Critical Morphological Sampling and Its Applications to Image Coding

In this paper we introduce a new morphological sampling theory and show some of its applications to image coding. As in previous works on morphological sampling, we establish conditions that the signal should satisfy before (sub)sampling in order to meet a prescribed reconstruction error criteria. In contrast to previous theorems, however, the whole process is self dual. When compared to previous morphological schemes, Critical Morphological Sampling can save up to half the number of samples. We also establish a set of conditions under which the new theorem is Critical, i.e., a more sparse sampling grid could produce an unbounded reconstruction error (in a Hausdorff sense). We use the theorem to design a Morphological Pyramid Coder, similar to a Laplacian Pyramid Coder. The results not only are superior to the Laplacian Pyramid, but are found to be competitive with more complex linear coders, like the DCT-based JPEG.