Geometric methods for analysis of ridges in n-dimensional images
David H. Eberly · 1994
Image segmentation is a process which identifies and labels objects in an image. The goals of this dissertation are to produce an algorithm for segmenting an image in the way that a front-end vision system does, using the local geometry induced by the intensity values of the image, to create multiscale representations of the objects that allow exploration of the details of the image via an interactive computer system, and to provide a formal geometric foundation for multiscale image analysis. The geometric concept of ridges is discussed. These structures are used to describe the shape properties of objects in an image. Various definitions are given for d-dimensional ridge structures of n-dimensional images. Ridges are used in conjunction with multiscale methods to segment an image. The output of the segmentation is a single tree and the objects in the image are represented as unions and differences of subtrees. The tree and image are used as input to a visualization tool which allows the user to explore the image interactively. A formal foundation for multiscale analysis is given which involves non-Euclidean geometry. Metric selection for scale space is naturally related to invariances required for a particular application. The anisotropic diffusion process for generating multiscale data is automatically determined by the metric. Moreover, the metric is used as an aid in developing fast, stable, and adaptive numerical algorithms for solving the nonlinear diffusion equations. This geometric foundation for multiscale analysis provides a natural set of tools for extracting information about objects in an image.