Coarse - fine histograms bimodality analysis of circular
نویسندگان
چکیده
The bimodality of a population P can be measured by dividing its range into two intervals so as to maximize the Fisher distance between the resulting two subpopulations P1 and P2. If P is a mixture of two (approximately) Gaussian subpopulations, then P1 and P2 are good approximations to the original Gaussians, if their Fisher distance if great enough. For a histogram having n bins this method of bimodality analysis requires n-1 Fisher distance computations, since the range can be divided into two intervals in n-I ways. The method can also be applied to 'circular' histograms, e.g. of populations of slope or hue values; but for such histograms it is much more computationaly costly, since a circular histogram having n bins can be divided into two intervals (arcs) in n(n-1)/2 ways. The cost can be reduced by performing bimodality analysis on a 'reduced-resolution' histogram having n/k bins; finding the subdivision of this histogram that maximizes the Fisher distance; and then finding a maximum Fisher distance subdivision of the full-resolution histogram in the neighborhood of this subdivision. This reduces the required number of Fisher distance computations to n(n-1)/2k 2 + O(k). For histograms representing mixtures of two Gaussians, this method was found to work well for n/k as small as 8.
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تاریخ انتشار 1989