A neural model of contour integration in the primary visual cortex
Neural Computation
Multiple Contour Finding and Perceptual Grouping using Minimal Paths
Journal of Mathematical Imaging and Vision
A Probabilistic Interpretation of the Saliency Network
ECCV '00 Proceedings of the 6th European Conference on Computer Vision-Part II
Edge Based Probabilistic Relaxation for Sub-pixel Contour Extraction
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
Multiple Contour Finding and Perceptual Grouping as a Set of Energy Minimizing Paths
EMMCVPR '01 Proceedings of the Third International Workshop on Energy Minimization Methods in Computer Vision and Pattern Recognition
The generalized A* architecture
Journal of Artificial Intelligence Research
Spatiotemporal region enhancement and merging for unsupervized object segmentation
Journal on Image and Video Processing
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We describe a local parallel method for computing the stochastic completion field introduced in an earlier paper\cite{williams}. The stochastic completion field represents the likelihood that a completion joining two contour fragments passes through any given position and orientation in the image plane. It is based upon the assumption that the prior probability distribution of completion shape can be modeled as a random walk in a lattice of discrete positions and orientations. The local parallel method can be interpreted as a stable finite difference scheme for solving the underlying Fokker-Planck equation identified by Mumford\cite{mumford}. The resulting algorithm is significantly faster than the previously employed method which relied on convolution with large-kernel filters computed by Monte Carlo simulation. The complexity of the new method is O(n3m) while that of the previous algorithm was O(n4m2) (for an n X n image with m discrete orientations). Perhaps most significantly, the use of a local method allows us to model the probability distribution of completion shape using stochastic processes which are neither homogenous nor isotropic. For example, it is possible to modulate particle decay rate by a directional function of local image brightnesses (i.e., anisotropic decay). The effect is that illusory contours can be made to respect the local image brightness structure. Finally, we note that the new method is more plausible as a neural model since 1) unlike the previous method, it can be computed in a sparse, locally connected network; and 2) the network dynamics are consistent with psychophysical measurements of the time course of illusory contour formation.