Detection and Correction of Invalid Slope Districts in Separatrix-Based Image Segmentation

There have been notable advances in high level segmentation techniques in different medical applications, but there has been less progress in general-purpose low level segmentation. Data-driven segmentation is needed for constructing object-based image descriptions, which allows detection and categorisation of novel objects and for high-level model matching. A promising approach for the first stages of such a system is based on separatrices. However, significant topological problems can arise when the approach is used with real, discretely sampled images, in particular relating to contacts between separatrices. We analyze these contacts systematically in a selection of 2-D images and identify the occurrence of separatrix crossings. We show that these generate invalid slope districts and propose an algorithm for their correction.