Machine Learning in Morphological Segmentation

Background

Mathematical Morphology is a very well established theory to process images (Serra, 1988). The watershed is the basic tool of Mathematical Morphology for segmentation. It has proved to be a powerful tool and it is used in a large number of applications, such as, medicine, remote sensing, robotics, and multimedia (Meyer, 2001). The parameters for a watershed are marker and input images (Soille, 2004). The watershed grows the markers based on a flooding simulation process by considering the input image as a topographic surface. The problem is to produce the divide-line image on this surface (Roerdink, 2000). Each marker is associated to a color. The topography is flooded from below by letting colored water rise from the holes with its associated color, at an uniform rate across the entire image. When the rising water of distinct colors would merge, a dam is built to prevent the merging. Figure 1 illustrates such a process on a color hematology image with two different sets of markers (provided by the user or by a machine learning algorithm). The most difficult problem when using watershed is of course the definition of appropriate markers with minimal efforts (Rivest, 1992; Meyer, 2001). User provided markers can be attractive for interactive segmentation but for automatic segmentation other techniques have to be considered. An accurate extraction of reliable markers requires prior knowledge on the latter (color, texture, shape, etc.). To incorporate such prior knowledge for the automatic extraction of markers, machine-learning techniques (Derivaux, 2007; Lezoray, 2002; Levner 2007) are the most natural candidates. Figure 2 provides a schematic view of all components involved in the design of a morphological segmentation scheme relying on machine learning algorithms for marker extraction. To perform morphological color image segmentation, a machine learning based classification of pixel feature vectors is done. The result is labeled in connected components and refined by a color watershed. To infer a proper machine learning based pixel classifier, an image database with an associated ground truth is constructed and pixel feature vectors are shared among classes as a basis for supervised learning. In the following Sections, conceiving of each one of these components is described.