Patent ID: 8280150
Filing Date: 2012-10-02
Classification: G06K

Abstract:
1. A method of determining similarity between a non-planar probe surface represented by a probe point-cloud and a non-planar model surface represented by a model point-cloud, the surfaces representing physical objects, the method comprising: calculating a matrix of geodesic distances characterizing said non-planar model surface represented by said model point-cloud; embedding said probe surface into an embedding space having a non-constant sectional curvature, wherein said embedding space is a polyhedral approximation of the model surface; defining an objective function based on said embedding space adapted to map either said probe surface onto said model surface or said model surface onto said probe surface; and wherein said objective function is selected so as to allow calculation of at least one of: a partial embedding distance between the probe surface and the model surface; and a Gromov-Hausdorff distance between the probe surface and the model surface; calculating an extremal value of said objective function by an iterative process, said iterative process comprising starting with a plurality of initial values of the optimization variables of the objective function, and iteratively updating the locations on said model surface so as to produce a decreasing sequence of function values; wherein said iterative process is selected from the group consisting of the steepest descent method, the fixed step gradient method, the conjugate gradient method, the Newton method, coordinate-wise descent and any combination thereof; and determining similarity between the probe surface and the model surface based on said extremal value.