Adaptive Sampling via Histogram Equalization using an Active Walker Model

We propose a novel, progressive, adaptive sampling method, that efficiently varies the sampling rate in local regions of a function based on the distribution of already collected samples. We show that for many functions, increasing the sampling rate in a region of a function with relatively higher complexity is achieved by the equalization of the histogram of the sampled function values. The sampling scheme thus achieves two purposes that are shown to be equivalent; efficiently adapted sampling rates based on local function complexity, and an improvement in diversity in the sampled function values. We achieve the sampling, progressively, through an active walker model. The sample points are placed based on the location of simulated active walkers whose movement is adapted at each stage to achieve the required histogram equalization. The only requirement by this algorithm is the ability to obtain the value of the function at each sample point; no a priori information on the relative levels of local variation of the function being sampled is required. We illustrate this concept with some examples, and discuss practical applications in the two broad areas of adaptive sampling, and improving diversity in samples