Adaptive sharpening of multimodal distributions

In this work we derive a novel framework rendering measured distributions into approximated distributions of their mean. This is achieved by exploiting constraints imposed by the Gauss-Markov theorem from estimation theory, being valid for mono-modal Gaussian distributions. It formulates the relation between the variance of measured samples and the so-called standard error, being the standard deviation of their mean. However, multi-modal distributions are present in numerous image processing scenarios, e.g. local gray value or color distributions at object edges, or orientation or displacement distributions at occlusion boundaries in motion estimation or stereo. Our method not only aims at estimating the modes of these distributions together with their standard error, but at describing the whole multi-modal distribution. We utilize the method of channel representation, a kind of soft histogram also known as population codes, to represent distributions in a non-parametric, generic fashion. Here we apply the proposed scheme to general mono- and multimodal Gaussian distributions to illustrate its effectiveness and compliance with the Gauss-Markov theorem