Pseudo-invariant image transformations on a hexagonal lattice

Sheridan, Phil; Hintz, Tom; Alexander, David

doi:10.1016/s0262-8856(00)00036-6

Cited by 54 publications

(41 citation statements)

References 6 publications

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“…SE(2, 6). -We can exploit the Spiral Architecture introduced by Sheridan [16,17]. This is a way to index hexagons of the grid with only one index which allows to introduce an operation, spiral multiplication, that, with the same complexity of a normal multiplication, computes rotations by multiples π/3.…”

Section: Implementation and Numerical Experimentsmentioning

confidence: 99%

Image Processing in the Semidiscrete Group of Rototranslations

Prandi

Boscain

Gauthier

2015

Lecture Notes in Computer Science

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Section: Implementation and Numerical Experimentsmentioning

confidence: 99%

Image Processing in the Semidiscrete Group of Rototranslations

Prandi

Boscain

Gauthier

2015

Lecture Notes in Computer Science

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“…This is a data structure that embodies important properties of the natural visual constraints imposed by the primate eye (Sheridan et al, 2000). In particular, SHIA has a discrete, finite and bounded domain which mimics the distribution of photo receptors on the retinal field.…”

Section: Mathematical Backgroundmentioning

confidence: 99%

Cortical Specification of a Fast Fourier Transform Supports a Convolution Model of Visual Perception

Sheridan¹

2012

Fourier Transform Applications

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“…By definition, invariant representations have the property that they encode all relevant variations of a percept as a single representation. Pseudo-invariant representations differ from invariant ones in that the variations of the representation are translations, or displaced copies, of each other (Sheridan et al 2000). In the dynamic generalization theory, pseudo-invariance is hypothesized to be property of cortical maps.…”

Section: Map-based Invariancementioning

confidence: 99%

“…Alternative formulations of the concept of pseudo-invariance have previously been explicated (Pitts and McCulloch 1947;Agu 1988;Sheridan et al 2000). We illustrate Eqs.…”

Section: Map-based Invariancementioning

confidence: 99%

Generalization of learning by synchronous waves: from perceptual organization to invariant organization

et al. 2010

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From a few presentations of an object, perceptual systems are able to extract invariant properties such that novel presentations are immediately recognized. This may be enabled by inferring the set of all representations equivalent under certain transformations. We implemented this principle in a neurodynamic model that stores activity patterns representing transformed versions of the same object in a distributed fashion within maps, such that translation across the map corresponds to the relevant transformation. When a pattern on the map is activated, this causes activity to spread out as a wave across the map, activating all the transformed versions represented. Computational studies illustrate the efficacy of the proposed mechanism. The model rapidly learns and successfully recognizes rotated and scaled versions of a visual representation from a few prior presentations. For topographical maps such as primary visual cortex, the mechanism simultaneously represents identity and variation of visual percepts whose features change through time.

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Pseudo-invariant image transformations on a hexagonal lattice

Cited by 54 publications

References 6 publications

Image Processing in the Semidiscrete Group of Rototranslations

Image Processing in the Semidiscrete Group of Rototranslations

Cortical Specification of a Fast Fourier Transform Supports a Convolution Model of Visual Perception

Generalization of learning by synchronous waves: from perceptual organization to invariant organization

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