Scale Space Versus Topographic Map for Natural Images

We call “natural” image any photograph of an outdoor or indoor scene taken by a standard camera. In such images, most observed objects undergo occlusions and the illumination condition and contrast response of the camera are unknown. Actual Scale Space theories do not incorporate obvious restrictions imposed by the physics of image generation. The heat equation (linear scale space) is not contrast invariant and destroys T-junctions. The same is true for the recently proposed curvature equations (mean curvature motion and affine shortening): They break the symmetry of junctions. To apply directly these models to natural world images, with occlusions, is irrevelant. Returning to the edge detection problem, in which scale space theory originates, we show how level lines can be found in an image without smoothing. As an alternative to edge detection/scale space, we propose to define the line structure in a natural image by its topographic map (set of all level lines). We also show that a modification of morphological scale space can help to the visualization of the topographic map.