(a) Suppose that the intensities of an image f(x, y)are in the range [0,1] and that a threshold, T, successfully segmented the image into objects and background. Show that the threshold T = 1 − T will successfully segment the negative of f(x, y)into the same regions. The term negative is used here in the sense defined in Section 3.2.1.
(b) The intensity transformation function in (a) that maps an image into its negative is a linear function with negative slope. State the conditions that an arbitrary intensity transformation function must satisfy for the segmentability of the original image with respect to a threshold, T, to be preserved. What would be the value of the threshold after the intensity transformation?
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