Sheet7ipSolution - Tanta university Faculty of engineering Computer and automatic control department Image processing course Fourth year students Sheet

Sheet7ipSolution - Tanta university Faculty of engineering...

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Tanta university Faculty of engineering Computer and automatic control department Image processing course Fourth year students Sheet 7, Date : 23/11/2011 ------------------------------------------------------------------------------------------------------------------------------------------- --------------------------------------------------------------------------------------------------------------------------------------- Instructor: Dr. Hamed Hemeda Sheet 7 solution (histogram equalization) 1. (a) The integration ( ) in the right hand side of the mapping is the cumulative distribution function (CDF) of the random variable R. Any CDF has the properties that it’s always monotonically increasing function, the minimum value of the integration is zero and the maximum value of the integration is 1. Using a monotonically increasing function in image intensity mapping is desirable since it avoids getting artifacts in the produced image. Since the minimum and maximum values of the integration are 0 and 1, respectively, the minimum and maximum values for the mapped intensity values are zero and (L-1), respectively. This is again a desirable property of the mapping where it produces an image in the same range of intensities as in the input image. Hence, no scaling is required after the mapping. (b) The application in which this mapping is used is histogram equalization. An image with arbitrary histogram is given ( ) is given. We apply the mapping on the intensity values of the input image to produce and image that has ( ) given by ( ) ( ) | | ( ) | | ( ) | ( ) ( ) | ( ) It’s clear that the resulting normalized histogram (PDF) is not a function in s. Hence, it has the
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  • Fall '15
  • Hamed Hemeda
  • Image processing, Pixel, Cumulative distribution function, Monotonic function, Handedness

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