3D shape representation by contours
Computer Vision, Graphics, and Image Processing
On minimal energy trajectories
Computer Vision, Graphics, and Image Processing
Local parallel computation of stochastic completion fields
Neural Computation
IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Transactions on Mathematical Software (TOMS)
Introduction to Algorithms
Sketches with Curvature: The Curve Indicator Random Field and Markov Processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
The Perceptual Organization of Texture Flow: A Contextual Inference Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
Euler Spiral for Shape Completion
International Journal of Computer Vision - Special Issue on Computational Vision at Brown University
Biophysiologically plausible implementations of the maximum operation
Neural Computation
A Cortical Based Model of Perceptual Completion in the Roto-Translation Space
Journal of Mathematical Imaging and Vision
A biologically-inspired theory for non-axiomatic parametric curve completion
ACCV'10 Proceedings of the 10th Asian conference on Computer vision - Volume Part II
A Tangent Bundle Theory for Visual Curve Completion
IEEE Transactions on Pattern Analysis and Machine Intelligence
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We propose a theory for cortical representation and computation of visually completed curves that are generated by the visual system to fill in missing visual information (e.g., due to occlusions). Recent computational theories and physiological evidence suggest that although such curves do not correspond to explicit image evidence along their length, their construction emerges from corresponding activation patterns of orientation-selective cells in the primary visual cortex. Previous theoretical work modeled these patterns as least energetic 3D curves in the mathematical continuous space , which abstracts the mammalian striate cortex. Here we discuss the biological plausibility of this theory and present a neural architecture that implements it with locally connected parallel networks. Part of this contribution is also a first attempt to bridge the physiological literature on curve completion with the shape problem and a shape theory. We present completion simulations of our model in natural and synthetic scenes and discuss various observations and predictions that emerge from this theory in the context of curve completion.