Application of two-dimensional Fourier transforms to problems of visual perception (original) (raw)
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Perception, 2001
The historical roots of the Fourier theory of spatial visual perception are traced. The development of the underlying concepts and the psychophysical experiments that led to them, and that they in turn spawned, are examined, as well as their relation to the current knowledge of neural substrates in the retina and primary visual cortex. Allowing nonlinearities or even substituting other types of basis functions does not eliminate the difficulties faced by any theory of visual perception that is built on the notion of fixed spatial filters.
Spatial Frequency Analysis in the Visual System
Annual Review of Neuroscience, 1985
Within the last 15 years, a method called "spatial frequency analysis" has been applied widely to the study of receptive fields of neurons in the visual pathway. Out of this work have emerged new concepts of how the brain analyzes and recognizes visual images. The aim of this paper is to explain why "spatial frequency analysis" is useful, and to review the insights into visual function that have resulted from its application. It is important to note at the outset that while spatial frequency analysis can provide a comprehensive description of the behavior of neurons in which signals are summed linearly (see below), it has much more limited application to the behavior of neurons that combine signals nonlinearly. Because of this, the greatest insights into visual information processing have come and probably will continue to come from a combined use of space, time, spatial frequency, and temporal frequency measurements.
Geometric Fourier analysis for computational vision
Journal of Fourier Analysis and Applications, 2005
Projective Fourier analysis-geometric Fourier analysis of the group SL(2, C), the group identified in the conformal camera that provides image perspective transformations-is discussed in the framework of representation theory of semisimple Lie groups. The compact model of projective Fourier analysis is constructed, complementing the noncompact model proposed before. Detailed mathematical formulation of both models is presented. It is demonstrated that the projective Fourier analysis provides the data model for efficient perspectively covariant digital image representation well adapted to the retino-cortical mapping of biological visual system, and therefore, explicitly designed for the foveated sensors of a silicon retina, the use of which in active vision systems is presently limited due to the lack of such a model.
Channels for spatial frequency selection and the detection of single bars by the human visual system
Vision research, 1972
SEVERAL psychophysical experiments upon the visibility of sinusoidal and other periodic gratings have been interpreted as providing evidence that the human visual system contains channels tuned to specific spatial frequencies (CAMPBELL and ROBSON, 1968; BLAKEMORE and CAMPBELL, 1969; BLAKEMORE, NACHMIA~ and SUTTON, 1970). CAMPBELL and MAFFEI (1970) have also put forward electrophysiological evidence to support this view. At least two issues raised by this approach remain outstanding, and can be tackled by adaptation experiments of the type introduced by PANTLE and SEKULER (1968).
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Real-time Imaging, 1997
The use of visual representations in which pixel-size and local neighborhood topology are not constant is termed space-variant vision. This is the dominant visual architecture in all higher vertebrate visual systems, and is coming to play an important role in real-time active vision applications in the form of log-polar, foveating pyramid, and related approaches to machine vision.
Vision Research, 2005
Psychophysical thresholds were measured for discriminating small changes in spatial features of naturalistic scenes (morph sequences), for foveal and peripheral vision, and under M-scaling. Sensitivity was greatest for scenes with near natural Fourier amplitude slope, perhaps implying that human vision is optimised for natural scene statistics. A low-level model calculated differences in local contrast between pairs of images within a few spatial frequency channels with bandwidth like neurons in V1. The model was ''customised'' to each observerÕs contrast sensitivity function for sinusoidal gratings, and it could replicate the ''U-shaped'' relationships between discrimination threshold and spectral slope, and many differences between picture sets and observers. A single-channel model and an ideal-observer analysis both failed to capture the U-shape.