A. Ion, Y. Haxhimusa, W. Kropatsch:

"Skewed Coordinate System for Dense Point Correspondences Inside Articulated Shapes";

Report for PRIP-TR-126; Report No. PRIP-TR-126, 2011; 31 pages.

This report considers using a non-rigid coordinate system to find corresponding points in

different poses of the same articulated 2D shape. The shape-centered coordinate system

is mapped on top of the eccentricity transform of the shape, which uses maximal geodesic

distances and is bounded under articulation. The isolines of the eccentricity transform

are used as one of the coordinates, the radial-like, and the other one, the angular-like, is

stretched to compensate for changes in the widths of parts. The polar-like coordinate system

is first computed on inter-pixel isolines and then mapped to the pixels. The angular-like

coordinates are aligned using the 1D signals of the eccentricity values along the boundaries

of the two shapes. Correspondences between points are established by minimizing the

difference of their coordinates. Detecting failed correspondences is done using an adaptive

threshold which adjusts to the changing local variation of the coordinates. Experimental

results are shown on a set of hand poses, ranging from minor movement to touching or

missing fingers.

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