Image quality and perception: introduction.

This feature issue focuses on image quality and perception, including image and video quality, subjective and objective quality, and enhancement. The feature issue contains papers on several important topics, such as contrast discrimination, analysis of color imaging in cameras, image quality assessment, and more. The papers represent different important aspects in image quality and perception, contributing to the advancement of the field.

The Quantum Nature of Color Perception: Uncertainty Relations for Chromatic Opposition.

In this paper, we provide an overview on the foundation and first results of a very recent quantum theory of color perception, together with novel results about uncertainty relations for chromatic opposition. The major inspiration for this model is the 1974 remarkable work by H.L. Resnikoff, who had the idea to give up the analysis of the space of perceived colors through metameric classes of spectra in favor of the study of its algebraic properties. This strategy permitted to reveal the importance of hyperbolic geometry in colorimetry. Starting from these premises, we show how Resnikoff's construction can be extended to a geometrically rich quantum framework, where the concepts of achromatic color, hue and saturation can be rigorously defined. Moreover, the analysis of pure and mixed quantum chromatic states leads to a deep understanding of chromatic opposition and its role in the encoding of visual signals. We complete our paper by proving the existence of uncertainty relations for the degree of chromatic opposition, thus providing a theoretical confirmation of the quantum nature of color perception.

Geometry of color perception. Part 1: structures and metrics of a homogeneous color space.

This is the first half of a two-part paper dealing with the geometry of color perception. Here we analyze in detail the seminal 1974 work by H.L. Resnikoff, who showed that there are only two possible geometric structures and Riemannian metrics on the perceived color space [Formula: see text] compatible with the set of Schrödinger's axioms completed with the hypothesis of homogeneity. We recast Resnikoff's model into a more modern colorimetric setting, provide a much simpler proof of the main result of the original paper, and motivate the need of psychophysical experiments to confute or confirm the linearity of background transformations, which act transitively on [Formula: see text]. Finally, we show that the Riemannian metrics singled out by Resnikoff through an axiom on invariance under background transformations are not compatible with the crispening effect, thus motivating the need of further research about perceptual color metrics.

Origins of Hyperbolicity in Color Perception.

In 1962, H. Yilmaz published a very original paper in which he showed the striking analogy between Lorentz transformations and the effect of illuminant changes on color perception. As a consequence, he argued that a perceived color space endowed with the Minkowski metric is a good approximation to model color vision. The contribution of this paper is twofold: firstly, we provide a mathematical formalization of Yilmaz's argument about the relationship between Lorentz transformations and the perceptual effect of illuminant changes. Secondly, we show that, within Yilmaz's model, the color space can be coherently endowed with the Minkowski metric only by imposing the Euclidean metric on the hue-chroma plane. This fact motivates the need of further investigation about both the proper definition and interrelationship among the color coordinates and also the geometry and metrics of perceptual color spaces.

On the second order spatiochromatic structure of natural images.

We provide a theoretical analysis of some empirical facts about the second order spatiochromatic structure of natural images in color. In particular, we show that two simple assumptions on the covariance matrices of color images yield eigenvectors made by the Kronecker product of Fourier features times the triad given by luminance plus color opponent channels. The first of these assumptions is second order stationarity while the second one is commutativity between color correlation matrices. The validity of these assumptions and the predicted shape of the PCA components of color images are experimentally observed on two large image databases. As a by-product of this experimental study, we also provide novel data to support an exponential decay law of the spatiochromatic covariance between pairs of pixels as a function of their spatial distance.

An Analysis of Visual Adaptation and Contrast Perception for Tone Mapping.

Tone Mapping is the problem of compressing the range of a High-Dynamic Range image so that it can be displayed in a Low-Dynamic Range screen, without losing or introducing novel details: The final image should produce in the observer a sensation as close as possible to the perception produced by the real-world scene. We propose a tone mapping operator with two stages. The first stage is a global method that implements visual adaptation, based on experiments on human perception, in particular we point out the importance of cone saturation. The second stage performs local contrast enhancement, based on a variational model inspired by color vision phenomenology. We evaluate this method with a metric validated by psychophysical experiments and, in terms of this metric, our method compares very well with the state of the art.

A perceptually inspired variational framework for color enhancement.

Basic phenomenology of human color vision has been widely taken as an inspiration to devise explicit color correction algorithms. The behavior of these models in terms of significative image features (such as, e.g., contrast and dispersion) can be difficult to characterize. To cope with this, we propose to use a variational formulation of color contrast enhancement that is inspired by the basic phenomenology of color perception. In particular, we devise a set of basic requirements to be fulfilled by an energy to be considered as 'perceptually inspired', showing that there is an explicit class of functionals satisfying all of them. We single out three explicit functionals that we consider of basic interest, showing similarities and differences with existing models. The minima of such functionals is computed using a gradient descent approach. We also present a general methodology to reduce the computational cost of the algorithms under analysis from O(N2) to O(N logN), being N the number of pixels of the input image.

A spatially variant white-patch and gray-world method for color image enhancement driven by local contrast.

Starting from the revolutionary Retinex by Land and McCann, several further perceptually inspired color correction models have been developed with different aims, e.g. reproduction of color sensation, robust features recognition, enhancement of color images. Such models have a differential, spatially-variant and non-linear nature and they can coarsely be distinguished between white-patch (WP) and gray-world (GW) algorithms. In this paper we show that the combination of a pure WP algorithm (Random Spray Retinex (RSR) )and an essentially GW one (Automatic Color Equalization (ACE)) leads to a more robust and better performing model (RACE). The choice of RSR and ACE follows from the recent identification of a unified spatially-variant approach for both algorithms. Mathematically, the originally distinct non-linear and differential mechanisms of RSR and ACE have been fused using the spray technique and local average operations. The investigation of RACE allowed us to put in evidence a common drawback of differential models: corruption of uniform image areas. To overcome this intrinsic defect, we devised a local and global contrast-based and image-driven regulation mechanism that has a general applicability to perceptually inspired color correction algorithms. Tests, comparisons and discussions are presented.

Perceptual color correction through variational techniques.

In this paper, we present a discussion about perceptual-based color correction of digital images in the framework of variational techniques. We propose a novel image functional whose minimization produces a perceptually inspired color enhanced version of the original. The variational formulation permits a more flexible local control of contrast adjustment and attachment to data. We show that a numerical implementation of the gradient descent technique applied to this energy functional coincides with the equation of automatic color enhancement (ACE), a particular perceptual-based model of color enhancement. Moreover, we prove that a numerical approximation of the Euler-Lagrange equation reduces the computational complexity of ACE from theta(N2) to theta(N log N), where N is the total number of pixels in the image.

Random spray Retinex: a new Retinex implementation to investigate the local properties of the model.

In order to investigate the local filtering behavior of the Retinex model, we propose a new implementation in which paths are replaced by 2-D pixel sprays, hence the name "random spray Retinex." A peculiar feature of this implementation is the way its parameters can be controlled to perform spatial investigation. The parameters' tuning is accomplished by an unsupervised method based on quantitative measures. This procedure has been validated via user panel tests. Furthermore, the spray approach has faster performances than the path-wise one. Tests and results are presented and discussed.

Mathematical definition and analysis of the retinex algorithm.

We present a detailed mathematical analysis of the original Retinex algorithm due to Land and McCann [J. Opt. Soc. Am. 61, 1 (1071)]. To this end, we propose an analytic formula that describes the algorithm behavior. More than one Retinex version (e.g., with and without threshold) is examined. The behavior of Retinex varying the number of paths is predicted, and its recursive iterations are mathematically analyzed using the formula. The mathematical setting presented serves as a common ground for the various Retinex implementations. Its validity is confirmed by the tests on images that we have performed.