# Maximal Max-tree Simplification Methodology

# Methodology

The filtering methodology proposed consists of applying the EF, the attribute used by the EF vary according to the problem, followed by the MMS filter. The EF sets the number of leaves in the Max-Tree, and the MMS filter transforms each sub-branch in a trivial sub-branch, therefore the number of nodes in the resulting tree will be bounded between and .

The criteria to be used depends on the problem. If we are interested in detecting distinguished regions, the MSER criterion is best, but if we are just looking to simplify the image, the normalized threshold criterion with usually yields good results and it is faster than the MSER criterion.

The image resulting of the methodology proposed loses information when compared to the original image, but we believe that with the right criterion, the information necessary to solve the problem at hand is preserved. The curve percentage of leaves filtered versus the nodes reduction rate after applying the methodology proposed is illustrated in Figure 1. All curves have a reduction rate higher than when the abscissa axis reaches , and after that point the reduction rate starts to increase much faster. Our experience tells us that keeping between and of the relevant maxima of natural images usually yields a high nodes reduction rate, and preserves most of the image information.

Figure 1. Curve percentage of relevant maxima preserved versus the nodes reduction rate after applying the methodology proposed.