| Mathematical morphology, developed in the early 1960's for single-component signals, has been applied to a number of image processing applications. This investigation examines the systematic extension of mathematical morphology to multi-variate signals.; Two approaches are considered. The first approach, the extension of the theory of single-component morphological filters to multi-variate case, fails for reason of the lack of ordering within signal range space. Therefore, as a second approach, a two stage processing technique was proposed, consisting of the maximum separation of the object from its background feature and separate morphological filtering of each component. To separate the object from its background, a mapping technique, based upon the normalization and simultaneous diagonalization of sample covariance matrices (NAD-CVM), was applied. Sample variance morphological measure interpretation demonstrated that NAD-CVM mapping constitutes an excellent preprocessing tool for morphological filtering of multi-variate signals. An unsupervised NAD-CVM implementation and a morphological edge detector were tested experimentally to verify the properties of the theoretical algorithm. In addition, a method for the application of the proposed method to the analysis of color images was presented. |
