IEEE Transactions on Pattern Analysis and Machine Intelligence
ACM Transactions on Mathematical Software (TOMS)
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
The perceptual organization of visual flows
The perceptual organization of visual flows
A Cortical Based Model of Perceptual Completion in the Roto-Translation Space
Journal of Mathematical Imaging and Vision
Computer vision for fruit harvesting robots state of the art and challenges ahead
International Journal of Computational Vision and Robotics
Tangent bundle curve completion with locally connected parallel networks
Neural Computation
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Visual curve completion is typically handled in an axiomatic fashion where the shape of the sought-after completed curve follows formal descriptions of desired, image-based perceptual properties (e.g, minimum curvature, roundedness, etc...). Unfortunately, however, these desired properties are still a matter of debate in the perceptual literature. Instead of the image plane, here we study the problem in the mathematical space R2 × S1 that abstracts the cortical areas where curve completion occurs. In this space one can apply basic principles from which perceptual properties in the image plane are derived rather than imposed. In particular, we show how a "least action" principle in R2 × S1 entails many perceptual properties which have support in the perceptual curve completion literature. We formalize this principle in a variational framework for general parametric curves, we derive its differential properties, we present numerical solutions, and we show results on a variety of images.