A Graph-Theoretical Approach for Tracing Filamentary Structures in Neuronal and Retinal Images

The aim of this study is about tracing filamentary structures in both neuronal and retinal images. It is often crucial to identify single neurons in neuronal networks, or separate vessel tree structures in retinal blood vessel networks, in applications such as drug screening for neurological disorders or computer-aided diagnosis of diabetic retinopathy. Both tasks are challenging as the same bottleneck issue of filament crossovers is commonly encountered, which essentially hinders the ability of existing systems to conduct large-scale drug screening or practical clinical usage. To address the filament crossovers' problem, a two-step graph-theoretical approach is proposed in this paper. The first step focuses on segmenting filamentary pixels out of the background. This produces a filament segmentation map used as input for the second step, where they are further separated into disjointed filaments. Key to our approach is the idea that the problem can be reformulated as label propagation over directed graphs, such that the graph is to be partitioned into disjoint sub-graphs, or equivalently, each of the neurons (vessel trees) is separated from the rest of the neuronal (vessel) network. This enables us to make the interesting connection between the tracing problem and the digraph matrix-forest theorem in algebraic graph theory for the first time. Empirical experiments on neuronal and retinal image datasets demonstrate the superior performance of our approach over existing methods.