Geodesy on label images, and applications to video sequence processing

Morphological operators based on the numerical ordering of grey-levels are used to filter regional minima and maxima in images. It is argued that label images constitute an appropriate framework for morphological filtering of regions which are neither minima nor maxima. Following a previous paper where we introduced morphological operations on label images [C. Ronse, V. Agnus, Morphology on label images: flat-type operators and connections, Journal of Mathematical Imaging and Vision 22 (2/3) (2005) 283–307], we study geodesic dilation (or erosion) and reconstruction. Since the lattice of label images is not distributive, some strange results may happen, so the standard definition of geodesic dilation and reconstruction must be modified in order to be effective; standard properties of geodesic operations are preserved only if we make some restrictions on the labels present in the mask or marker image. We give the relation between geodesic reconstruction and the flat zone connection on label images. We illustrate the theory with an application of morphology and geodesy on label images, to the segmentation of moving objects in video sequences.