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In this work we propose a photorealistic style transfer method for image and video that is based on vision science principles and on a recent mathematical formulation for the deterministic decoupling of sample statistics. The novel aspects of our approach include matching decoupled moments of higher order than in common style transfer approaches, and matching a descriptor of the power spectrum so as to characterize and transfer diffusion effects between source and target, which is something that has not been considered before in the literature. The results are of high visual quality, without spatio-temporal artifacts, and validation tests in the form of observer preference experiments show that our method compares very well with the state-of-the-art. The computational complexity of the algorithm is low, and we propose a numerical implementation that is amenable for real-time video application. Finally, another contribution of our work is to point out that current deep learning approaches for photorealistic style transfer don't really achieve photorealistic quality outside of limited examples, because the results too often show unacceptable visual artifacts.

Three decades ago, Atick et al. suggested that human frequency sensitivity may emerge from the enhancement required for a more efficient analysis of retinal images. Here we reassess the relevance of low-level vision tasks in the explanation of the Contrast Sensitivity Functions (CSFs) in light of (1) the current trend of using artificial neural networks for studying vision, and (2) the current knowledge of retinal image representations. As a first contribution, we show that a very popular type of convolutional neural networks (CNNs), called autoencoders, may develop human-like CSFs in the spatio-temporal and chromatic dimensions when trained to perform some basic low-level vision tasks (like retinal noise and optical blur removal), but not others (like chromatic adaptation or pure reconstruction after simple bottlenecks). As an illustrative example, the best CNN (in the considered set of simple architectures for enhancement of the retinal signal) reproduces the CSFs with an RMSE error of 11\% of the maximum sensitivity. As a second contribution, we provide experimental evidence of the fact that, for some functional goals (at low abstraction level), deeper CNNs that are better in reaching the quantitative goal are actually worse in replicating human-like phenomena (such as the CSFs). This low-level result (for the explored networks) is not necessarily in contradiction with other works that report advantages of deeper nets in modeling higher-level vision goals. However, in line with a growing body of literature, our results suggests another word of caution about CNNs in vision science since the use of simplified units or unrealistic architectures in goal optimization may be a limitation for the modeling and understanding of human vision., Comment: Accepted in the Journal of Vision

In the film industry, the same movie is expected to be watched on displays of vastly different sizes, from cinema screens to mobile phones. But visual induction, the perceptual phenomenon by which the appearance of a scene region is affected by its surroundings, will be different for the same image shown on two displays of different dimensions. This presents a practical challenge for the preservation of the artistic intentions of filmmakers, as it can lead to shifts in image appearance between viewing destinations. In this work we show that a neural field model based on the efficient representation principle is able to predict induction effects, and how by regularizing its associated energy functional the model is still able to represent induction but is now invertible. From this we propose a method to pre-process an image in a screen-size dependent way so that its perception, in terms of visual induction, may remain constant across displays of different size. The potential of the method is demonstrated through psychophysical experiments on synthetic images and qualitative examples on natural images., Comment: pre-print

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.

We consider the evolution model proposed in [9, 6] to describe illusory contrast perception phenomena induced by surrounding orientations. Firstly, we highlight its analogies and differences with the widely used Wilson-Cowan equations [48], mainly in terms of efficient representation properties. Then, in order to explicitly encode local directional information, we exploit the model of the primary visual cortex (V1) proposed in [20] and largely used over the last years for several image processing problems [24,38,28]. The resulting model is thus defined in the space of positions and orientation and it is capable to describe assimilation and contrast visual bias at the same time. We report several numerical tests showing the ability of the model to reproduce, in particular, orientation-dependent phenomena such as grating induction and a modified version of the Poggendorff illusion. For this latter example, we empirically show the existence of a set of threshold parameters differentiating from inpainting to perception-type reconstructions and describing long-range connectivity between different hypercolumns in V1., Comment: This is the revised extended invited journal version of the SSVM 2019 conference proceeding arXiv:1812.07425

In this work we have aimed to reproduce supra-threshold perception phenomena, specifically visual illusions, with Wilson-Cowan-type models of neuronal dynamics. We have found that it is indeed possible to do so, but that the ability to replicate visual illusions is related to how well the neural activity equations comply with the efficient representation principle. Our first contribution is to show that the Wilson-Cowan equations can reproduce a number of brightness and orientation-dependent illusions, and that the latter type of illusions require that the neuronal dynamics equations consider explicitly the orientation, as expected. Then, we formally prove that there can't be an energy functional that the Wilson-Cowan equations are minimizing, but that a slight modification makes them variational and yields a model that is consistent with the efficient representation principle. Finally, we show that this new model provides a better reproduction of visual illusions than the original Wilson-Cowan formulation.

In this work we study the communication efficiency of a psychophysically-tuned cascade of Wilson-Cowan and Divisive Normalization layers that simulate the retina-V1 pathway. This is the first analysis of Wilson-Cowan networks in terms of multivariate total correlation. The parameters of the cortical model have been derived through the relation between the steady state of the Wilson-Cowan model and the Divisive Normalization model. The communication efficiency has been analyzed in two ways: First, we provide an analytical expression for the reduction of the total correlation among the responses of a V1-like population after the application of the Wilson-Cowan interaction. Second, we empirically study the efficiency with visual stimuli and statistical tools that were not available before: (1) we use a recent, radiometrically calibrated, set of natural scenes, and (2) we use a recent technique to estimate the multivariate total correlation in bits from sets of visual responses which only involves univariate operations, thus giving better estimates of the redundancy. The theoretical and the empirical results show that although this cascade of layers was not optimized for statistical independence in any way, the redundancy between the responses gets substantially reduced along the neural pathway. Specifically, we show that (1)~the efficiency of a Wilson-Cowan network is similar to its equivalent Divisive Normalization model, (2) while initial layers (Von-Kries adaptation and Weber-like brightness) contribute to univariate equalization, the bigger contributions to the reduction in total correlation come from the computation of nonlinear local contrast and the application of local oriented filters, and (3)~psychophysically-tuned models are more efficient (reduce more total correlation) in the more populated regions of the luminance-contrast plane.

We consider a differential model describing neuro-physiological contrast perception phenomena induced by surrounding orientations. The mathematical formulation relies on a cortical-inspired modelling [10] largely used over the last years to describe neuron interactions in the primary visual cortex (V1) and applied to several image processing problems [12,19,13]. Our model connects to Wilson-Cowan-type equations [23] and it is analogous to the one used in [3,2,14] to describe assimilation and contrast phenomena, the main novelty being its explicit dependence on local image orientation. To confirm the validity of the model, we report some numerical tests showing its ability to explain orientation-dependent phenomena (such as grating induction) and geometric-optical illusions [21,16] classically explained only by filtering-based techniques [6,18].

Visual illusions teach us that what we see is not always what it is represented in the physical world. Its special nature make them a fascinating tool to test and validate any new vision model proposed. In general, current vision models are based on the concatenation of linear convolutions and non-linear operations. In this paper we get inspiration from the similarity of this structure with the operations present in Convolutional Neural Networks (CNNs). This motivated us to study if CNNs trained for low-level visual tasks are deceived by visual illusions. In particular, we show that CNNs trained for image denoising, image deblurring, and computational color constancy are able to replicate the human response to visual illusions, and that the extent of this replication varies with respect to variation in architecture and spatial pattern size. We believe that this CNNs behaviour appears as a by-product of the training for the low level vision tasks of denoising, color constancy or deblurring. Our work opens a new bridge between human perception and CNNs: in order to obtain CNNs that better replicate human behaviour, we may need to start aiming for them to better replicate visual illusions.

The interaction between wavelet-like sensors in Divisive Normalization is classically described through Gaussian kernels that decay with spatial distance, angular distance and frequency distance. However, simultaneous explanation of (a) distortion perception in natural image databases and (b) contrast perception of artificial stimuli requires very specific modifications in classical Divisive Normalization. First, the wavelet response has to be high-pass filtered before the Gaussian interaction is applied. Then, distinct weights per subband are also required after the Gaussian interaction. In summary, the classical Gaussian kernel has to be left- and right-multiplied by two extra diagonal matrices. In this paper we provide a lower-level justification for this specific empirical modification required in the Gaussian kernel of Divisive Normalization. Here we assume that the psychophysical behavior described by Divisive Normalization comes from neural interactions following the Wilson-Cowan equations. In particular, we identify the Divisive Normalization response with the stationary regime of a Wilson-Cowan model. From this identification we derive an expression for the Divisive Normalization kernel in terms of the interaction kernel of the Wilson-Cowan equations. It turns out that the Wilson-Cowan kernel is left- and-right multiplied by diagonal matrices with high-pass structure. In conclusion, symmetric Gaussian inhibitory relations between wavelet-like sensors wired in the lower-level Wilson-Cowan model lead to the appropriate non-symmetric kernel that has to be empirically included in Divisive Normalization to explain a wider range of phenomena., Comment: MODVIS-18 and Celebration of Cowan's 50th anniv. at Univ. Chicago

Subjective image quality databases are a major source of raw data on how the visual system works in naturalistic environments. These databases describe the sensitivity of many observers to a wide range of distortions (of different nature and with different suprathreshold intensities) seen on top of a variety of natural images. They seem like a dream for the vision scientist to check the models in realistic scenarios. However, while these natural databases are great benchmarks for models developed in some other way (e.g. by using the well-controlled artificial stimuli of traditional psychophysics), they should be carefully used when trying to fit vision models. Given the high dimensionality of the image space, it is very likely that some basic phenomenon (e.g. sensitivity to distortions in certain environments) are under-represented in the database. Therefore, a model fitted on these large-scale natural databases will not reproduce these under-represented basic phenomena that could otherwise be easily illustrated with well selected artificial stimuli. In this work we study a specific example of the above statement. A wavelet+divisive normalization layer of a sensible cascade of linear+nonlinear layers fitted to maximize the correlation with subjective opinion of observers on a large image quality database fails to reproduce basic crossmasking. Here we outline a solution for this problem using artificial stimuli. Then, we show that the resulting model is also a competitive solution for the large-scale database. In line with Rust and Movshon (2005), our report (misrepresentation of basic visual phenomena in subjectively-rated natural image databases) is an additional argument in praise of artifice.

Image dehazing deals with the removal of undesired loss of visibility in outdoor images due to the presence of fog. Retinex is a color vision model mimicking the ability of the Human Visual System to robustly discount varying illuminations when observing a scene under different spectral lighting conditions. Retinex has been widely explored in the computer vision literature for image enhancement and other related tasks. While these two problems are apparently unrelated, the goal of this work is to show that they can be connected by a simple linear relationship. Specifically, most Retinex-based algorithms have the characteristic feature of always increasing image brightness, which turns them into ideal candidates for effective image dehazing by directly applying Retinex to a hazy image whose intensities have been inverted. In this paper, we give theoretical proof that Retinex on inverted intensities is a solution to the image dehazing problem. Comprehensive qualitative and quantitative results indicate that several classical and modern implementations of Retinex can be transformed into competing image dehazing algorithms performing on pair with more complex fog removal methods, and can overcome some of the main challenges associated with this problem., Comment: 13 pages, 5 figures

In vision science, cascades of Linear+Nonlinear transforms are very successful in modeling a number of perceptual experiences [Carandini&Heeger12]. However, the conventional literature is usually too focused on only describing the input->output transform. Instead, here we present the maths of such cascades beyond the forward transform, namely the Jacobians and the inverse. The fundamental reason for this analytical treatment is that it offers useful insight into the psychophysics, the physiology, and the function of the visual system. For instance, we show how the trends of the sensitivity (discrimination regions) and the adaptation of the receptive fields can be seen in the expression of the Jacobian wrt the stimulus. This matrix also tells us which regions of the stimulus space are encoded more efficiently in multi-information terms. The Jacobian wrt the parameters shows which aspects of the model have bigger impact in the response, and hence bigger relevance. The analytic inverse implies conditions for the response and the model to ensure decoding. From an applied perspective, (a) the Jacobian wrt the stimulus is necessary in new experimental methods based on the synthesis of visual stimuli with interesting geometry, (b) the Jacobian matrices wrt the parameters are convenient to learn the model from classical experiments or alternative optimization goals, and (c) the inverse is a model-based alternative to blind machine-learning neural decoding that does not include meaningful biological information. The theory is checked by building a derivable and invertible vision model that actually follows the modular program suggested by Carandini&Heeger. To stress the generality of this modular setting we show examples where some of the canonical Divisive Normalization layers are substituted by equivalent layers such as the Wilson-Cowan model at V1, or a tone-mapping model at the retina., Comment: Reproducible results: associated Matlab toolbox available at http://isp.uv.es/docs/BioMultiLayer_L_NL.zip

Linear-nonlinear transforms are interesting in vision science because they are key in modeling a number of perceptual experiences such as color, motion or spatial texture. Here we first show that a number of issues in vision may be addressed through an analytic expression of the Jacobian of these linear-nonlinear transforms. The particular model analyzed afterwards (an extension of [Malo & Simoncelli SPIE 2015]) is illustrative because it consists of a cascade of standard linear-nonlinear modules. Each module roughly corresponds to a known psychophysical mechanism: (1) linear spectral integration and nonlinear brightness-from-luminance computation, (2) linear pooling of local brightness and nonlinear normalization for local contrast computation, (3) linear frequency selectivity and nonlinear normalization for spatial contrast masking, and (4) linear wavelet-like decomposition and nonlinear normalization for frequency-dependent masking. Beyond being the appropriate technical report with the missing details in [Malo & Simoncelli SPIE 2015], the interest of the presented analytic results and numerical methods transcend the particular model because of the ubiquity of the linear-nonlinear structure. Part of this material was presented at MODVIS 2016 (see slides of the conference talk in the appendix at the end of this document)., Comment: Paper: 26 pages, 49 references, plus 32 slides from MODVIS-16 presentation

We present a novel segmentation algorithm based on a hierarchical representation of images. The main contribution of this work is to explore the capabilities of the A Contrario reasoning when applied to the segmentation problem, and to overcome the limitations of current algorithms within that framework. This exploratory approach has three main goals. Our first goal is to extend the search space of greedy merging algorithms to the set of all partitions spanned by a certain hierarchy, and to cast the segmentation as a selection problem within this space. In this way we increase the number of tested partitions and thus we potentially improve the segmentation results. In addition, this space is considerably smaller than the space of all possible partitions, thus we still keep the complexity controlled. Our second goal aims to improve the locality of region merging algorithms, which usually merge pairs of neighboring regions. In this work, we overcome this limitation by introducing a validation procedure for complete partitions, rather than for pairs of regions. The third goal is to perform an exhaustive experimental evaluation methodology in order to provide reproducible results. Finally, we embed the selection process on a statistical A Contrario framework which allows us to have only one free parameter related to the desired scale., Comment: Siam Journal on Imaging Sciences