4/23/13CMPS 3120 Computational Geometry1 CMPS 3120: Computational Geometry Spring 2013 Shape Matching II A B   (B,A)

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Presentation transcript:

4/23/13CMPS 3120 Computational Geometry1 CMPS 3120: Computational Geometry Spring 2013 Shape Matching II A B   (B,A)

Two geometric shapes, each composed of a number of basic objects such as Given: An application dependant distance measure , e.g., the Hausdorff distance A set of transformations T, e.g., translations, rigid motions, or none Matching Task: Compute min  (T(A),B)  pointsline segmentstriangles Geometric Shape Matching 4/23/13CMPS 3120 Computational Geometry2

Hausdorff distance Directed Hausdorff distance   (A,B) = max min || a-b || Undirected Hausdorff-distance  (A,B) = max (   (A,B),   (B,A) ) If A, B are discrete point sets, |A|=m, |A|=n In d dimensions: Compute in O(mn) time brute-force In 2 dimensions: Compute in O((m+n) log (m+n) time Compute   (A,B) by computing VD(B) and performing nearest neighbor search for every point in A A B   (B,A)   (A,B) a  A b  B 4/23/13CMPS 3120 Computational Geometry3

Shape Matching - Applications Character Recognition Fingerprint Identification Molecule Docking, Drug Design Image Interpretation and Segmentation Quality Control of Workpieces Robotics Pose Determination of Satellites Puzzling... 4/23/13CMPS 3120 Computational Geometry4

Hausdorff distance  (m 2 n 2 ) lower bound construction for directed Hausdorff distance of line segments under translations 4/23/13CMPS 3120 Computational Geometry5