A Computational Approach to Edge Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
The geometry of fractal sets
Computer Vision, Graphics, and Image Processing
Solid shape
Two stages of curve detection suggest two styles of visual computation
Neural Computation
Potentials, valleys, and dynamic global coverings
International Journal of Computer Vision
The Design and Use of Steerable Filters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Identifying salient circular arcs on curves
CVGIP: Image Understanding
A Bayesian multiple-hypothesis approach to edge grouping and contour segmentation
International Journal of Computer Vision
Variational methods in image segmentation
Variational methods in image segmentation
Perceptual completion of occluded surfaces
Computer Vision and Image Understanding
The sciences of the artificial (3rd ed.)
The sciences of the artificial (3rd ed.)
Inferring global perceptual contours from local features
International Journal of Computer Vision - Special issue on computer vision research at the University of Southern California
Convergence rates of algorithms for visual search: detecting visual contours
Proceedings of the 1998 conference on Advances in neural information processing systems II
Complexity, Confusion, and Perceptual Grouping. Part II: Mapping Complexity
Journal of Mathematical Imaging and Vision
Perceptual Organization for Artificial Vision Systems
Perceptual Organization for Artificial Vision Systems
Filtering, Segmentation, and Depth
Filtering, Segmentation, and Depth
Logical/Linear Operators for Image Curves
IEEE Transactions on Pattern Analysis and Machine Intelligence
Contour Continuity in Region Based Image Segmentation
ECCV '98 Proceedings of the 5th European Conference on Computer Vision-Volume I - Volume I
Toward discrete geometric models for early vision
Toward discrete geometric models for early vision
Chaos and Fractals
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Intermediate-level vision is central to form perception, and we outline an approach to intermediate-level segmentation based on complexity analysis. We focus on the problem of edge detection, and how edge elements might be grouped together. This is typical because, once the local structure is established, the transition to global structure must be effected and context is critical. To illustrate, consider an edge element inferred from an unknown image. Is this local edge part of a long curve, or part of a texture? If the former, which is the next element along the curve? If the latter, is the texture like a hair pattern, in which nearby elements are oriented similarly, or like a spaghetti pattern, in which they are not? Are there other natural possibilities? Such questions raise issues of dimensionality, since curves are 1-D and textures are 2-D, and also of complexity. Working toward a measure of representational complexity for vision, in this first of a pair of papers we develop a foundation based on geometric measure theory. The main result concerns the distribution of tangents in space and in orientation, which serves as a formal basis for the concrete measure of representational complexity developed in the companion paper.