Having been studied since long by statisticians, multivariate medianconcepts found their way into the image processing literature in thecourse of the last decades, being used to construct robust and efficientdenoising filters for multivariate images such as colour images but alsomatrix-valued images.Based on the similarities between image and geometric data as results ofthe sampling of continuous physical quantities, it can be expected that theunderstanding of multivariate median filters for images provides a startingpoint for the development of shape processing techniques.This paper presents an overview of multivariate median concepts relevantfor image and shape processing. It focusses on their mathematical principlesand discusses important properties especially in the context of imageprocessing.
On Multivariate Median Regression
