ted in the first stage of retinal processing, the photoreceptor layer. In this work we measure the spectral distributions of light present in natural images by using a hyperspectral camera, 12--15 which provides a complete spectrum at each pixel. We derive human cone responses at each spatial location from the spectra, and from these we gather cone response statistics for analysis. This approach is related to that of Webster and Mollon, with the key difference that whereas they contrast the differences between various images, we study the ensemble statistics as averaged over images. Our results are qualitatively similar to those of Buchsbaum and Gottschalk, who sought to understand theoretically, by using model stimuli, how the visual system might decorrelate natural cone signals through an orthogonal linear transformation. They found that under certain conditions this can be achieved through a transformation to a luminancelike channel and a pair of blue-- yellow and red--gre

Statistical analysis of images reveals two interesting properties: (i) invariance of image statistics to scaling of images, and (ii) non-Gaussian behavior of image statistics, i.e. high kurtosis, heavy tails, and sharp central cusps. In this paper we review some recent results in statistical modeling of natural images that attempt to explain these patterns. Two categories of results are considered: (i) studies of probability models of images or image decompositions (such as Fourier or wavelet decompositions), and (ii) discoveries of underlying image manifolds while restricting to natural images. Applications of these models in areas such as texture analysis, image classification, compression, and denoising are also considered.

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One of the most robust qualities of our visual world is the scaleinvariance of natural images. Not only has scaling been found in different visual environments, but the phenomenon also appears to be calibration independent. This paper proposes a simple property of natural images which explains this robustness: They are collages of regions corresponding to statistically independent "objects". Evidence is provided for these objects having a power-law distribution of sizes within images, from which follows scaling in natural images. It is commonly suggested that scaling instead results from edges, each with power spectrum 1/k². This hypothesis is refuted by example.

The paper proposes a number of models to examine through what mech-anisms a population of autonomous agents could arrive at a repertoire of perceptually grounded categories that is sufficiently shared to allow successful communication. The models are inspired by the main approaches to human categorisation being discussed in the literature: nativism, empiricism, and culturalism. Colour is taken as a case study. Although the paper takes no stance on which position is to be accepted as final truth with respect to hu-man categorisation and naming, it points to theoretical constraints that make each position more or less likely and contains clear suggestions on what the best engineering solution would be. Specifically, it argues that the collective choice of a shared repertoire must integrate multiple constraints, including constraints coming from communication.

The spatial filtering applied by the human visual system appears to be low-pass for chromatic stimuli and band-pass for luminance stimuli. Here we explore whether this observed difference in contrast sensitivity reflects a real difference in the components of chrominance and luminance in natural scenes. For this purpose a digital set of 29 hyper-spectral images of natural scenes has been acquired and its spatial frequency content analyzed in terms of chrominance and luminance defined according to existing models of the human cone responses and visual signal processing. The statistical 1/f amplitude spatial frequency distribution is confirmed for a variety of chromatic conditions across the visible spectrum. Our analysis suggests that natural scenes are relatively rich in high spatial-frequency chrominance information which does not appear to be transmitted by the human visual system. This result is unlikely to have arisen from errors in the original measurements. Several reasons may combine to explain a failure to transmit high spatial-frequency chrominance: (a) its minor importance for primate visual tasks, (b) its removal by filtering applied to compensate for chromatic aberration of the eye's optics, or (c) a biological bottleneck blocking its transmission. In addition, we graphically compare the ratios of luminance to chrominance measured by our hyperspectral camera and those measured psychophysically over an equivalent spatial frequency range. 1

Natural images contain an overwhelming number of visual patterns generated by diverse stochastic processes. Defining and modeling these patterns is of fundamental importance for generic vision tasks, such as perceptual organization, segmentation, and recognition. The objective of this epistemological paper is to summarize various threads of research in the literature and to pursue a unified framework for conceptualization, modeling, learning, and computing visual patterns. This paper starts with reviewing four research streams: 1) the study of image statistics, 2) the analysis of image components, 3) the grouping of image elements, and 4) the modeling of visual patterns. The models from these research streams are then divided into four categories according to their semantic structures: 1) descriptive models, i.e., Markov random fields (MRF) or Gibbs, 2) variants of descriptive models (causal MRF and "pseudodescriptive" models), 3) generative models, and 4) discriminative models. The objectives, principles, theories, and typical models are reviewed in each category and the relationships between the four types of models are studied. Two central themes emerge from the relationship studies.

A number of researchers have suggested that in order to understand the response properties of cells in the visual pathway, we must consider the statistical structure of the natural environment. In this paper, we focus on one aspect of that structure, namely, the correlational structure which is described by the amplitude or power spectra of natural scenes. We propose that the principle insight one gains from considering the image spectra is in understanding the relative sensitivity of cells tuned to different spatial frequencies. This study employs a model in which the peak sensitivity is constant as a function of frequency with linear bandwith increasing (i.e., approximately constant in octaves). In such a model, the "response magnitude " (i.e., vector length) of cells increases as a function of their optimal (or central) spatial frequency out to about 20 cyc/deg. The result is a code in which the response to natural scenes, whose amplitude spectra typically fall as 1/f, is roughly constant out to 20 cyc/deg. An important consideration in evaluating this model of sensitivity is the fact that natural scenes show considerable variability in their amplitude spectra, with individual scenes showing falloffs which are often steeper or shallower than 1/f. Using a new measure of image structure (the "rectified contrast spectrum " or "RCS") on a set of calibrated natural images, it is shown that a large part of the variability in the spectra is due to differences in the sparseness of local

A major problem a visual system faces is how to fit the large intensity variation of natural image streams into the limited dynamic range of its neurons. One of the means to accomplish this is through the use of gain control. In order to investigate this, natural time series of intensities were measured, as well as the responses of blowfly photoreceptors and Large Monopolar Cells (LMCs) to these time series. Time series representative of what each photoreceptor of a real visual system would normally receive were measured with an optical system measuring the light intensity of a spot comparable to the field of view of single human foveal cones. This system was worn on a head-band by a freely walking person. Resulting time series have rms-contrasts ranging from an average of 0.45 for 1 second segments to 1.39 for 100 second segments (both when limited to frequencies up to 100 Hz). Power spectra behave approximately as 1/f (f: temporal frequency). Measured time series were subsequently presented to fly photoreceptors and LMCs by playing them back on an LED. The results show that fast gain controls indeed keep the response within the dynamic range of the cells and that a large part of this range is actually used for packing the information in natural time series.

We examined contrast sensitivity and suprathreshold apparent contrast with natural images. The spatialfrequency components within single octaves of the images were removed (notch filtered), their phases were randomized, or the polarity of the images was inverted. Of Michelson contrast, root-mean-square (RMS) contrast, and band-limited contrast, RMS contrast was the best index of detectability. Negative images had lower apparent contrast than their positives. Contrast detection thresholds showed spatial-frequency-dependent elevation following both notch filtering and phase randomization. The peak of the spatial-frequency tuning function was approximately 0.5–2 cycles per degree (c/deg). Suprathreshold contrast matching functions also showed spatial-frequency-dependent contrast loss for both notch-filtered and phase-randomized images. The peak of the spatial-frequency tuning function was approximately 1–3 c/deg. There was no detectable difference between the effects of phase randomization and notch filtering on contrast sensitivity. We argue that these observations are consistent with changes in the activity within spatial-frequency channels caused by the higher-order phase structure of natural images that is responsible for the presence of edges and specularities.