An efficient image representation for multiscale analysis

In order to analyze an image, one needs to separate the signal changes occurring at different scales because they often correspond to distinct physical structures. Since Rosenfeld's work, people have tried to solve this problem by analyzing the image at several resolutions. They reproduce the image at different scales, process each of these and eventually infer some interesting information by comparing the outputs. In such an approach one increases the volume of data. This is computationally and conceptually inefficient. Indeed, after processing an image at a certain scale we are only concerned with the supplement of information available at a bigger scale and we do not need to reprocess the redundant details. With a new mathematical model, researchers show how to extract this information and isolate the signal changes occurring at the different scales. It will enable researchers to build a convenient and efficient image representation for multiscale analysis. The mathematical insight with the practical computer implementation is introduced without justifying every result in detail.