Authors: [tex2html_wrap4114]B. Dubuc, S. W. Zucker
Investigator username: zucker
Subcategory: computer vision
In differential geometry curves are characterized as mappings from an interval to the plane. In topology curves are characterized as a Hausdorff space with certain countability properties. Neither of these definitions captures the role that curves play in vision, however, in which curves can denote simple objects (such as a straight line), or complicated objects (such as a jumble of string). The difference between these situations is in part a measure of their complexity, and in part a measure of their dimensionality. Our long-term goal is to develop a formal theory of curves appropriate for computational vision in general, and for problems like separating straight lines from strings in particular. We propose a theory of the complexity of curves that is sufficient to separate those which extend along their length (e.g., in one dimension) from those that cover an area (e.g., 2-D). The theory is based on original results in geometric measure theory, and is applied to the problems of perceptual grouping and physiological interpretation of axonal arbours in developing neurons.