Lecture5IP - Lecture 5 Mathematical tools for image processing continued Spatial versus transform operations Spatial operations are performed in spatial

Lecture5IP - Lecture 5 Mathematical tools for image...

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Lecture 5 Mathematical tools for image processing, continued
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Spatial versus transform operations Spatial operations are performed in spatial domain Image is represented as f(x,y) X=0,1,2,…,M Y=0,1,2,…,N Single pixel based operations, neighborhood operations, geometric transformation Transform operation Image is transformed to other domain g(u,v) Operations are performed in the other domain Transformed operated image is inverse-transformed to the spatial domain
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Single pixel spatial operations Intensity mapping s=T(z) z: input image intensity s : Output image intensity T : the operation Example: getting the negative of 8 bit image T(z)= 2 8 -z
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Neighborhood spatial operations The value of the pixel at x,y in the output image is calculated from a set of neighbor pixels centered at x,y in the input image Example, the calculated value = the average of the neighbors rectangle of dimensions M by N centered at the pixel S set neighbor MxN in the index column and row are c r, ) , ( 1 ) , ( , ) , ( y x S c r c r f MN y x g
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Geometric spatial transformation Geometric transformation is the mapping of the coordinates of each pixel in an input image to another (displaced/rotated,..) pixel in the output image. Intensity interpolation is used to assign intensities for the relocated pixels in processed image Forward mapping: for each pixel in the input image, find its location in the output image and assign its value Multiple output values are assigned to the same output pixel Some output locations may not assigned values Inverse mapping: for each pixel in the output image, find the location in the input image by applying the inverse transform, use the interpolation to calculate intensity value based on the intensities in the input image location ed concatenat be can tion tranforma Affine matrix tion transorma the is T 1 0 0 1 , , 1 , , 1 , , tion
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