Lecture4IP - Lecture 4 Digital image fundamentals Mathematical tools(array and matrix operations linear and nonlinear operations arithmetic operation

Lecture4IP - Lecture 4 Digital image fundamentals...

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Lecture 4 Digital image fundamentals: Mathematical tools (array and matrix operations, linear and nonlinear operations, arithmetic operation, sets and logic operation)
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Mathematic operations on images Array or matrix operations? Array operation (default) : each pixel is operated with its corresponding pixel in the second image Matrix operation (if stated): standard matrix operations Linear and nonlinear operations An operation is linear if homogeneity and additively are applicable An operation is nonlinear if it’s not linear ) (additvety , ( ) , ( ) , ( ) , ( and ty), (homogenei ) , ( ) , ( applicable are conditions two followinh the if linear is H y) g(x, image the produce to y) f(x, image an on H operation an Consider y x f H a y x f H a y x f a y x f a H y x f aH y x af H j j i i j j i i
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Linear and nonlinear operation: examples The sum of all pixel values in an image The maximum pixel value in an image linear is operation Sum the Hence ) , ( ) , ( ) , ( ) , ( ) , ( ) , ( y x f a y x f a y x f a y x f a y x f a y x f a j j i i j j i i j j i i nonlinear is operation the general in Hence, -4 7 - 3 7 4 5 6 ) 1 ( 3 2 2 0 ) 1 ( while 2 4 2 3 6 7 4 5 6 ) 1 ( 3 2 2 0 ) 1 ( Max Max Max Max
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