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Tangent Bundle Curve Completion with Locally Connected Parallel Networks
, 2012
"... 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 corr ..."
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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 orientationselective cells in the primary visual cortex. Previous theoretical work modeled these patterns as least energetic 3D curves in the mathematical continuous space R 2 × S 1, 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.
Tangent Bundle Elastica and Computer Vision
"... AbstractVisual curve completion, an early visual process that completes the occluded parts between observed boundary fragments (a.k.a. inducers), is a major problem in perceptual organization and a critical step toward higher level visual tasks in both biological and machine vision. Most computati ..."
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AbstractVisual curve completion, an early visual process that completes the occluded parts between observed boundary fragments (a.k.a. inducers), is a major problem in perceptual organization and a critical step toward higher level visual tasks in both biological and machine vision. Most computational contributions to solving this problem suggest desired perceptual properties that the completed contour should satisfy in the image plane, and then seek the mathematical curves that provide them. Alternatively, few studies (including by the authors) have suggested to frame the problem not in the image plane but rather in the unit tangent bundle R 2 Â S 1 , the space that abstracts the primary visual cortex, where curve completion allegedly occurs. Combining both schools, here we propose and develop a biologically plausible theory of elastica in the tangent bundle that provides not only perceptually superior completion results but also a rigorous computational prediction that inducer curvatures greatly affects the shape of the completed curve, as indeed indicated by human perception.
Bayesian Hierarchical Grouping: Perceptual Grouping as Mixture Estimation
"... We propose a novel framework for perceptual grouping based on the idea of mixture models, called Bayesian hierarchical grouping (BHG). In BHG, we assume that the configuration of image elements is generated by a mixture of distinct objects, each of which generates image elements according to some ge ..."
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We propose a novel framework for perceptual grouping based on the idea of mixture models, called Bayesian hierarchical grouping (BHG). In BHG, we assume that the configuration of image elements is generated by a mixture of distinct objects, each of which generates image elements according to some generative assumptions. Grouping, in this framework, means estimating the number and the parameters of the mixture components that generated the image, including estimating which image elements are “owned ” by which objects. We present a tractable implementation of the framework, based on the hierarchical clustering approach of Heller and Ghahramani (2005). We illustrate it with examples drawn from a number of classical perceptual grouping problems, including dot clustering, contour integration, and part decomposition. Our approach yields an intuitive hierarchical representation of image elements, giving an explicit decomposition of the image into mixture components, along with estimates of the probability of various candidate decompositions. We show that BHG accounts well for a diverse range of empirical data drawn from the literature. Because BHG provides a principled quantification of the plausibility of grouping interpretations over a wide range of grouping problems, we argue that it provides an appealing unifying account of the elusive Gestalt notion of Prägnanz.
A Gauge Field Model of Modal Completion
"... Perceptual completion of figures is a basic process revealing the deep architecture of low level vision. In this paper a complete gauge field Lagrangian is proposed allowing to couple the retinex equation with neurogeometrical models and to solve the problem of modal completion, i.e. the pop up of t ..."
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Perceptual completion of figures is a basic process revealing the deep architecture of low level vision. In this paper a complete gauge field Lagrangian is proposed allowing to couple the retinex equation with neurogeometrical models and to solve the problem of modal completion, i.e. the pop up of the Kanizsa triangle. EulerLagrange equations are derived by variational calculus and numerically solved. Plausible neurophysiological implementations of the particle and field equations are discussed and a model of the interaction between LGN and visual cortex is proposed. 1
On the Cuspless SubRiemannian Geodesics in R3 o S2
, 2013
"... We study the cuspless curves in three dimensional Euclidean space that minimize the energy functional ..."
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We study the cuspless curves in three dimensional Euclidean space that minimize the energy functional
J Math Imaging Vis (2014) 49:384–417 DOI 10.1007/s108510130475y Association Fields via
, 2013
"... © The Author(s) 2013. This article is published with open access at Springerlink.com Abstract To model association fields that underly perceptional organization (gestalt) in psychophysics we consider the problem Pcurve of minimizing 0 ξ2 + κ2(s)ds for a planar curve having fixed initial and final p ..."
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© The Author(s) 2013. This article is published with open access at Springerlink.com Abstract To model association fields that underly perceptional organization (gestalt) in psychophysics we consider the problem Pcurve of minimizing 0 ξ2 + κ2(s)ds for a planar curve having fixed initial and final positions and directions. Here κ(s) is the curvature of the curve with free total length . This problem comes from a model of geometry of vision due to Petitot (in J. Physiol. Paris 97:265–309,