Maps and Distances between Spaces - Mathematical Tools for Shape Analysis and Description - page 47

Figure 6.4: Casting the correspondence problem between two surfaces as the Möbius transformation
between unit spheres.
1. Samples three points from each mesh; this is done by selecting the local maxima of Gauss
curvature then adding the (geodesics) farthest points;
2. Computes the Möbius transformation that aligns the three point pairs;
3. Transforms all (sampled) points from both meshes by that Möbius transformation;
4. Evaluates the intrinsic deformation error between mapped points (deviation from isome-
try);
5. Produces “votes” for predicted correspondences between the mutually closest points with
magnitude representing their estimated deviation from isometry.
e computed deformation errors are accumulated in a fuzzy correspondence matrix, which can
be analyzed to determine a consistent set of discrete correspondences through a voting strategy.
Figure 6.5: Pipeline of the shape correspondence algorithm [ 128 ].
e algorithm works in polynomial time and is (theoretically, in the smooth case) guar-
anteed to find the optimal set of correspondences for perfect isometries and extends well to near