A Pattern-Theoretic Formulation of Shape in R3
Final rept. 1 Jan 1987-31 Dec 1988
VIRGINIA UNIV CHARLOTTESVILLE DEPT OF STATISTICS
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The goal of this grant was the formulation of a theory of shape in the plane with the theory being applied to problems in image processing. This development was completed in the case of object recognitionimage restoration where the planar objects are characterized by their one-dimensional boundaries, such as in many biological shapes. For example, given a two-dimensional noisy image from some technology, such as a visible-light camera, the methods allow me to build in a priori information concerning the object or objects in the image, resulting in an a posteriori probability measure on the possible objects in the scene. This approach is designed to capture the structure of those objects which have a large number of degrees of freedom in shape while all still maintain a certain common form this invariance is not captured by the traditional geometries.
- Theoretical Mathematics