Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this paper, we propose a solution to this problem by using a family of rotation-based iterative Gaussianization (RBIG) transforms. The general framework consists of the sequential application of a univariate marginal Gaussianization transform followed by an orthonormal transform. The proposed procedure looks for differentiable transforms to a known PDF so that the unknown PDF can be estimated at any point of the original domain. In particular, we aim at a zero-mean unit-covariance Gaussian for convenience. RBIG is formally similar to classical iterative projection pursuit algorithms. However, we show that, unlike in PP methods, the particular class of rotations used has no special qualitative relevance in this context, since looking for interestingness is not a critical issue for PDF estimation. The key difference is that our approach focuses on the univariate part (marginal Gaussianization) of the problem rather than on the multivariate part (rotation). This difference implies that one may select the most convenient rotation suited to each practical application. The differentiability, invertibility, and convergence of RBIG are theoretically and experimentally analyzed. Relation to other methods, such as radial Gaussianization, one-class support vector domain description, and deep neural networks is also pointed out. The practical performance of RBIG is successfully illustrated in a number of multidimensional problems such as image synthesis, classification, denoising, and multi-information estimation.

Structural similarity metrics and information-theory-based metrics have been proposed as completely different alternatives to the traditional metrics based on error visibility and human vision models. Three basic criticisms were raised against the traditional error visibility approach: (1) it is based on near-threshold performance, (2) its geometric meaning may be limited, and (3) stationary pooling strategies may not be statistically justified. These criticisms and the good performance of structural and information-theory-based metrics have popularized the idea of their superiority over the error visibility approach. In this work we experimentally or analytically show that the above criticisms do not apply to error visibility metrics that use a general enough divisive normalization masking model. Therefore, the traditional divisive normalization metric [1] is not intrinsically inferior to the newer approaches. In fact, experiments on a number of databases including a wide range of distortions show that divisive normalization is fairly competitive with the newer approaches, robust, and easy to interpret in linear terms. These results suggest that, despite the criticisms of the traditional error visibility approach, divisive normalization masking models should be considered in the image quality discussion.

We present an adaptation algorithm focused on the description of the data changes under different acquisition conditions. When considering a source and a destination domain, the adaptation is carried out by transforming one data set to the other using an appropriate nonlinear deformation. The eventually nonlinear transform is based on vector quantization and graph matching. The transfer learning mapping is defined in an unsupervised manner. Once this mapping has been defined, the samples in one domain are projected onto the other, thus allowing the application of any classifier or regressor in the transformed domain. Experiments on challenging remote sensing scenarios, such as multitemporal very high resolution image classification and angular effects compensation, show the validity of the proposed method to match-related domains and enhance the application of cross-domains image processing techniques.

The conventional approach in computational neuroscience in favor of the efficient coding hypothesis goes from image statistics to perception. It has been argued that the behavior of the early stages of biological visual processing (e.g., spatial frequency analyzers and their nonlinearities) may be obtained from image samples and the efficient coding hypothesis using no psychophysical or physiological information. In this work we address the same issue in the opposite direction: from perception to image statistics. We show that psychophysically fitted image representation in V1 has appealing statistical properties, for example, approximate PDF factorization and substantial mutual information reduction, even though no statistical information is used to fit the V1 model. These results are complementary evidence in favor of the efficient coding hypothesis.

Mechanisms of human color vision are characterized by two phenomenological aspects: the system is nonlinear and adaptive to changing environments. Conventional attempts to derive these features from statistics use separate arguments for each aspect. The few statistical explanations that do consider both phenomena simultaneously follow parametric formulations based on empirical models. Therefore, it may be argued that the behavior does not come directly from the color statistics but from the convenient functional form adopted. In addition, many times the whole statistical analysis is based on simplified databases that disregard relevant physical effects in the input signal, as, for instance, by assuming flat Lambertian surfaces. In this work, we address the simultaneous statistical explanation of the nonlinear behavior of achromatic and chromatic mechanisms in a fixed adaptation state and the change of such behavior (i.e., adaptation) under the change of observation conditions. Both phenomena emerge directly from the samples through a single data-driven method: the sequential principal curves analysis (SPCA) with local metric. SPCA is a new manifold learning technique to derive a set of sensors adapted to the manifold using different optimality criteria. Here sequential refers to the fact that sensors (curvilinear dimensions) are designed one after the other, and not to the particular (eventually iterative) method to draw a single principal curve. Moreover, in order to reproduce the empirical adaptation reported under D65 and A illuminations, a new database of colorimetrically calibrated images of natural objects under these illuminants was gathered, thus overcoming the limitations of available databases. The results obtained by applying SPCA show that the psychophysical behavior on color discrimination thresholds, discount of the illuminant, and corresponding pairs in asymmetric color matching emerge directly from realistic data regularities, assuming no a priori functional form. These results provide stronger evidence for the hypothesis of a statistically driven organization of color sensors. Moreover, the obtained results suggest that the nonuniform resolution of color sensors at this low abstraction level may be guided by an error-minimization strategy rather than by an information-maximization goal.