Models for preattentive texture discrimination: Fourier analysis and local feature processing in a unified framework

1988 ◽  
Vol 3 (4) ◽  
pp. 263-280 ◽  
Author(s):  
Jonathan D. Victor
Keyword(s):  
Fourier Analysis ◽  
Local Feature ◽  
Unified Framework ◽  
Texture Discrimination ◽  
Feature Processing

scholarly journals A unified mode decomposition method for physical fields in homogeneous cosmology

2014 ◽  
Vol 26 (03) ◽  
pp. 1430001 ◽  
Author(s):  
Zhirayr G. Avetisyan
Keyword(s):  
Fourier Transform ◽  
Field Equation ◽  
Scalar Field ◽  
Vector Bundle ◽  
Fourier Analysis ◽  
Homogeneous Spaces ◽  
Unified Framework ◽  
Mode Decomposition ◽  
Physical Fields ◽  
Homogeneous Vector Bundle

The methods of mode decomposition and Fourier analysis of classical and quantum fields on curved spacetimes previously available mainly for the scalar field on Friedman–Robertson–Walker (FRW) spacetimes are extended to arbitrary vector bundle fields on general spatially homogeneous spacetimes. This is done by developing a rigorous unified framework which incorporates mode decomposition, harmonic analysis and Fourier analysis. The limits of applicability and uniqueness of mode decomposition by separation of the time variable in the field equation are found. It is shown how mode decomposition can be naturally extended to weak solutions of the field equation under some analytical assumptions. It is further shown that these assumptions can always be fulfilled if the vector bundle under consideration is analytic. The propagator of the field equation is explicitly mode decomposed. A short survey on the geometry of the models considered in mathematical cosmology is given and it is concluded that practically all of them can be represented by a semidirect homogeneous vector bundle. Abstract harmonic analytical Fourier transform is introduced in semidirect homogeneous spaces and it is explained how it can be related to the spectral Fourier transform. The general form of invariant bi-distributions on semidirect homogeneous spaces is found in the Fourier space which generalizes earlier results for the homogeneous states of the scalar field on FRW spacetimes.

scholarly journals The role of local feature processing in face and car detection

2010 ◽  
Vol 7 (9) ◽  
pp. 1036-1036
Author(s):  
H. Suh ◽  
K. Grill-Spector
Keyword(s):  
Local Feature ◽  
Car Detection ◽  
Feature Processing

Orientation-Specific Adaptation: Effects of Checkerboards on the Detectability of Gratings

Perception ◽  
1980 ◽  
Vol 9 (4) ◽  
pp. 369-377 ◽  
Author(s):  
Marc Green
Keyword(s):  
Fourier Analysis ◽  
Adaptation Effect ◽  
Local Feature ◽  
Feature Analysis ◽  
Predictive Values ◽  
Specific Adaptation ◽  
Adaptation Experiment ◽  
Adaptation Effects

The predictive values of Fourier analysis and local-feature analysis of spatial stimuli were compared in an orientation-specific adaptation experiment. Observers adapted to checkerboard patterns, which have fundamental Fourier components oriented 45° away from the edges. Detection of gratings was found to be maximally impaired when fundamental Fourier components of adaptation and test patterns were in the same orientation and minimal when edges were aligned. The orientation spread and amount of adaptation effect were similar to that found in previous experiments which employed sinusoids as adaptation and test stimuli.

Making Mayhew and Frisby Effortlessly Discriminable

Perception ◽  
1989 ◽  
Vol 18 (2) ◽  
pp. 231-235 ◽  
Author(s):  
Peter Thompson ◽  
David Travis
Keyword(s):  
Spatial Frequency ◽  
Fourier Analysis ◽  
Striate Cortex ◽  
Visual Pathway ◽  
Direct Access ◽  
Frequency Content ◽  
Texture Discrimination ◽  
Primal Sketch ◽  
Orientation Specificity

Mayhew and Frisby (1978) demonstrated that patterns which differ markedly in their spatial-frequency content may be very hard to discriminate. This they took as evidence against any model which proposes that the processes underlying texture discrimination have direct access to some local piecewise Fourier analysis of the patterns performed by spatial-frequency channels. It is shown that Mayhew and Frisby's patterns can be discriminated easily if their components have been incorporated into a pattern-contingent colour aftereffect. This demonstration suggests that the location in the visual pathway for contingent aftereffect adaptation must lie before the construction of the raw primal sketch, to which, according to Marr, we have conscious access. This location must also allow the orientation specificity seen in the aftereffect. This points to a locus in the striate cortex.

scholarly journals Hermite Functions, Lie Groups and Fourier Analysis

Entropy ◽  
2018 ◽  
Vol 20 (11) ◽  
pp. 816 ◽  
Author(s):  
Enrico Celeghini ◽  
Manuel Gadella ◽  
Mariano del Olmo
Keyword(s):  
Fourier Transform ◽  
Fourier Analysis ◽  
Hilbert Spaces ◽  
Fractional Fourier Transform ◽  
Close Relation ◽  
Hermite Functions ◽  
Symmetry Groups ◽  
Laguerre Functions ◽  
Unified Framework ◽  
Hermite And Laguerre Functions

In this paper, we present recent results in harmonic analysis in the real line R and in the half-line R + , which show a closed relation between Hermite and Laguerre functions, respectively, their symmetry groups and Fourier analysis. This can be done in terms of a unified framework based on the use of rigged Hilbert spaces. We find a relation between the universal enveloping algebra of the symmetry groups with the fractional Fourier transform. The results obtained are relevant in quantum mechanics as well as in signal processing as Fourier analysis has a close relation with signal filters. In addition, we introduce some new results concerning a discretized Fourier transform on the circle. We introduce new functions on the circle constructed with the use of Hermite functions with interesting properties under Fourier transformations.

Texture discrimination and Fourier analysis in human vision

Nature ◽  
1978 ◽  
Vol 275 (5679) ◽  
pp. 438-439 ◽  
Author(s):  
J. E. W. MAYHEW ◽  
J. P. FRISBY
Keyword(s):  
Fourier Analysis ◽  
Human Vision ◽  
Texture Discrimination
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