Cmps 3120 computational geometry spring 2013
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CMPS 3120: Computational Geometry Spring 2013. A. B. d  (B,A). Shape Matching. Translate. When are two shapes similar?. Are these shapes similar?. Translate & Rotate. Translate. When are two shapes similar?. Are these shapes similar?. Translate & Rotate. Translate. Translate & Scale.

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Cmps 3120 computational geometry spring 2013

CMPS 3120: Computational GeometrySpring 2013

A

B

d(B,A)

Shape Matching

CMPS 3120 Computational Geometry


Are these shapes similar

Translate

When are two shapes similar?

Are these shapes similar?


Are these shapes similar1

Translate & Rotate

Translate

When are two shapes similar?

Are these shapes similar?


Are these shapes similar2

Translate & Rotate

Translate

Translate & Scale

When are two shapes similar?

Are these shapes similar?


Are these shapes similar3

Translate & Rotate

Translate

Translate & Scale

Translate & Reflect

When are two shapes similar?

Are these shapes similar?


Are these shapes similar4

Translate & Rotate

Translate

Translate & Scale

Translate & Reflect

Partial Matching

When are two shapes similar?

Are these shapes similar?


Are these shapes similar5

Translate & Rotate

Translate

Translate & Scale

Translate & Reflect

Partial Matching

When are two shapes similar?

Are these shapes similar?


Cmps 3120 computational geometry spring 2013

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