Multivariate Medians for Image and Shape Analysis
This is an incremental review paper that addresses the need for robust filtering techniques in image and shape analysis for researchers and practitioners in these fields.
The paper provides an overview of multivariate median concepts, tackling the problem of robust denoising for multivariate images like color and matrix-valued data, and explores their potential application to shape processing, but does not report specific results or numbers.
Having been studied since long by statisticians, multivariate median concepts found their way into the image processing literature in the course of the last decades, being used to construct robust and efficient denoising filters for multivariate images such as colour images but also matrix-valued images. Based on the similarities between image and geometric data as results of the sampling of continuous physical quantities, it can be expected that the understanding of multivariate median filters for images provides a starting point for the development of shape processing techniques. This paper presents an overview of multivariate median concepts relevant for image and shape processing. It focusses on their mathematical principles and discusses important properties especially in the context of image processing.