Selection of the right distances

Different measures presented above should be selected based on the nature of the problem at hand. In the case of texture boundary detection for tracking, usually we should resort to distances which are accurate even with small number of observations. For small sample sizes, parametric distances such as WMV or Fisher which have few number of parameters to estimate perform best. These distances only estimate means and variances and are less sensitive to sampling noise. EMD also performs well for small sample size. In general, marginal distributions do better than multidimensional distributions when we have few samples. On the other hand distances like $\chi^{2}$, JD and KL perform better with large number of observations. In terms of speed parametric distances WMV and Fisher are the fastest while EMD requires heavy computations.