doing so in a way that is hardly sensitive to outliers in the data, makes multivariate medians also an interesting candidate for the analysis of geometric data such as point clouds in the real affine space, or more generally on manifolds. Resulting from the sampling of continuous-scale physical quantities, such geometric data are not far from image data, and image analysis techniques have been adapted successfully for their processing, see [@Clarenz-vis00] for an example, or [@Clarenz-TIP04] for combined processing of shape and image data in the case of textured surfaces. Although few references to median filtering of geometric data can be found in the literature so far – see e.g. [@Small-ISR90 Sec. 7] for a short discussion of medians for points on a sphere –, it can therefore be expected that a thorough understanding of multivariate median filtering of images can serve as a starting point for robust shape processing techniques.

This paper aims at giving an overview of multivariate median concepts that can be useful for processing images and shapes. In the course of the paper, the underlying mathematical structures and principles are presented, and linked to resulting properties of the filters that are particularly relevant for the processing 