Skewed Coordinate System for Dense Point Correspondences Inside Articulated Shapes

This report considers using a non-rigid coordinate system to find corresponding points indifferent poses of the same articulated 2D shape. The shape-centered coordinate systemis mapped on top of the eccentricity transform of the shape, which uses maximal geodesicdistances and is bounded under articulation. The isolines of the eccentricity transformare used as one of the coordinates, the radial-like, and the other one, the angular-like, isstretched to compensate for changes in the widths of parts. The polar-like coordinate systemis first computed on inter-pixel isolines and then mapped to the pixels. The angular-likecoordinates are aligned using the 1D signals of the eccentricity values along the boundariesof the two shapes. Correspondences between points are established by minimizing thedifference of their coordinates. Detecting failed correspondences is done using an adaptivethreshold which adjusts to the changing local variation of the coordinates. Experimentalresults are shown on a set of hand poses, ranging from minor movement to touching ormissing fingers.