CS 450: Level operations - Part 2 presents the effect of level operations on histograms; histograms equantization; adaptive histograms equantization; histograms specification and something else.
CS 450 Level Operations - Part The Effect of Level Operations on Histograms Suppose that we have a monotonic level operation such that f (a) = a f (b) = b Then the histogram H becomes H such that b b H(D) dD = a H (D) dD a CS 450 Level Operations - Part 2 The Effect of Level Operations on Histograms (cont’d) Suppose that we let b = a + ∆ for some very small ∆ Then f (b) ≈ f (a) + f (a)∆ Thus a +f (a)∆ a+∆ H(D) dD ≈ a H (D) dD a or approximating: ≈ H (a ) (f (a)∆) H(a)∆ H (a ) ≈ f (a)∆ H(a) = f (a) H(a)∆ H (D) = H(f −1 (D)) f (f −1 (D)) CS 450 Level Operations - Part Histogram Equalization Sometimes we may want to constrast enhancement automatically Basic idea: choose to allocate the most output levels to the sections of the input range that occur most frequently Look at the histogram of the input signal If we properly allocate our output levels proportional to the frequency of occurrence for our input levels, the histogram of the output should be uniform This process is known as histogram equalization CS 450 Level Operations - Part Histogram Equalization b f (b) = Dmax p(x) dx where • b is the input level • f (b) is the corresponding output level • p is the probability density function (normalized histogram) of the input signal CS 450 Level Operations - Part Adaptive Histogram Equalization Remap based on local, not global histogram Allows localized contrast enhancement Example: × window around the point Problem: ringing artifacts (Partial) solutions: constrain the remapping CS 450 Level Operations - Part Histogram Specification Histogram equalization makes the output histogram uniform We can instead make it whatever we want it to be Use histogram equalization as an intermediate step First, equalize the histogram of the input signal: b f1 (b) = Dmax p1 (x) dx Then histogram equalize the desired output histogram: b f2 (b) = Dmax p2 (x) dx Histogram specification is f (b) = f2−1 (f1 (b)) .. .CS 450 Level Operations - Part 2 The Effect of Level Operations on Histograms (cont’d) Suppose that we let b = a + ∆ for some... (D)) f (f −1 (D)) CS 450 Level Operations - Part Histogram Equalization Sometimes we may want to constrast enhancement automatically Basic idea: choose to allocate the most output levels to the sections... Example: × window around the point Problem: ringing artifacts (Partial) solutions: constrain the remapping CS 450 Level Operations - Part Histogram Specification Histogram equalization makes the