Abstract
The segmentation of microscopic images is a challenging application that can have numerous applications ranging from prognosis to diagnosis. Mathematical morphology is a very well established theory to process images. Segmentation by morphological means is based on watershed that considers an image as a topographic surface. Watershed requires input and marker image. The user can provide the latter but far more relevant results can be obtained for watershed segmentation if marker extraction relies on prior knowledge. Parameters governing marker extraction varying from image to image, machine learning approaches are of interest for robust extraction of markers. We review different strategies for extracting markers by machine learning: single classifier, multiple classifier, single classifier optimized by model selection.
TopBackground
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.
Key Terms in this Chapter
Support Vector Machines: SVM map input vector to a higher dimensional space where a maximal hyperplane is constructed.
Mathematical Morphology: Mathematical morphology (MM) is a theoretical model for digital images built upon lattice theory and topology. It is the foundation of morphological image processing, which is based on shift-invariant (translation invariant) operators based principally on Minkowski addition.
Classifier Combination: Classifier combination consists in combining results obtained from a set of classifiers to achieve higher performance than each single classifier.
Watershed: Segmentation by watershed designs a family of segmentation methods that consider an image as a topographic relief the flooding of which is simulated.
Classi fication: The process of deriving a mathematical function that can predict the membership of a class based on input data.
Ground Truth: A ground-truth database is a database that provides a list of the objects in each image.
Machine Learning: As a broad subfield of artificial intelligence, machine learning is concerned with the design and development of algorithms and techniques that allow computers to “learn”.
Model Selection: Selection of an optimal model to predict outputs from inputs by fitting adjustable parameters.