Alyson Wilson

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Professor of Statistics
North Carolina State University


Statistical Models for Shapes and Deformations

Bayesian methods are valuable in image analysis because there is often a priori information that can contribute to the analysis of an image. This prior knowledge may be general (e.g., intensities vary smoothly across the image), or may be more specific (e.g., this is an image of a brain that may have a tumor). This dissertation develops flexible methods to incorporate prior knowledge from templates into algorithms for image analysis within a Bayesian framework. Classes of priors on landmark locations are developed that assign high probability to images “like” the template and low probability to images “unlike” the template. The priors build on previous work in Bayesian image analysis by incorporating ideas from Markov random field priors and deformable template models. The prior models differ from standard applications of MRF models in that the sites in the fields represent image objects, and the random variables associated with the sites represent their locations. Another crucial idea grows from methods in computer vision research. Features in an image occur at a variety of scales, and to effectively model spatial and scale relationships, this variety of scales must be modeled. Scale space is an image representation that handles image structure at all resolutions simultaneously and allows efficient calculation using features at multiple scales. It also allows models to be specified that are rotation, translation, and zoom invariant. Other important aspects of the prior include quantifying feature similarity between images, locating landmarks within images, and measuring distances and spatial relationships between landmarks. The priors address these issues and incorporate the feature and location information into a hierarchical model. The hierarchical framework is natural for handling deformations and obstructions. Further, it allows the modeling of such properties as “the location of large-scale features is less variable than the location of small-scale features.” The priors on landmarks are used to perform automatic landmark identification. They also hold promise for tasks like automatic object recognition.