Perceptible Level Lines and Isoperimetric Ratio

This paper introduces a simple criterion to select the most important level lines from the numerous set obtained with a topographic map. A topographic map gives a morphological and a geometrical representation of the information contained in natural images. Most of level lines are perceptually negligible and may be removed without noticeable distortion. Such curves, which do not carry information on the shape of the objects, are oscillating very quickly. They can be discriminated from the others by means of the isoperimetric ratio of the region they delimit. The main advantage of the isoperimetric criterion lies in its invariance with respect to contrast changes. As a result of, the topographic map of the remaining level lines achieves a segmentation of the image with most borders matching the perceptual edges. This segmentation being invariant under changes of contrast is a great alternative to classical segmentation or edge detection methods, when to be used to compare the content of two images, such as in stereo matching or motion analysis applications.