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CMPS 3120: Computational Geometry Spring 2013

CMPS 3120: Computational Geometry Spring 2013. A. B. d  (B,A). Shape Matching II. Geometric Shape Matching. Given:. Two geometric shapes , each composed of a number of basic objects such as. points. line segments. triangles.

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CMPS 3120: Computational Geometry Spring 2013

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  1. CMPS 3120: Computational GeometrySpring 2013 A B d(B,A) Shape Matching II CMPS 3120 Computational Geometry

  2. Geometric Shape Matching Given: Twogeometric shapes, each composed of a number of basic objects such as points line segments triangles An application dependantdistance measured, e.g., the Hausdorff distance A set of transformations T, e.g., translations, rigid motions, or none min d(T(A),B) Matching Task: Compute TÎT CMPS 3120 Computational Geometry

  3. Hausdorff distance • Directed Hausdorff distance d(A,B) = max min || a-b || • Undirected Hausdorff-distance d(A,B) = max (d(A,B) , d(B,A) ) A B a A bB d(B,A) d(A,B) • 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 d(A,B) by computing VD(B) and performing nearest neighbor search for every point in A CMPS 3120 Computational Geometry

  4. 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 • . . . CMPS 3120 Computational Geometry

  5. Hausdorff distance • W(m2n2) lower bound construction for directed Hausdorff distance of line segments under translations CMPS 3120 Computational Geometry

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