Towards processing fields of general real-valued square matrices

Abstract

In this paper, a general framework is presented that allows for the fundamental morphological operations such as dilation and erosion for real-valued square matrix fields. Hence, it is also possible to process any field consisting of a subgroup of general matrices with examples like the general linear, symmetric, skew-symmetric, Hermitian, and orthonormal group. Therefore, from the theoretical point of view it is possible to process any field with entries consisting of the aforementioned groups. Extended examples illustrated the different conversion processes and the definition of corresponding pseudo-suprema and pseudo-infima. Furthermore, some possible applications are illustrated.