Extracting meaningful curves from images
Since the beginning, Mathematical Morphology has proposed to extract shapes from images as connected components of level sets. These methods have proved very efficient in shape recognition and shape analysis. In this paper, we present an improved method to select the most meaningful level lines (boundaries of level sets) from an image. This extraction can be based on statistical arguments, leading to a parameter free algorithm. It permits to roughly extract all pieces of level lines of an image, that coincide with pieces of edges. By this method, the number of encoded level lines is reduced by a factor 100, without any loss of shape contents. In contrast to edge detection algorithms or snakes methods, such a level lines selection method delivers accurate shape elements, without user parameter since selection parameters can be computed by the Helmholtz Principle. The paper aims at improving the original method proposed in [10]. We give a mathematical interpretation of the model, which explains why some pieces of curve are overdetected. We introduce a multiscale approach that makes the method more robust to noise. A more local algorithm is introduced, taking local contrast variations into account. Finally, we empirically prove that regularity makes detection more robust but does not qualitatively change the results.
level lines edge detection shapes elements helmholtz principle topographic maps