Problem

You may assume in both of the following cases that the threshold value during iteration is...

You may assume in both of the following cases that the threshold value during iteration is bounded in the open interval (0, L 1).

(a) Prove that if the histogram of an image is uniform over all possible intensity levels, the basic global thresholding algorithm in Section 10.3.2 converges to the average intensity of the image, (L 1)/2.


(b) Prove that if the histogram of an image is bimodal, with identical modes that are symmetric about their means, then the basic global algorithm will converge to the point halfway between the means of the modes.

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