Curve Extraction by Geodesics Fusion: Application to Polymer Reptation Analysis

Abstract : In the molecular field, researchers analyze dynamics of polymers by microscopy: several measurements such as length and curvature are performed in their studies. To achieve correct analysis they need to extract the curve representing as good as possible the observed polymer shape which is a grayscale thick curve with noise and blur. We propose, in this paper, a method to extract such a curve. A polymer chain moves in a snake-like fashion (Reptation): it can self-intersect and form several complex geometries. To efficiently extract the different geometries, we generate the curve by computing a piecewise centerline browsing the shape by geodesics: each shape gives a set of separate geodesics. By fusion, we obtain the complete curve traveling the shape. To keep the correct curve orientation, the fusion is considered as a graph traversal problem. Promising results show that the extracted curve properly represents the shape and can be used for polymer study.