  We propose a novel tree-like curvilinear structure reconstruction algorithm
based on supervised learning and graph theory. In this work we analyze image
patches to obtain the local major orientations and the rankings that correspond
to the curvilinear structure. To extract local curvilinear features, we compute
oriented gradient information using steerable filters. We then employ
Structured Support Vector Machine for ordinal regression of the input image
patches, where the ordering is determined by shape similarity to latent
curvilinear structure. Finally, we progressively reconstruct the curvilinear
structure by looking for geodesic paths connecting remote vertices in the graph
built on the structured output rankings. Experimental results show that the
proposed algorithm faithfully provides topological features of the curvilinear
structures using minimal pixels for various datasets.
