Stochastic completion fields: A neural model of illusory contour shape and salience.
Abstract
We describe an algorithm- and representation-level theory of illusory contour shape and salience. Unlike previous theories, our model is derived from a single assumption: that the prior probability distribution of boundary completion shape can be modeled by a random walk in a lattice whose points are positions and orientations in the image plane (i.e., the space that one can reasonably assume is represented by neurons of the mammalian visual cortex). Our model does not employ numerical relaxation or other explicit minimization, but instead relies on the fact that the probability that a particle following a random walk will pass through a given position and orientation on a path joining two boundary fragments can be computed directly as the product of two vector-field convolutions. We show that for the random walk we define, the maximum likelihood paths are curves of least energy, that is, on average, random walks follow paths commonly assumed to model the shape of illusory contours. A computer model is demonstrated on numerous illusory contour stimuli from the literature.
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Lee and Mumford suggested that the formation of illusory contours is primarily a top-down mechanism, in combination with lateral mechanisms.
“Lee and Mumford [1] suggested that the formation of illusory contours is primarily a top-down mechanism, as also suggested in our experiments, in combination with lateral mechanisms proposed in [66].”
From Towards a mathematical theory of cortical micro-circuits (2009) · cites this paper as [66]
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- Authors
- Williams, L. R., & Jacobs, D. W.
- Affiliations
- NEC Research Institute, Princeton, NJ 08540, USA
- ORCID
- Jacobs, David W.
- Venue
- Neural Computation
- Publisher
- MIT Press - Journals
- Published
- 1997-05-01
- Volume
- 9
- Issue
- 4
- Pages
- 837-858
- ISSN
- 0899-7667 (ISSN-L)
- 1530-888X
- OpenAlex
- W1992336406
- Cited by
- 331
- References
- 27
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 1 · 2022: 2 · 2021: 3 · 2020: 2 · 2019: 9 · 2018: 9 · 2017: 8 · 2016: 13 · 2015: 13 · 2014: 13 · 2013: 11 · 2012: 10
- FWCI
- 8.18
- Type
- journal article
- Language
- en
- Open access
- closed
- Locations
- Neural Computation (publishedVersion)
- PubMed (publishedVersion)
- Topics
- Life Sciences › Neuroscience › Cognitive Neuroscience › Visual perception and processing mechanisms
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Visual Attention and Saliency Detection
- Physical Sciences › Computer Science › Computer Vision and Pattern Recognition › Advanced Vision and Imaging
- Keywords
- illusory contours, contour completion, random walks, lattice model, visual cortex, boundary completion, shape priors
- MeSH terms
- Algorithms, Form Perception, Models, Neurological, Random Allocation, Stochastic Processes, Visual Fields, Neural Networks, Computer
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