Multiresolution representations are effective for analyzing the information content of images. The properties of the operator which approximates a signal at a given resolution were studied. It is shown that the difference of information between the approximation of a signal at the resolutions 2/sup j+1/ and 2/sup j/ (where j is an integer) can be extracted by decomposing this signal on a wavelet orthonormal basis of L/sup 2/(R/sup n/), the vector space of measurable, square-integrable n-dimensional functions. In L/sup 2/(R), a wavelet orthonormal basis is a family of functions which is built by dilating and translating a unique function psi (x). This decomposition defines an orthogonal multiresolution representation called a wavelet representation. It is computed with a pyramidal algorithm based on convolutions with quadrature mirror filters. Wavelet representation lies between the spatial and Fourier domains. For images, the wavelet representation differentiates several spatial orientations. The application of this representation to data compression in image coding, texture discrimination and fractal analysis is discussed. >

/pdf/a-theory-for-multiresolution-signal-decomposition-the-530tw5pzq7.pdf

A theory for multiresolution signal decomposition: the wavelet representation

A theory of edge detection is presented. The analysis proceeds in two parts. (1) Intensity changes, which occur in a natural image over a wide range of scales, are detected separately at different scales. An appropriate filter for this purpose at a given scale is found to be the second derivative of a Gaussian, and it is shown that, provided some simple conditions are satisfied, these primary filters need not be orientation-dependent. Thus, intensity changes at a given scale are best detected by finding the zero values of delta 2G(x,y)*I(x,y) for image I, where G(x,y) is a two-dimensional Gaussian distribution and delta 2 is the Laplacian. The intensity changes thus discovered in each of the channels are then represented by oriented primitives called zero-crossing segments, and evidence is given that this representation is complete. (2) Intensity changes in images arise from surface discontinuities or from reflectance or illumination boundaries, and these all have the property that they are spatially. Because of this, the zero-crossing segments from the different channels are not independent, and rules are deduced for combining them into a description of the image. This description is called the raw primal sketch. The theory explains several basic psychophysical findings, and the operation of forming oriented zero-crossing segments from the output of centre-surround delta 2G filters acting on the image forms the basis for a physiological model of simple cells (see Marr & Ullman 1979).

http://www.hms.harvard.edu/bss/neuro/bornlab/qmbc/beta/day4/marr-hildreth-edge-prsl1980.pdf

Theory of Edge Detection

In this paper, we propose a computational model of the recognition of real world scenes that bypasses the segmentation and the processing of individual objects or regions. The procedure is based on a very low dimensional representation of the scene, that we term the Spatial Envelope. We propose a set of perceptual dimensions (naturalness, openness, roughness, expansion, ruggedness) that represent the dominant spatial structure of a scene. Then, we show that these dimensions may be reliably estimated using spectral and coarsely localized information. The model generates a multidimensional space in which scenes sharing membership in semantic categories (e.g., streets, highways, coasts) are projected closed together. The performance of the spatial envelope model shows that specific information about object shape or identity is not a requirement for scene categorization and that modeling a holistic representation of the scene informs about its probable semantic category.

Modeling the Shape of the Scene: A Holistic Representation of the Spatial Envelope

Recent studies of eye movements in reading and other information processing tasks, such as music reading, typing, visual search, and scene perception, are reviewed. The major emphasis of the review is on reading as a specific example of cognitive processing. Basic topics discussed with respect to reading are (a) the characteristics of eye movements, (b) the perceptual span, (c) integration of information across saccades, (d) eye movement control, and (e) individual differences (including dyslexia). Similar topics are discussed with respect to the other tasks examined. The basic theme of the review is that eye movement data reflect moment-to-moment cognitive processes in the various tasks examined. Theoretical and practical considerations concerning the use of eye movement data are also discussed.

/pdf/eye-movements-in-reading-and-information-processing-20-years-3z5ay8hdwc.pdf

Eye movements in reading and information processing: 20 years of research.

Psychophysical and physiological evidence indicates that the visual system of primates and humans has evolved a specialized processing focus moving across the visual scene. This study addresses the question of how simple networks of neuron-like elements can account for a variety of phenomena associated with this shift of selective visual attention. Specifically, we propose the following: (1) A number of elementary features, such as color, orientation, direction of movement, disparity etc. are represented in parallel in different topographical maps, called the early representation. (2) There exists a selective mapping from the early topographic representation into a more central non-topographic representation, such that at any instant the central representation contains the properties of only a single location in the visual scene, the selected location. We suggest that this mapping is the principal expression of early selective visual attention. One function of selective attention is to fuse information from different maps into one coherent whole. (3) Certain selection rules determine which locations will be mapped into the central representation. The major rule, using the conspicuity of locations in the early representation, is implemented using a so-called Winner-Take-All network. Inhibiting the selected location in this network causes an automatic shift towards the next most conspicious location. Additional rules are proximity and similarity preferences. We discuss how these rules can be implemented in neuron-like networks and suggest a possible role for the extensive back-projection from the visual cortex to the LGN.

Shifts in selective visual attention: towards the underlying neural circuitry.

1. The contrast thresholds of a variety of grating patterns have been measured over a wide range of spatial frequencies.2. Contrast thresholds for the detection of gratings whose luminance profiles are sine, square, rectangular or saw-tooth waves can be simply related using Fourier theory.3. Over a wide range of spatial frequencies the contrast threshold of a grating is determined only by the amplitude of the fundamental Fourier component of its wave form.4. Gratings of complex wave form cannot be distinguished from sine-wave gratings until their contrast has been raised to a level at which the higher harmonic components reach their independent threshold.5. These findings can be explained by the existence within the nervous system of linearly operating independent mechanisms selectively sensitive to limited ranges of spatial frequencies.

Application of fourier analysis to the visibility of gratings

1. It was found that an occipital evoked potential can be elicited in the human by moving a grating pattern without changing the mean light flux entering the eye. Prolonged viewing of a high contrast grating reduces the amplitude of the potential evoked by a low contrast grating.

2. This adaptation to a grating was studied psychophysically by determining the contrast threshold before and after adaptation. There is a temporary fivefold rise in contrast threshold after exposure to a high contrast grating of the same orientation and spatial frequency.

3. By determining the rise of threshold over a range of spatial frequency for a number of adapting frequencies it was found that the threshold elevation is limited to a spectrum of frequencies with a bandwidth of just over an octave at half amplitude, centred on the adapting frequency.

4. The amplitude of the effect and its bandwidth are very similar for adapting spatial frequencies between 3 c/deg. and 14 c/deg. At higher frequencies the bandwidth is slightly narrower. For lower adapting frequencies the peak of the effect stays at 3 c/deg.

5. These and other findings suggest that the human visual system may possess neurones selectively sensitive to spatial frequency and size. The orientational selectivity and the interocular transfer of the adaptation effect implicate the visual cortex as the site of these neurones.

6. This neural system may play an essential preliminary role in the recognition of complex images and generalization for magnification.

/pdf/on-the-existence-of-neurones-in-the-human-visual-system-3pxi9uujkp.pdf

On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images.

If a scene containing fine spatial detail is viewed at constant high photopic luminance, there are two main factors which limit the perception of the fine detail-the quality of the optics of the eye forming the image on the retina and the ability of the retina (coupled to the brain) to resolve the details of that image. In the past there have been many theoretical studies of the potential resolving power of the optics based on consideration of diffraction and the chromatic and spherical aberrations of the eye. It is only recently that objective measurements of the quality of the optics of man in vivo have been obtained (Flamant, 1955; Westheimer & Campbell, 1962; Krauskopf 1962; R6hler, 1962). As will be demonstrated, it is not possible to use these findings to determine the relative weighting that should be given to the optics and the retina in determining a given threshold. This paper reports the results of experiments using an improved version of the well-known interference fringe technique (Le Grand, 1937; Byram 1944; Westheimer, 1960; Arnulf & Dupuy, 1960) which theoretically allows a sinusoidal pattern of very high contrast to be formed directly on the retina. The practical difficulty in using this technique is to obtain a light source of high intrinsic brightness and coherence with which to form high-luminance interference fringes on the retina; this has been solved by using a neon-helium gas laser. By decreasing the contrast (Fig. 1) of the interference fringes with another source of light it was possible to determine the contrasts on the retina at which the fringes are just detected. Thus a measure of the resolving power of the retina-brain is obtained without prior modification by the optics of the eye. Measurements have also been made of the visual resolution of external gratings whose intensity varied sinusoidally with distance across the gratings and which were imaged on to the retina by the optical components of the eye. By comparing the threshold contrasts of these external sinusoidal gratings with thresholds for sinusoidal fringes of the same spatial frequency formed through interference, the quality of the

https://physoc.onlinelibrary.wiley.com/doi/pdf/10.1113/jphysiol.1965.sp007784

Optical and retinal factors affecting visual resolution.

1. Optical quality of the eye was measured at eight pupil sizes between 1.5 and 6.6 mm diameter by recording the faint light emerging from the eye; this light was reflected from the bright image of a thin line on the fundus.2. The nature of the fundus reflexion was examined; it was found that the fundus acts very much like a perfect diffuser while retaining polarization.3. Using the result that the fundus acts like a diffuser, the recorded line images were Fourier analysed to provide modulation transfer functions. These functions indicate an optical quality considerably higher than that found in previous physical studies.4. Linespread profiles were then derived from the modulation transfer functions. These profiles are 40% narrower than those of previous physical studies for a 3.0 mm pupil. The narrowest profile occurred with a 2.4 mm pupil.5. Our results demonstrate that physical and psychophysical studies can yield similar estimates of optical quality. The influence of optical factors not common to both techniques is discussed. Evidence for the existence of neural ;image sharpening' mechanisms is reviewed.

Optical quality of the human eye.

THIS communication describes experiments in which the threshold contrast of gratings viewed monocularly and binocularly have been determined (Fig. 1). We have modified the technique of Schade1 so that a grating target is generated on an oscilloscope by supplying suitable signals to the x, y and z axes. It could be continuously varied both in contrast and fineness (spatial frequency) without the mean luminance of the screen changing. The energy distribution across the grating varied sinuosoidally. The grating filled a rectangular area subtending 2° by 1.3°, and was surrounded by a circular field of 12° diameter of the same luminance as the oscilloscope screen (80 cd/m2). The screen was viewed from 57 in., and in all the experiments particular care was taken to correct the eye to within 0.12 diopter with spectacle lenses.

F. W. Campbell

Papers

Application of fourier analysis to the visibility of gratings

On the existence of neurones in the human visual system selectively sensitive to the orientation and size of retinal images.

Optical and retinal factors affecting visual resolution.

Optical quality of the human eye.

Monocular versus Binocular Visual Acuity