geodesics. Key innovations include adaptive action-space exploration, lazy edge evaluation, and a reconstruction step that glues segment endpoints with inter-segment geodesics under a $\mathcal{F}$-based metric, yielding coherent centerlines. Empirical results on retinal vessels, roads, and rivers show that DSG-RL improves accuracy while reducing computational costs compared to both point-wise and segment-wise baselines, demonstrating strong practical impact for diverse tubular-structure analysis tasks. The approach offers a scalable, topology-robust paradigm for automatic tubular tracking without heavy reliance on prior full-graph knowledge.

Abstract

Optimal curve methods provide a fundamental framework for tubular centerline tracking. Point-wise approaches, such as minimal paths, are theoretically elegant but often suffer from shortcut and short-branch combination problems in complex scenarios. Nonlocal segment-wise methods address these issues by mapping pre-extracted centerline fragments onto a segment-proposal graph, performing optimization in this abstract space, and recovering the target tubular centerline from the resulting optimal path. In this paradigm, graph construction is critical, as it directly determines the quality of the final result. However, existing segment-wise methods construct graphs in a static manner, requiring all edges and their weights to be pre-computed, i.e. the graph must be sufficiently complete prior to search. Otherwise, the true path may be absent from the candidate space, leading to search failure. To address this limitation, we propose a dynamic exploration scheme for constructing segment-proposal graphs, where the graph is built on demand during the search for optimal paths. By formulating the problem as a Markov decision process, we apply Q-learning to compute edge weights only for visited transitions and adaptively expand the action space when connectivity is insufficient. Experimental results on retinal vessels, roads, and rivers demonstrate consistent improvements over state-of-the-art methods in both accuracy and efficiency.

Figures (8)

• Figure 1: Demonstration of the proposed method on a retinal image and comparison with other approaches. (a) Input image with start (green) and end (yellow) points. (b) Generated disjoint centerline segments. (c) The initial graph that traditional segment-wise methods must construct, requiring all edge weights to be computed. (d) Our method dynamically explores a much smaller subgraph, saving significant computational cost. (e) and (f) Point-wise methods (anisotropic and curvature-penalized, respectively) struggle to navigate through high-contrast regions. (g) Existing segment-wise methods fail when the initial graph is incomplete and does not contain a path from source to destination. (h) Our proposed method successfully finds the correct minimal path by adaptively exploring the graph.
• Figure 2: The framework of the proposed DSG-RL model.
• Figure 3: Visualization of the generation of a set of disjoint segments. (a) An image that contains complex tubular structures. (b) Visualization of the vesselness map that indicates the probability that a point belongs to a tubular structure. (c) The skeleton structure of the tubular structures. (d) Visualization of the generated disjoint segments where all the junction points in the skeleton map are removed.
• Figure 4: Illustration of the graph representation derived from disjoint segments. (a) Nodes corresponding to disjoint segments, colored for identification. (b) Associated graph structure with a short extension length ($\ell=1$). (c) A more densely connected graph resulting from a larger extension length ($\ell=10$). (d) The weighted graph for the $\ell=10$ case, where edge widths are proportional to their weights.
• Figure 5: The minimal path tracking process via Q-Learning. The process starts with an initial graph that may not connect the source ($v_{is}$) and destination ($v_{it}$) nodes (top). The agent then learns through episodes (middle), where it iteratively: (1) generates a dynamic action space, (2) selects an action, (3) evaluates the new edge on-demand, (4) calculates a reward, (5) updates the Q-table, and (6) transitions to a new state. This allows the agent to expand its knowledge of the graph and ultimately extract the optimal path (bottom).