1007_match-1.pdf - ECE4445 MBP4445 ECE9201 ECE9021 BME9509 MBP9509 Page 1 ECE4445 MBP4445 ECE9201 ECE9021 BME9509 MBP9509 INTRODUCTION TO DIGITAL IMAGE

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ECE4445 / MBP4445 / ECE9201 / ECE9021 / BME9509 / MBP9509 - Page 1 ECE4445 / MBP4445 / ECE9201 / ECE9021 / BME9509 / MBP9509 INTRODUCTION TO DIGITAL IMAGE PROCESSING Lecture Notes: Histogram Matching (Specification) DERIVATION OF EQUATION FOR HISTOGRAM MATCHING Given Information (1) Input image A ( x , y ) from which we can compute its histogram H A ( D A ). (2) Desired output histogram, H C ( D C ). Goal Derive a point operation, ( ) D f D C A = , that maps the input image into an output image, C ( x , y ) that has the user-specified histogram, H C ( D C ). Approach Define the following: an intermediate image B ( x , y ) with a flat histogram, H B ( D B ) (see figure in slides). the GST ( ) D f D B A = 1 that transforms image A ( x , y ) into image B ( x , y ) the GST ( ) D f D B C = 2 that transforms image C ( x , y ) into image B ( x , y ) Derivation The transformation ( ) D f D B A = 1 that equalizes image A ( x , y ) to produce image B ( x , y ) is given by: (1) where P A ( D A ) is the cumulative distribution function (CDF) of image A ( x , y ). The transformation ( ) D f D B C = 2 that equalizes image C ( x , y ) to produce image B ( x , y ) is given by: (2)

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