2-D digital curve analysis: A regularity measure

A regularity measure for discrete line geometry is presented. This quantitative measure based on a ratio between line lengths at different scales is analyzed in the framework of Brownian motion theory. The measure at a given scale is always computed from the maximum precision image, so that it does not introduce any subresolution assumption. A scale choice determines the quantity of global information vs. local information to be measured. Its statistical behavior is studied on two extremal models of curves: the Brownian motion and the digitized straight line. It is shown that this quantitative measure leads to relevant shape information. To illustrate this fact, an image segmentation application example is discussed based essentially on geometry criteria of region boundaries. Some experimental results performed on real-scene images are presented