A Multi-Scale Regularity Measure as Geometric Criterion for Image Segmentation

Recent ezperimental results [I] on human &ion show that low fractal dimension lines are highly capable to evocate namable objects. In other t e r n , regular lines are recognized by human vision as object edges. In this paper, a regularity measure of discrete lines geometry is presented. This quantitative measure based on a ratio between lines lengths at different scale is analyzed in the framework of brownian motion theory. The measure at a given scale is always computed from the mazimum precision image, so that it doesn't introduce any sub-resolution assumption. A scale choice determines the quantity of global information w. local information one wants to measure. We show how this quantitative measure lea& to a relevant shape information. To illustmte this, an image segmentation application ezample is realized. The segmentation based essentially on geometry criteria uses a region growing process which depends on a single parameter that can be Jized in a natural way, comparing contour regularity to a geometric model regularity. We pnsent ezperimental results performed on real-scene images, including indoor and outdoor images.