Natural Image Coding in V1: How Much Use is Orientation Selectivity?

Orientation selectivity is the most striking feature of simple cell coding in V1 which has been shown to emerge from the reduction of higher-order correlations in natural images in a large variety of statistical image models. The most parsimonious one among these models is linear Independent Component Analysis (ICA), whereas second-order decorrelation transformations such as Principal Component Analysis (PCA) do not yield oriented filters. Because of this finding it has been suggested that the emergence of orientation selectivity may be explained by higher-order redundancy reduction. In order to assess the tenability of this hypothesis, it is an important empirical question how much more redundancies can be removed with ICA in comparison to PCA, or other second-order decorrelation methods. This question has not yet been settled, as over the last ten years contradicting results have been reported ranging from less than five to more than hundred percent extra gain for ICA. Here, we aim at resolving this conflict by presenting a very careful and comprehensive analysis using three evaluation criteria related to redundancy reduction: In addition to the multi-information and the average log-loss we compute, for the first time, complete rate-distortion curves for ICA in comparison with PCA. Without exception, we find that the advantage of the ICA filters is surprisingly small. Furthermore, we show that a simple spherically symmetric distribution with only two parameters can fit the data even better than the probabilistic model underlying ICA. Since spherically symmetric models are agnostic with respect to the specific filter shapes, we conlude that orientation selectivity is unlikely to play a critical role for redundancy reduction

Cortical Surround Interactions and Perceptual Salience via Natural Scene Statistics

Spatial context in images induces perceptual phenomena associated with salience and modulates the responses of neurons in primary visual cortex (V1). However, the computational and ecological principles underlying contextual effects are incompletely understood. We introduce a model of natural images that includes grouping and segmentation of neighboring features based on their joint statistics, and we interpret the firing rates of V1 neurons as performing optimal recognition in this model. We show that this leads to a substantial generalization of divisive normalization, a computation that is ubiquitous in many neural areas and systems. A main novelty in our model is that the influence of the context on a target stimulus is determined by their degree of statistical dependence. We optimized the parameters of the model on natural image patches, and then simulated neural and perceptual responses on stimuli used in classical experiments. The model reproduces some rich and complex response patterns observed in V1, such as the contrast dependence, orientation tuning and spatial asymmetry of surround suppression, while also allowing for surround facilitation under conditions of weak stimulation. It also mimics the perceptual salience produced by simple displays, and leads to readily testable predictions. Our results provide a principled account of orientation-based contextual modulation in early vision and its sensitivity to the homogeneity and spatial arrangement of inputs, and lends statistical support to the theory that V1 computes visual salience

Image Modeling and Denoising With Orientation-Adapted Gaussian Scale Mixtures

We develop a statistical model to describe the spatially varying behavior of local neighborhoods of coefficients in a multiscale image representation. Neighborhoods are modeled as samples of a multivariate Gaussian density that are modulated and rotated according to the values of two hidden random variables, thus allowing the model to adapt to the local amplitude and orientation of the signal. A third hidden variable selects between this oriented process and a nonoriented scale mixture of Gaussians process, thus providing adaptability to the local orientedness of the signal. Based on this model, we develop an optimal Bayesian least squares estimator for denoising images and show through simulations that the resulting method exhibits significant improvement over previously published results obtained with Gaussian scale mixtures

Inversion pour image texturée : déconvolution myope non supervisée, choix de modèles, déconvolution-segmentation

This thesis is addressing a series of inverse problems of major importance in the fieldof image processing (image segmentation, model choice, parameter estimation, deconvolution)in the context of textured images. In all of the aforementioned problems theobservations are indirect, i.e., the textured images are affected by a blur and by noise. Thecontributions of this work belong to three main classes: modeling, methodological andalgorithmic. From the modeling standpoint, the contribution consists in the development of a newnon-Gaussian model for textures. The Fourier coefficients of the textured images are modeledby a Scale Mixture of Gaussians Random Field. The Power Spectral Density of thetexture has a parametric form, driven by a set of parameters that encode the texture characteristics.The methodological contribution is threefold and consists in solving three image processingproblems that have not been tackled so far in the context of indirect observationsof textured images. All the proposed methods are Bayesian and are based on the exploitingthe information encoded in the a posteriori law. The first method that is proposed is devotedto the myopic deconvolution of a textured image and the estimation of its parameters.The second method achieves joint model selection and model parameters estimation froman indirect observation of a textured image. Finally, the third method addresses the problemof joint deconvolution and segmentation of an image composed of several texturedregions, while estimating at the same time the parameters of each constituent texture.Last, but not least, the algorithmic contribution is represented by the development ofa new efficient version of the Metropolis Hastings algorithm, with a directional componentof the proposal function based on the”Newton direction” and the Fisher informationmatrix. This particular directional component allows for an efficient exploration of theparameter space and, consequently, increases the convergence speed of the algorithm.To summarize, this work presents a series of methods to solve three image processingproblems in the context of blurry and noisy textured images. Moreover, we present twoconnected contributions, one regarding the texture models andone meant to enhance theperformances of the samplers employed for all of the three methods.Ce travail est dédié à la résolution de plusieurs problèmes de grand intérêt en traitement d’images : segmentation, choix de modèle et estimation de paramètres, pour le cas spécifique d’images texturées indirectement observées (convoluées et bruitées). Dans ce contexte, les contributions de cette thèse portent sur trois plans différents : modéle, méthode et algorithmique.Du point de vue modélisation de la texture, un nouveaumodèle non-gaussien est proposé. Ce modèle est défini dans le domaine de Fourier et consiste en un mélange de Gaussiennes avec une Densité Spectrale de Puissance paramétrique.Du point de vueméthodologique, la contribution est triple –troisméthodes Bayésiennes pour résoudre de manière :–optimale–non-supervisée–des problèmes inverses en imagerie dans le contexte d’images texturées ndirectement observées, problèmes pas abordés dans la littérature jusqu’à présent.Plus spécifiquement,1. la première méthode réalise la déconvolution myope non-supervisée et l’estimation des paramètres de la texture,2. la deuxième méthode est dédiée à la déconvolution non-supervisée, le choix de modèle et l’estimation des paramètres de la texture et, finalement,3. la troisième méthode déconvolue et segmente une image composée de plusieurs régions texturées, en estimant au même temps les hyperparamètres (niveau du signal et niveau du bruit) et les paramètres de chaque texture.La contribution sur le plan algorithmique est représentée par une nouvelle version rapide de l’algorithme Metropolis-Hastings. Cet algorithme est basé sur une loi de proposition directionnelle contenant le terme de la ”direction de Newton”. Ce terme permet une exploration rapide et efficace de l’espace des paramètres et, de ce fait, accélère la convergence