Ultimate grain filter

This work introduces a residual operator called ultimate grain filter which is a powerful image operator based on numerical residues. With a multi-scale approach, the ultimate grain filter analyzes an image under a series of grain filters of increasing grain sizes. Thus, contrasted objects can be detected if a relevant residue is generated when they are filtered out by one of these grain filters. We also present an efficient algorithm for ultimate grain filter computation by using a structure called tree of shapes. In fact, since the result of a given grain filter can be obtained by pruning the corresponding tree and reconstructing it, we show that the result of the ultimate grain filter (which is based on numerical residues from a family of grain filters) can be obtained by the computation of the difference (remaining nodes) of the corresponding pruned trees. Finally, we propose the use of ultimate grain filter to extract contrasted objects using a priori knowledge of an application.