Abstract
This work extends the scope of mathematical morphology from complete lattices to complete semilattices, and presents some applications of this extension. More specifically, we first define and briefly analyze basic morphological operators in complete inf-semilattices. Then, difference and reference semilattices are introduced. Finally, some video processing applications in these semilattices are presented, namely: Detection of fast motion, innovation extraction, and contour compression for segmentation-based coding.