International Journal of Computer Vision
Complexity, Confusion, and Perceptual Grouping. Part II: Mapping Complexity
Journal of Mathematical Imaging and Vision
Complexity, Confusion, and Perceptual Grouping. Part II: Mapping Complexity
International Journal of Computer Vision - Joint special issue on image analysis
Computing in Cortical Columns: Curve Inference and Stereo Correspondence
BMVC '00 Proceedings of the First IEEE International Workshop on Biologically Motivated Computer Vision
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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. Note that the map defining such curves is unknown, as is the proper way to represent them. We propose a formal complexity theory of curves appropriate for computational vision in general, and for problems like separating straight lines from jumbles in particular. The theory is applied to the problem of perceptual grouping.