Image representation by a new optimal non-uniform morphological sampling

This paper presents a new non-uniform subsampling strategy based on mathematical morphology. This sampling scheme is determinist and iterative. At each iteration, a sample position is determined in order to minimize the overall absolute reconstruction error. We show that satisfying this criterion is equivalent to maximizing the volume of reconstructed image. The sample selection strategy is repeated until reaching either a previously determined number of samples, or a maximal admissible error. The correspondent reconstruction procedure is also described. The algorithm is first presented using only one structuring element, then, extended to the case of a family of structuring elements. Experiments on the choice of structuring elements in the family, allow us to choose the optimal description set. Finally, we present an application of this novel image representation method on image compression. A comparison of results with JPEG standard shows the good performance of our approach, especially for high compression ratios. (C) 2000 Pattern Recognition Society. Published by Elsevier Science Ltd. All rights reserved.