Shape preservation in morphological filtering and segmentation

The paper discusses the behavior of some image filtering and segmentation approaches, focusing on techniques that belong to mathematical morphology. In particular, the article studies some morphological operators and filters that consider connectivity in a special way and that therefore satisfactorily preserve the significant shapes and contours of an input image. Such morphological connected filters compare favorably to other filtering techniques that attempt to preserve shapes, such as for example, anisotropic filtering or morphological non-connected filtering. Some locality and adjacency relationships are satisfied by openings and closings by reconstruction, the "building" pieces of the filter by reconstruction class. In addition, the composition properties of some filters by reconstruction make them suitable for multi-scale image representation. The extension of the connect filtering philosophy to the image segmentation problem achieves segmentation methods that avoid the so called resolution problem that affects some techniques. Some examples are shown that illustrate the ideas described in the paper.