Segmentation tools in mathematical morphology

This paper presents a general methodology for picture segmentation using tools provided by mathematical morphology. This methodology is based on the marking of the objects to be segmented. The marking (using techniques which may differ according to the kind of picture to be analyzed) provides a " marker set" which is used to modify the gradient of the image. This modification using geodesic image reconstruction produces a new gradient image. The main characteristic of this modified gradient is that its minima exactly fit the various connected components of the " marker set" . In a second step a morphological transform called " watersheds" is performed on this gradient image. The watershed transform produces a partition of the image into homogeneous regions called " catchment basins" . Every catchment basin contains only one marker and its boundary corresponds to the pixels of the image where the contrast is locally maximum. Thus the transformed image exhibits the contours of the marked objects. Some examples illustrate the use of this process when objects marking is not too complex. Then we extend this method to situations where the marking step is not obvious and we show how the watershed transform together with the simplification of the image can provide efficient tools for detecting homogeneous regions in an image.