Multivariate Medians for Image and Shape Analysis

TL;DR

This paper reviews multivariate median concepts and their mathematical foundations, highlighting their application in robust image denoising and potential for shape processing techniques.

Contribution

It provides a comprehensive overview of multivariate median methods, emphasizing their properties and relevance for image and shape analysis.

Findings

Multivariate medians are effective for robust denoising of multivariate images.

Mathematical principles of median filters are crucial for understanding their properties.

The paper discusses potential extensions to shape processing techniques.

Abstract

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.