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# CMPS 3120: Computational Geometry Spring 2013 - PowerPoint PPT Presentation

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 GeometrySpring 2013

A

B

d(B,A)

Shape Matching II

CMPS 3120 Computational Geometry

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)

TÎT

CMPS 3120 Computational Geometry

• 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

• 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

• W(m2n2) lower bound construction for directed Hausdorff distance of line segments under translations

CMPS 3120 Computational Geometry