Discrete Scale-Space Formulation and Multiscale Edge Extraction toward Higher Dimensions
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This thesis addresses the problem of a discrete scale-space formulation in the context of multiscale edge extraction extended toward higher dimensions. The first part of the thesis focuses on the discrete scale-space formulation. After analyzing the problem of the commonly used sampled Gaussian for approximating the continuous Gaussian, we propose a supplemented discrete scale-space formulation for 2-D and 3-D signals starting out from Lindeberg's 2-D discrete scale-space formulation. Moreover, we investigate the properties of the derived discrete scale-space kernels and carry out a validation study with respect to smoothing and differentiation performance. In the second part, based on classifying higher dimensional edges according to local curvature, we exemplarily establish 2-D edge models for straight edges as well as for circular edges. Utilizing these models, we develop a theoretical framework for optimal scale selection, where the effects of curvature as related to scale in multiscale edge extraction are analyzed. An experimental validation is carried out.