Information Flow in Color Appearance Neural Networks

Color Appearance Models are biological networks that 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 get perceptually Euclidean color representations (similar to dimensionwise 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 done using data and methods that were not available before: (1) new colorimetrically calibrated scenes in different CIE illuminations for proper evaluation of chromatic adaptation, and (2) new statistical tools to estimate (multivariate) information-theoretic quantities between multidimensional sets based on Gaussianization. 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

Psychophysics of Artificial Neural Networks Questions Classical Hue Cancellation Experiments

We show that classical hue cancellation experiments lead to human-like opponent curves even if the task is done by trivial (identity) artificial networks. Specifically, human-like opponent spectral sensitivities always emerge in artificial networks as long as (i) the retina converts the input radiation into any tristimulus-like representation, and (ii) the post-retinal network solves the standard hue cancellation task, e.g. the network looks for the weights of the cancelling lights so that every monochromatic stimulus plus the weighted cancelling lights match a grey reference in the (arbitrary) color representation used by the network. In fact, the specific cancellation lights (and not the network architecture) are key to obtain human-like curves: results show that the classical choice of the lights is the one that leads to the best (more human-like) result, and any other choices lead to progressively different spectral sensitivities. We show this in two ways: through artificial psychophysics using a range of networks with different architectures and a range of cancellation lights, and through a change-of-basis theoretical analogy of the experiments. This suggests that the opponent curves of the classical experiment are just a by-product of the front-end photoreceptors and of a very specific experimental choice but they do not inform about the downstream color representation. In fact, the architecture of the post-retinal network (signal recombination or internal color space) seems irrelevant for the emergence of the curves in the classical experiment. This result in artificial networks questions the conventional interpretation of the classical result in humans by Jameson and Hurvich.Comment: 17 pages, 7 figure

Learning efficient image representations: Connections between statistics and neuroscience

This thesis summarizes different works developed in the framework of analyzing the relation between image processing, statistics and neuroscience. These relations are analyzed from the efficient coding hypothesis point of view (H. Barlow [1961] and Attneave [1954]). This hypothesis suggests that the human visual system has been adapted during the ages in order to process the visual information in an efficient way, i.e. taking advantage of the statistical regularities of the visual world. Under this classical idea different works in different directions are developed. One direction is analyzing the statistical properties of a revisited, extended and fitted classical model of the human visual system. No statistical information is used in the model. Results show that this model obtains a representation with good statistical properties, which is a new evidence in favor of the efficient coding hypothesis. From the statistical point of view, different methods are proposed and optimized using natural images. The models obtained using these statistical methods show similar behavior to the human visual system, both in the spatial and color dimensions, which are also new evidences of the efficient coding hypothesis. Applications in image processing are an important part of the Thesis. Statistical and neuroscience based methods are employed to develop a wide set of image processing algorithms. Results of these methods in denoising, classification, synthesis and quality assessment are comparable to some of the most successful current methods

Divisive Normalization from Wilson-Cowan Dynamics

Divisive Normalization and the Wilson-Cowan equations are influential models of neural interaction and saturation [Carandini and Heeger Nat.Rev.Neurosci. 2012; Wilson and Cowan Kybernetik 1973]. However, they have not been analytically related yet. In this work we show that Divisive Normalization can be obtained from the Wilson-Cowan model. Specifically, assuming that Divisive Normalization is the steady state solution of the Wilson-Cowan differential equation, we find that the kernel that controls neural interactions in Divisive Normalization depends on the Wilson-Cowan kernel but also has a signal-dependent contribution. A standard stability analysis of a Wilson-Cowan model with the parameters obtained from our relation shows that the Divisive Normalization solution is a stable node. This stability demonstrates the consistency of our steady state assumption, and is in line with the straightforward use of Divisive Normalization with time-varying stimuli. The proposed theory provides a physiological foundation (a relation to a dynamical network with fixed wiring among neurons) for the functional suggestions that have been done on the need of signal-dependent Divisive Normalization [e.g. in Coen-Cagli et al., PLoS Comp.Biol. 2012]. Moreover, this theory explains the modifications that had to be introduced ad-hoc in Gaussian kernels of Divisive Normalization in [Martinez et al. Front. Neurosci. 2019] to reproduce contrast responses. The proposed relation implies that the Wilson-Cowan dynamics also reproduces visual masking and subjective image distortion metrics, which up to now had been mainly explained via Divisive Normalization. Finally, this relation allows to apply to Divisive Normalization the methods which up to now had been developed for dynamical systems such as Wilson-Cowan networks

The Role of Non-Linearities in Visual Perception studied with a Computational Model of the Vertebrate Retina

Processing of visual stimuli in the vertebrate retina is complex and diverse. The retinal output to the higher centres of the nervous system, mediated by ganglion cells, consists of several different channels. Neurons in these channels can have very distinct response properties, which originate in different retinal pathways. In this work, the retinal origins and possible functional implications of the segregation of visual pathways will be investigated with a detailed, biologically realistic computational model of the retina. This investigation will focus on the two main retino-cortical pathways in the mammalian retina, the parvocellular and magnocellular systems, which are crucial for conscious visual perception. These pathways differ in two important aspects. The parvocellular system has a high spatial, but low temporal resolution. Conversely, the magnocellular system has a high temporal fidelity, spatial sampling however is less dense than for parvocellular cells. Additionally, the responses of magnocellular ganglion cells can show pronounced nonlinearities, while the parvocellular system is essentially linear. The origin of magnocellular nonlinearities is unknown and will be investigated in the first part of this work. As their main source, the results suggest specific properties of the photoreceptor response and a specialised amacrine cell circuit in the inner retina. The results further show that their effect combines in a multiplicative way. The model is then used to examine the influence of nonlinearities on the responses of ganglion cells in the presence of involuntary fixational eye movements. Two different stimulus conditions will be considered: visual hyperacuity and motion induced illusions. In both cases, it is possible to directly compare properties of the ganglion cell population response with psychophysical data, which allows for an analysis of the influence of different components of the retinal circuitry. The simulation results suggest an important role for nonlinearities in the magnocellular stream for visual perception in both cases. First, it will be shown how nonlinearities, triggered by fixational eye movements, can strongly enhance the spatial precision of magnocellular ganglion cells. As a result, their performance in a hyperacuity task can be equal to or even surpass that of the parvocellular system. Second, the simulations imply that the origin of some of the illusory percepts elicited by fixational eye movements could be traced back to the nonlinear properties of magnocellular ganglion cells. As these activity patterns strongly differ from those in the parvocellular system, it appears that the magnocellular system can strongly dominate visual perception in certain conditions. Taken together, the results of this theoretical study suggest that retinal nonlinearities may be important for and strongly influence visual perception. The model makes several experimentally verifiable predictions to further test and quantify these findings. Furthermore, models investigating higher visual processing stages may benefit from this work, which could provide the basis to produce realistic afferent input