Estimating information from image colors: an application to digital cameras and natural scenes

Little information loss with red-green color deficient vision in natural environments

Inherited color vision deficiency affects red-green discrimination in about one in twelve men from European populations. Its effects have been studied mainly in primitive foraging but also in detecting blushing and breaking camouflage. Yet there is no obvious relationship between these specific tasks and vision in the real world. The aim here was to quantify the impact of color vision deficiency by estimating computationally the information available to observers about colored surfaces in natural scenes. With representative independent sets of 50 and 100 hyperspectral images, estimated information was found to be only a little less in red-green color vision deficiency than in normal trichromacy. Colorimetric analyses revealed the importance of large lightness variations within scenes, small redness-greenness variations, and uneven frequencies of different colored surfaces. While red-green color vision deficiency poses challenges in some tasks, it has much less effect on gaining information from natural environments.

Efficient quantization of painting images by relevant colors

Realistic images often contain complex variations in color, which can make economical descriptions difficult. Yet human observers can readily reduce the number of colors in paintings to a small proportion they judge as relevant. These relevant colors provide a way to simplify images by effectively quantizing them. The aim here was to estimate the information captured by this process and to compare it with algorithmic estimates of the maximum information possible by colorimetric and general optimization methods. The images tested were of 20 conventionally representational paintings. Information was quantified by Shannon's mutual information. It was found that the estimated mutual information in observers' choices reached about 90% of the algorithmic maxima. For comparison, JPEG compression delivered somewhat less. Observers seem to be efficient at effectively quantizing colored images, an ability that may have applications in the real world.

Information Flow in Biological Networks for Color Vision

Biological neural networks for color vision (also known as color appearance models) consist of a cascade of linear + nonlinear layers that modify the linear measurements at the retinal photo-receptors leading to an internal (nonlinear) representation of color that correlates with psychophysical experience. The basic layers of these networks include: (1) chromatic adaptation (normalization of the mean and covariance of the color manifold); (2) change to opponent color channels (PCA-like rotation in the color space); and (3) saturating nonlinearities to obtain perceptually Euclidean color representations (similar to dimension-wise equalization). The Efficient Coding Hypothesis argues that these transforms should emerge from information-theoretic goals. In case this hypothesis holds in color vision, the question is what is the coding gain due to the different layers of the color appearance networks? In this work, a representative family of color appearance models is analyzed in terms of how the redundancy among the chromatic components is modified along the network and how much information is transferred from the input data to the noisy response. The proposed analysis is performed using data and methods that were not available before: (1) new colorimetrically calibrated scenes in different CIE illuminations for the proper evaluation of chromatic adaptation; and (2) new statistical tools to estimate (multivariate) information-theoretic quantities between multidimensional sets based on Gaussianization. The results confirm that the efficient coding hypothesis holds for current color vision models, and identify the psychophysical mechanisms critically responsible for gains in information transference: opponent channels and their nonlinear nature are more important than chromatic adaptation at the retina.

Information gains from commercial spectral filters in anomalous trichromacy

Red-green color discrimination is compromised in anomalous trichromacy, the most common inherited color vision deficiency. This computational analysis tested whether three commercial optical filters with medium-to-long-wavelength stop bands increased information about colored surfaces. The surfaces were sampled from 50 hyperspectral images of outdoor scenes. At best, potential gains in the effective number of surfaces discriminable solely by color reached 9% in protanomaly and 15% in deuteranomaly, much less than with normal trichromacy. Gains were still less with lower scene illumination and more severe color vision deficiency. Stop-band filters may offer little improvement in objective real-world color discrimination.

Application of offset estimator of differential entropy and mutual information with multivariate data

Numerical estimators of differential entropy and mutual information can be slow to converge as sample size increases. The offset Kozachenko–Leonenko (KLo) method described here implements an offset version of the Kozachenko–Leonenko estimator that can markedly improve convergence. Its use is illustrated in applications to the comparison of trivariate data from successive scene color images and the comparison of univariate data from stereophonic music tracks. Publicly available code for KLo estimation of both differential entropy and mutual information is provided for R, Python, and MATLAB computing environments at https://github.com/imarinfr/klo.

Fluctuating environmental light limits number of surfaces visually recognizable by colour

Small changes in daylight in the environment can produce large changes in reflected light, even over short intervals of time. Do these changes limit the visual recognition of surfaces by their colour? To address this question, information-theoretic methods were used to estimate computationally the maximum number of surfaces in a sample that can be identified as the same after an interval. Scene data were taken from successive hyperspectral radiance images. With no illumination change, the average number of surfaces distinguishable by colour was of the order of 10,000. But with an illumination change, the average number still identifiable declined rapidly with change duration. In one condition, the number after two minutes was around 600, after 10 min around 200, and after an hour around 70. These limits on identification are much lower than with spectral changes in daylight. No recoding of the colour signal is likely to recover surface identity lost in this uncertain environment.

Spatio-chromatic information available from different neural layers via Gaussianization

How much visual information about the retinal images can be extracted from the different layers of the visual pathway? This question depends on the complexity of the visual input, the set of transforms applied to this multivariate input, and the noise of the sensors in the considered layer. Separate subsystems (e.g. opponent channels, spatial filters, nonlinearities of the texture sensors) have been suggested to be organized for optimal information transmission. However, the efficiency of these different layers has not been measured when they operate together on colorimetrically calibrated natural images and using multivariate information-theoretic units over the joint spatio-chromatic array of responses.In this work, we present a statistical tool to address this question in an appropriate (multivariate) way. Specifically, we propose an empirical estimate of the information transmitted by the system based on a recent Gaussianization technique. The total correlation measured using the proposed estimator is consistent with predictions based on the analytical Jacobian of a standard spatio-chromatic model of the retina-cortex pathway. If the noise at certain representation is proportional to the dynamic range of the response, and one assumes sensors of equivalent noise level, then transmitted information shows the following trends: (1) progressively deeper representations are better in terms of the amount of captured information, (2) the transmitted information up to the cortical representation follows the probability of natural scenes over the chromatic and achromatic dimensions of the stimulus space, (3) the contribution of spatial transforms to capture visual information is substantially greater than the contribution of chromatic transforms, and (4) nonlinearities of the responses contribute substantially to the transmitted information but less than the linear transforms.

Hyperspectral imaging in color vision research: tutorial

This tutorial offers an introduction to terrestrial and close-range hyperspectral imaging and some of its uses in human color vision research. The main types of hyperspectral cameras are described together with procedures for image acquisition, postprocessing, and calibration for either radiance or reflectance data. Image transformations are defined for colorimetric representations, color rendering, and cone receptor and postreceptor coding. Several example applications are also presented. These include calculating the color properties of scenes, such as gamut volume and metamerism, and analyzing the utility of color in observer tasks, such as identifying surfaces under illuminant changes. The effects of noise and uncertainty are considered in both image acquisition and color vision applications.

The Verriest Lecture: Color vision in an uncertain world

The natural world is optically unconstrained. Surface properties may vary from one point to another, and reflected light may vary from one instant to the next. The aim of this work is to quantify some of the physical failures of color vision performance that result from uncertainty. In computational simulations with images of vegetated and nonvegetated outdoor scenes, it is shown that color provides an unreliable guide to surface identity. It is also shown that changes in illuminant may cause colors to no longer match and the relations between individual colors to vary. These failures are generally well described by a measure of the randomness of the colors in scenes, the Shannon entropy. Although uncertainty is intrinsic to the environment, its consequences for color vision can be predicted.

Improving color constancy by discounting the variation of camera spectral sensitivity

It is an ill-posed problem to recover the true scene colors from a color biased image by discounting the effects of scene illuminant and camera spectral sensitivity (CSS) at the same time. Most color constancy (CC) models have been designed to first estimate the illuminant color, which is then removed from the color biased image to obtain an image taken under white light, without the explicit consideration of CSS effect on CC. This paper first studies the CSS effect on illuminant estimation arising in the inter-dataset-based CC (inter-CC), i.e., training a CC model on one dataset and then testing on another dataset captured by a distinct CSS. We show the clear degradation of existing CC models for inter-CC application. Then a simple way is proposed to overcome such degradation by first learning quickly a transform matrix between the two distinct CSSs (CSS-1 and CSS-2). The learned matrix is then used to convert the data (including the illuminant ground truth and the color-biased images) rendered under CSS-1 into CSS-2, and then train and apply the CC model on the color-biased images under CSS-2 without the need of burdensome acquiring of the training set under CSS-2. Extensive experiments on synthetic and real images show that our method can clearly improve the inter-CC performance for traditional CC algorithms. We suggest that, by taking the CSS effect into account, it is more likely to obtain the truly color constant images invariant to the changes of both illuminant and camera sensors.

Metrics and statistics of frequency of occurrence of metamerism in consumer cameras for natural scenes

This paper presents metrics and statistics of frequency of occurrence of metamerism in three consumer cameras, viz., Canon 1D Mark III, Nikon D40, and Sony α7, using spectral and RGB images of natural scenes. Both sensor metamerism and observer metamerism of the cameras' sensors are studied. We use the concept of dissimilarity of two spectral power distributions in the spectral domain and the RGB domain for studying the occurrence sensor metamerism. Specifically, we use angular difference and digital equivalence approaches for this purpose. For studying the occurrence observer metamerism, we use the weighted Nimeroff's index for dissimilarity in the spectral domain with respect to the CIE color space along with the conventionally used CIE LAB color difference for dissimilarity in the CIE color space. The statistics of the frequency of occurrence of metamerism are generated on a dataset of 423 spectral images of indoor scenes in 5 illumination conditions and outdoor scenes in natural illumination conditions. Experiments show that about 18%-22% of the pixels in the images are metameric in the sense of angular difference. It is also observed that 1%-4% of the colors that would have appeared similar to human eyes are reproduced as distinct colors in the cameras. Dataset and details can be found at https://sites.google.com/site/dilipprasad/source-codes.

Time-lapse ratios of cone excitations in natural scenes

The illumination in natural environments varies through the day. Stable inferences about surface color might be supported by spatial ratios of cone excitations from the reflected light, but their invariance has been quantified only for global changes in illuminant spectrum. The aim here was to test their invariance under natural changes in both illumination spectrum and geometry, especially in the distribution of shadows. Time-lapse hyperspectral radiance images were acquired from five outdoor vegetated and nonvegetated scenes. From each scene, 10,000 pairs of points were sampled randomly and ratios measured across time. Mean relative deviations in ratios were generally large, but when sampling was limited to short distances or moderate time intervals, they fell below the level for detecting violations in ratio invariance. When illumination changes with uneven geometry were excluded, they fell further, to levels obtained with global changes in illuminant spectrum alone. Within sampling constraints, ratios of cone excitations, and also of opponent-color combinations, provide an approximately invariant signal for stable surface-color inferences, despite spectral and geometric variations in scene illumination.

Spectral sharpening of color sensors: diagonal color constancy and beyond

It has now been 20 years since the seminal work by Finlayson et al. on the use of spectral sharpening of sensors to achieve diagonal color constancy. Spectral sharpening is still used today by numerous researchers for different goals unrelated to the original goal of diagonal color constancy e.g., multispectral processing, shadow removal, location of unique hues. This paper reviews the idea of spectral sharpening through the lens of what is known today in color constancy, describes the different methods used for obtaining a set of sharpening sensors and presents an overview of the many different uses that have been found for spectral sharpening over the years.