Numerical recipes in C: the art of scientific computing
Numerical recipes in C: the art of scientific computing
Trace Inference, Curvature Consistency, and Curve Detection
IEEE Transactions on Pattern Analysis and Machine Intelligence
Local parallel computation of stochastic completion fields
Neural Computation
CVPR '97 Proceedings of the 1997 Conference on Computer Vision and Pattern Recognition (CVPR '97)
Sketches with Curvature: The Curve Indicator Random Field and Markov Processes
IEEE Transactions on Pattern Analysis and Machine Intelligence
Segmentation of Multiple Salient Closed Contours from Real Images
IEEE Transactions on Pattern Analysis and Machine Intelligence
Journal of Mathematical Imaging and Vision
Learning Probabilistic Models for Contour Completion in Natural Images
International Journal of Computer Vision
Optimal contour integration: When additive algorithms fail
Neurocomputing
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A recent neural model of illusory contour formation is based on a distribution of natural shapes traced by particles moving with constant speed in directions given by Brownian motions. The input to that model consists of pairs of position and direction constraints, and the output consists of the distribution of contours joining all such pairs. In general, these contours will not be closed, and their distribution will not be scaleinvariant. In this article, we show how to compute a scale-invariant distribution of closed contours given position constraints alone and use this result to explain a well-known illusory contour effect.