16_geometric_transformx

# 16_geometric_transformx - Geometric Transformations COMP344...

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Geometric Transformations COMP344 COMP344 Geometric Transformations

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Geometric Transformations Also called rubber-sheet transformations Useful for image distortion correction Example X-ray image distortion distorted image g ( x 0 , y 0 ) corrected image f ( x , y ) COMP344 Geometric Transformations
Spatial Transformations f ( x , y ): original image, g ( x 0 , y 0 ): distorted image Spatial transformation function models the distortion between original and distorted images x 0 = r ( x , y ) , y 0 = s ( x , y ) COMP344 Geometric Transformations

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Translation of an Image x 0 = x - x 0 0 y 0 = y - y 0 0 COMP344 Geometric Transformations
Scaling of an Image x 0 = x · s x , y 0 = y · s y Example x 0 = x / 2 , y 0 = y / 2 shrinks the size of f ( x , y ) by one half in both spatial directions 0 < | s | < 1: contraction | s | > 1: dilation s < 0: opposite direction COMP344 Geometric Transformations

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Rotation of an Image Rotation around the origin x 0 = x cos( α ) + y sin( α ) , y 0 = - x sin( α ) + y cos( α ) COMP344 Geometric Transformations
Rotation of an Image. .. Rotation around the point (

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## This note was uploaded on 09/24/2010 for the course COMP 344 taught by Professor Albertk.wong during the Fall '09 term at HKUST.

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16_geometric_transformx - Geometric Transformations COMP344...

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