Extraction of the level lines of a Bilinear image

Abstract

We detail precisely an algorithm for the extraction of the level lines of a bilinear image, which is a continuous function interpolating bilinearly a discrete image. If we discard the levels of the discrete image, where topological diffoculties arise, a level line is a concatenation of branches of hyperbolas. The algorithm tracks these branches and provides a sampling of the level lines in the form of closed polygons. If the level line contains a saddle point, the hyperbola degenerates to orthogonal segments, where an arbitrary but consistent choice is adopted for the tracking at the bifurcation. In any case, the extracted polygons are disjoint and enclose a bounded region. This allows to order the level lines in an enclosure tree hierarchy, which may be used for a variety of filters. Recovering this tree is a simple post-processing of the extraction algorithm.