Geometric Transformations CSE P 576 Larry Zitnick ([email protected])

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Geometric Transformations CSE P 576 Larry Zitnick ([email protected])

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Transcript of Geometric Transformations CSE P 576 Larry Zitnick ([email protected])

Page 1: Geometric Transformations CSE P 576 Larry Zitnick (larryz@microsoft.com)

Geometric Transformations

CSE P 576Larry Zitnick ([email protected])

Page 2: Geometric Transformations CSE P 576 Larry Zitnick (larryz@microsoft.com)

What are geometric transformations?

Page 3: Geometric Transformations CSE P 576 Larry Zitnick (larryz@microsoft.com)

Translation

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Translation and rotation

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Scale

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Similarity transformations

Similarity transform (4 DoF) = translation + rotation + scale

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Aspect ratio

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Shear

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Affine transformations

Affine transform (6 DoF) = translation + rotation + scale + aspect ratio + shear

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What is missing?

Are there any other planar transformations?

Canaletto

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General affine

We already used these

How do we compute projective transformations?

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Homogeneous coordinates

One extra step:

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Projective transformationsa.k.a. Homographies

“keystone” distortions

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Finding the transformation

How can we find the transformation between these images?

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Finding the transformation

Translation = 2 degrees of freedomSimilarity = 4 degrees of freedomAffine = 6 degrees of freedomHomography = 8 degrees of freedom

How many corresponding points do we need to solve?


Windows XP SP2 Point de vue du développeur Gilles Guimard (gillesg@microsoft.com) gillesg@microsoft.com Jean Gautier (jeanga@microsoft.com ) jeanga@microsoft.com.

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CIDEr: Consensus-based Image Description … Consensus-based Image Description Evaluation Ramakrishna Vedantam Virginia Tech [email protected] C. Lawrence Zitnick Microsoft Research [email protected]

Geometric Transformations CSE 455 Ali Farhadi Many slides from Steve Seitz and Larry Zitnick.

Geometric Transformations CSE 455 Ali Farhadi Many slides from Steve Seitz and Larry Zitnick.

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Viren, Würmer, SP2 Uwe Baumann Dirk Primbs.NET Community Evangelists Microsoft Deutschland GmbH [email protected] [email protected] [email protected].