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For the transformation T(r) = [∫0^r pr(w) dw], r is gray value of input image, pr(r) is PDF of random variable r and w is a dummy variable. If, the PDF are always positive and that the function under integral gives the area under the function, the transformation is said to be __________

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For the transformation T(r) = [∫0^r pr(w) dw], r is gray value of input image, pr(r) is PDF of random variable r and w is a dummy variable. If, the PDF are always positive and that the function under integral gives the area under the function, the transformation is said to be __________

(a) Single valued

(b) Monotonically increasing

(c) All of the mentioned

(d) None of the mentioned

I have been asked this question in a national level competition.

I would like to ask this question from Histogram Equalization and Processing topic in division Image Enhancement of Digital Image Processing

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The correct answer is (c) All of the mentioned

Best explanation: For the given transformation, the PDF being positive and the integral providing area under the function, the transformation function is single valued as well as monotonically increasing.

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