I am on the search for a universal distance metric for comparison of two histograms. Consider the two figures below. Each of the figures contains a desired distribution (blue line) and a measured distribution (organge line). I want to compute a distance/similarity measure between the actual and the desired histograms which is independent from the actual outlook of the distribution. This means the measure should give me the same result for both cases shown in the figures. Reason for this is, I want to compare arbitrary patterns within a binary picture for automatic quality control. So I need to define a threshold for the distance measure, which is somehow independet of the outlook of the pattern, so no adjustment is neccessary when the pattern changes.
I tried the following measures:
- Bhattacharyya distance
- Hellinger distance
- Chi-square distance (not working, because of zero bins)
- Wasserstein metric (Earth Move Distance)
- Different vector norms (L1, L2, Inf)
All of them have the problem of giving similarity results, which are dependent on the actual outlook of the distribution (pattern). But instead I need to somehow normalize these measures to give constant values for the same amount of "fit" between patterns, regardless of the actual pattern outlook.