Abstract : To detect curvilinear structures in natural images, we propose a novel ranking
learning system and an abstract curvilinear shape inference algorithm based on graph theory. We
analyze the curvilinear structures as a set of small line segments. In this work, the rankings of
the line segments are exploited to systematize the topological feature of the curvilinear structures.
Structured Support Vector Machine is employed to learn the ranking function that predicts the
correspondence of the given line segments and the latent curvilinear structures. We first extract
curvilinear features using morphological profiles and steerable filtering responses. Also, we propose
an orientation-aware feature descriptor and a feature grouping operator to improve the structural
integrity during the learning process. To infer the curvilinear structure, we build a graph based on
the output rankings of the line segments. We progressively reconstruct the curvilinear structure
by looking for paths between remote vertices in the graph. Experimental results show that the
proposed algorithm faithfully detects the curvilinear structures within various datasets.