Multiresolution analysis of ridges and valleys in grey-scale images

Two methods for identifying and analyzing the multiresolution behavior of ridges and valleys in grey-scale images are described. The first method uses the tools of differential geometry to focus on local image behavior. The resulting vertex curves mark the tops of ridges and bottoms of valleys in an image. The second method focuses on the global drainage patterns of rainfall on a terrain map. The resulting watershed boundaries also identify the tops of ridges and bottoms of valleys in an image. By following these two geometric representations through scale space, the authors build resolution hierarchies on ridges and valleys in the image that can be utilized for interactive image segmentation