Disentangling the Link Between Image Statistics and Human Perception

In the 1950s Horace Barlow and Fred Attneave suggested a connection between sensory systems and how they are adapted to the environment: early vision evolved to maximise the information it conveys about incoming signals. Following Shannon's definition, this information was described using the probability of the images taken from natural scenes. Previously, direct accurate predictions of image probabilities were not possible due to computational limitations. Despite the exploration of this idea being indirect, mainly based on oversimplified models of the image density or on system design methods, these methods had success in reproducing a wide range of physiological and psychophysical phenomena. In this paper, we directly evaluate the probability of natural images and analyse how it may determine perceptual sensitivity. We employ image quality metrics that correlate well with human opinion as a surrogate of human vision, and an advanced generative model to directly estimate the probability. Specifically, we analyse how the sensitivity of full-reference image quality metrics can be predicted from quantities derived directly from the probability distribution of natural images. First, we compute the mutual information between a wide range of probability surrogates and the sensitivity of the metrics and find that the most influential factor is the probability of the noisy image. Then we explore how these probability surrogates can be combined using a simple model to predict the metric sensitivity, giving an upper bound for the correlation of 0.85 between the model predictions and the actual perceptual sensitivity. Finally, we explore how to combine the probability surrogates using simple expressions, and obtain two functional forms (using one or two surrogates) that can be used to predict the sensitivity of the human visual system given a particular pair of images.

Analysis of Deep Image Quality Models

Subjective image quality measures based on deep neural networks are very related to models of visual neuroscience. This connection benefits engineering but, more interestingly, the freedom to optimize deep networks in different ways, make them an excellent tool to explore the principles behind visual perception (both human and artificial). Recently, a myriad of networks have been successfully optimized for many interesting visual tasks. Although these nets were not specifically designed to predict image quality or other psychophysics, they have shown surprising human-like behavior. The reasons for this remain unclear. In this work, we perform a thorough analysis of the perceptual properties of pre-trained nets (particularly their ability to predict image quality) by isolating different factors: the goal (the function), the data (learning environment), the architecture, and the readout: selected layer(s), fine-tuning of channel relevance, and use of statistical descriptors as opposed to plain readout of responses. Several conclusions can be drawn. All the models correlate better with human opinion than SSIM. More importantly, some of the nets are in pair of state-of-the-art with no extra refinement or perceptual information. Nets trained for supervised tasks such as classification correlate substantially better with humans than LPIPS (a net specifically tuned for image quality). Interestingly, self-supervised tasks such as jigsaw also perform better than LPIPS. Simpler architectures are better than very deep nets. In simpler nets, correlation with humans increases with depth as if deeper layers were closer to human judgement. This is not true in very deep nets. Consistently with reports on illusions and contrast sensitivity, small changes in the image environment does not make a big difference. Finally, the explored statistical descriptors and concatenations had no major impact.

Orthonormal Convolutions for the Rotation Based Iterative Gaussianization

In this paper we elaborate an extension of rotation-based iterative Gaussianization, RBIG, which makes image Gaussianization possible. Although RBIG has been successfully applied to many tasks, it is limited to medium dimensionality data (on the order of a thousand dimensions). In images its application has been restricted to small image patches or isolated pixels, because rotation in RBIG is based on principal or independent component analysis and these transformations are difficult to learn and scale. Here we present the \emph{Convolutional RBIG}: an extension that alleviates this issue by imposing that the rotation in RBIG is a convolution. We propose to learn convolutional rotations (i.e. orthonormal convolutions) by optimising for the reconstruction loss between the input and an approximate inverse of the transformation using the transposed convolution operation. Additionally, we suggest different regularizers in learning these orthonormal convolutions. For example, imposing sparsity in the activations leads to a transformation that extends convolutional independent component analysis to multilayer architectures. We also highlight how statistical properties of the data, such as multivariate mutual information, can be obtained from \emph{Convolutional RBIG}. We illustrate the behavior of the transform with a simple example of texture synthesis, and analyze its properties by visualizing the stimuli that maximize the response in certain feature and layer.

Neural Networks with Divisive normalization for image segmentation with application in cityscapes dataset

One of the key problems in computer vision is adaptation: models are too rigid to follow the variability of the inputs. The canonical computation that explains adaptation in sensory neuroscience is divisive normalization, and it has appealing effects on image manifolds. In this work we show that including divisive normalization in current deep networks makes them more invariant to non-informative changes in the images. In particular, we focus on U-Net architectures for image segmentation. Experiments show that the inclusion of divisive normalization in the U-Net architecture leads to better segmentation results with respect to conventional U-Net. The gain increases steadily when dealing with images acquired in bad weather conditions. In addition to the results on the Cityscapes and Foggy Cityscapes datasets, we explain these advantages through visualization of the responses: the equalization induced by the divisive normalization leads to more invariant features to local changes in contrast and illumination.

On the relation between statistical learning and perceptual distances

It has been demonstrated many times that the behavior of the human visual system is connected to the statistics of natural images. Since machine learning relies on the statistics of training data as well, the above connection has interesting implications when using perceptual distances (which mimic the behavior of the human visual system) as a loss function. In this paper, we aim to unravel the non-trivial relationship between the probability distribution of the data, perceptual distances, and unsupervised machine learning. To this end, we show that perceptual sensitivity is correlated with the probability of an image in its close neighborhood. We also explore the relation between distances induced by autoencoders and the probability distribution of the data used for training them, as well as how these induced distances are correlated with human perception. Finally, we discuss why perceptual distances might not lead to noticeable gains in performance over standard Euclidean distances in common image processing tasks except when data is scarce and the perceptual distance provides regularization.

Information Theory in Density Destructors

Density destructors are differentiable and invertible transforms that map multivariate PDFs of arbitrary structure (low entropy) into non-structured PDFs (maximum entropy). Multivariate Gaussianization and multivariate equalization are specific examples of this family, which break down the complexity of the original PDF through a set of elementary transforms that progressively remove the structure of the data. We demonstrate how this property of density destructive flows is connected to classical information theory, and how density destructors can be used to get more accurate estimates of information theoretic quantities. Experiments with total correlation and mutual information inmultivariate sets illustrate the ability of density destructors compared to competing methods. These results suggest that information theoretic measures may be an alternative optimization criteria when learning density destructive flows.

Synthesizing Visual Illusions Using Generative Adversarial Networks

Visual illusions are a very useful tool for vision scientists, because they allow them to better probe the limits, thresholds and errors of the visual system. In this work we introduce the first ever framework to generate novel visual illusions with an artificial neural network (ANN). It takes the form of a generative adversarial network, with a generator of visual illusion candidates and two discriminator modules, one for the inducer background and another that decides whether or not the candidate is indeed an illusion. The generality of the model is exemplified by synthesizing illusions of different types, and validated with psychophysical experiments that corroborate that the outputs of our ANN are indeed visual illusions to human observers. Apart from synthesizing new visual illusions, which may help vision researchers, the proposed model has the potential to open new ways to study the similarities and differences between ANN and human visual perception.

PerceptNet: A Human Visual System Inspired Neural Network for Estimating Perceptual Distance

Traditionally, the vision community has devised algorithms to estimate the distance between an original image and images that have been subject to perturbations. Inspiration was usually taken from the human visual perceptual system and how the system processes different perturbations in order to replicate to what extent it determines our ability to judge image quality. While recent works have presented deep neural networks trained to predict human perceptual quality, very few borrow any intuitions from the human visual system. To address this, we present PerceptNet, a convolutional neural network where the architecture has been chosen to reflect the structure and various stages in the human visual system. We evaluate PerceptNet on various traditional perception datasets and note strong performance on a number of them as compared with traditional image quality metrics. We also show that including a nonlinearity inspired by the human visual system in classical deep neural networks architectures can increase their ability to judge perceptual similarity.

Nonlinearities and Adaptation of Color Vision from Sequential Principal Curves Analysis

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 approaches 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. Here we address the simultaneous statistical explanation of (i) the nonlinear behavior of achromatic and chromatic mechanisms in a fixed adaptation state, and (ii) the change of such behavior. 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. A new database of colorimetrically calibrated images of natural objects under these illuminants was collected. 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 color perception at this low abstraction level may be guided by an error minimization strategy rather than by the information maximization principle.

Iterative Gaussianization: from ICA to Random Rotations

Most signal processing problems involve the challenging task of multidimensional probability density function (PDF) estimation. In this work, 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 (PP) 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 (RG), one-class support vector domain description (SVDD), and deep neural networks (DNN) 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.