Graph-based deformable matching of 3D line with application in protein fitting

We present an algorithm for matching two sets of line segments in 3D that have undergone non-rigid deformations. This problem is motivated by a biology application that seeks a correspondence between the alpha-helices from two proteins, so that matching helices have similar lengths and these can be aligned by some low-distortion deformation. While matching between two feature sets have been extensively studied, particularly for point features, matching line segments has received little attention so far. As typical in point-matching methods, we formulate a graph matching problem and solve it using continuous relaxation. We make two technical contributions. First, we propose a graph construction for undirected line segments such that the optimal matching between two graphs represents an as-rigid-as-possible deformation between the two sets of segments. Second, we propose a novel heuristic for discretizing the continuous solution in graph matching. Our heuristic can be applied to matching problems (such as ours) that are not amenable to certain heuristics, and it produces better solutions than those applicable heuristics. Our method is compared with a state-of-art method motivated by the same biological application and demonstrates improved accuracy.