In this dissertation, a new method for multiscale segmentation of digital imagery is introduced. Image segmentation is the spatial partitioning of an image into a set of meaningful regions and is a crucial process in many image and video based applications. The method introduced here is based upon a new scale-space theory and a related multiscale edge detection algorithm. Segmentation is accomplished through a novel combination of multiscale edge information, with application to the problem of cell segmentation in microscopy.; The scale-space theory exploits the relationship between local monotonicity and mathematical morphology. In previous work, the degree of local monotonicity has been defined as a smoothness parameter of one-dimensional (1-D) signals. Here, the definition is extended to higher dimensions for application to digital image processing. Through the use of mathematical morphology, a theory of signal scale is developed wherein a signal is smoothed to a specified degree of local monotonicity. Within the scale-space, scaled edge detection operators are defined that exploit the properties of local monotonicity. The edge detection algorithm can be interpreted as the morphological analogy to the Laplacian of Gaussian method. This morphological version is advantageous for image processing due to the explicit treatment of non-ideal or step-like edges, which we define here. The edge detection theory is then incorporated into a novel multiscale segmentation algorithm. The segmentation is proposed as an enhancement of the standard watershed method, which partitions a topological relief representing edge strength and has the advantage of automatically producing closed region contours, This formulation integrates the assumptions of multiscale local monotonicity into an edge-based segmentation technique, which requires a modicum of user-defined parameters (scales of interest and a scale-independent edge threshold) and may be generalized to multispectral and multidimensional imagery.; Experimental results are shown for grayscale edge detection and image segmentation, with emphasis on the application to cell segmentation of 2-D microscopy imagery. Comparisons to previous methods are shown in terms of the Pratt figure of merit utilizing ground truth data, showing the advantages of the proposed method.
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