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Local Parallel Computation of Stochastic Completion Fields
 Neural Computation
, 1997
"... We describe a local parallel method for computing the stochastic completion field introduced in an earlier paper[Williams96]. 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 ..."
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Cited by 35 (5 self)
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We describe a local parallel method for computing the stochastic completion field introduced in an earlier paper[Williams96]. 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 FokkerPlanck equation identified by Mumford[Mumford94]. The resulting algorithm is significantly faster than the previously employed method which relied on convolution with largekernel filters computed by Monte Carlo simulation. The complexity of the new method is O(n 3 m) while that of the previous algorithm was O(n 4 m 2 ) (for an n \Theta n image with m discrete orientations). Perhaps most significa...
First order augmentations to tensor voting for boundary inference and multiscale analysis in 3d
 IEEE Trans. On Pattern Analysis and Machine Intelligence
, 2004
"... Abstract—Most computer vision applications require the reliable detection of boundaries. In the presence of outliers, missing data, orientation discontinuities, and occlusion, this problem is particularly challenging. We propose to address it by complementing the tensor voting framework, which was l ..."
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Cited by 23 (2 self)
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Abstract—Most computer vision applications require the reliable detection of boundaries. In the presence of outliers, missing data, orientation discontinuities, and occlusion, this problem is particularly challenging. We propose to address it by complementing the tensor voting framework, which was limited to second order properties, with first order representation and voting. First order voting fields and a mechanism to vote for 3D surface and volume boundaries and curve endpoints in 3D are defined. Boundary inference is also useful for a second difficult problem in grouping, namely, automatic scale selection. We propose an algorithm that automatically infers the smallest scale that can preserve the finest details. Our algorithm then proceeds with progressively larger scales to ensure continuity where it has not been achieved. Therefore, the proposed approach does not oversmooth features or delay the handling of boundaries and discontinuities until model misfit occurs. The interaction of smooth features, boundaries, and outliers is accommodated by the unified representation, making possible the perceptual organization of data in curves, surfaces, volumes, and their boundaries simultaneously. We present results on a variety of data sets to show the efficacy of the improved formalism. Index Terms—Tensor voting, first order voting, boundary inference, discontinuities, multiscale analysis, 3D perceptual organization. 1
Gestalt Isomorphism and the Primacy of Subjective Conscious Experience: A Gestalt Bubble Model
 Behavioral & Brain Sciences
, 2003
"... this paper that you hold in your hands. The question is whether the rich spatial structure of this experience before you is the physical paper itself, or whether it is an internal data structure or pattern of activation within your physical brain. Although this issue is not much discussed in contemp ..."
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Cited by 18 (2 self)
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this paper that you hold in your hands. The question is whether the rich spatial structure of this experience before you is the physical paper itself, or whether it is an internal data structure or pattern of activation within your physical brain. Although this issue is not much discussed in contemporary psychology, it is an old debate that has resurfaced several times in psychology, but the continued failure to reach consensus on this issue continues to bedevil the debate on the functional role of sensory processing. The reason for the continued confusion is that both direct and indirect realism are frankly incredible, although each is incredible for different reasons. 6 2.1 Problems with Direct Realism The direct realist view is incredible because it suggests that we can have experience of objects out in the world directly, beyond the sensory surface, as if bypassing the chain of sensory processing. For example if light from this paper is transduced by your retina into a neural signal which is transmitted from your eye to your brain, then the very first aspect of the paper that you can possibly experience is the information at the retinal surface, or the perceptual representation downstream of it in your brain. The physical paper itself lies beyond the sensory surface and therefore must be beyond your direct experience. But the perceptual experience of the page stubbornly appears out in the world itself instead of in your brain, in apparent violation of everything we know about the causal chain of vision. Gibson explicitly defended the notion of direct perception, and spoke as if perceptual processing occurs somehow out in the world itself rather than as a computation in the brain based on sensory input (Gibson 1972 p. 217 & 239). Significantly, Gibson refused to di...
Euclidean Group Invariant Computation of Stochastic Completion Fields Using ShiftableTwistable Functions
 J. Math. Imaging and Vision
, 2000
"... We describe a method for computing the likelihood that a completion joining two contour fragments passes through any given position and orientation in the image plane. Like computations in primary visual cortex (and unlike all previous models of contour completion), the output of our computation ..."
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Cited by 15 (2 self)
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We describe a method for computing the likelihood that a completion joining two contour fragments passes through any given position and orientation in the image plane. Like computations in primary visual cortex (and unlike all previous models of contour completion), the output of our computation is invariant under rotations and translations of the input pattern. This is achieved by representing input, output, and intermediate states of the computation in a basis of shiftabletwistable functions. Introduction Any computational model of human visual information processing must reconcile two apparently contradictory observations. First, computations in primary visual cortex are largely Euclidean invariantan arbitrary rotation and translation of the input pattern of light falling on the retina produces an identical rotation and translation of the output of the computation. Second, simple calculations based on the size of primary visual cortex (60 mm 80 mm) and the observed densit...
Computing Stochastic Completion Fields in LinearTime Using a Resolution Pyramid
, 1999
"... We describe a lineartime algorithm for computing the likelihood that a completion joining two contour fragments passes through any given position and orientation in the image plane. Our algorithm is a resolution pyramid based method for solving a partial differential equation (PDE) characterizing a ..."
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Cited by 7 (1 self)
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We describe a lineartime algorithm for computing the likelihood that a completion joining two contour fragments passes through any given position and orientation in the image plane. Our algorithm is a resolution pyramid based method for solving a partial differential equation (PDE) characterizing a distribution of short, smooth completion shapes. The PDE consists of a set of independent advection equations in (x; y) coupled in the ` dimension by the diffusion equation. A previously described algorithm used a firstorder, explicit finite difference scheme implemented on a rectangular grid. This algorithm required O(n 3 m) time for a grid of size n \Theta n with m discrete orientations. Unfortunately, systematic error in solving the advection equations produced unwanted anisotropic smoothing in the (x; y) dimension. This resulted in visible artifacts in the completion fields. The amount of error and its dependence on ` has been previously characterized. We observe that by careful addi...
Harmonic Resonance Theory: An Alternative to the "Neuron Doctrine" Paradigm of Neurocomputation to Address Gestalt properties of perception
, 2000
"... neurocomputation involves discrete signals communicated along fixed transmission lines between discrete computational elements. This concept is shown to be inadequate to account for invariance in recognition, as well as for the holistic global aspects of perception identified by Gestalt theory. A Ha ..."
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Cited by 1 (0 self)
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neurocomputation involves discrete signals communicated along fixed transmission lines between discrete computational elements. This concept is shown to be inadequate to account for invariance in recognition, as well as for the holistic global aspects of perception identified by Gestalt theory. A Harmonic Resonance theory is presented as an alternative paradigm of neurocomputation, that exhibits both the property of invariance, and the emergent Gestalt properties of perception, not as special mechanisms contrived to achieve those properties, but as natural properties of the resonance itself.