Frames for Exact Inversion of the Rank Order Coder

International audienceOur goal is to revisit rank order coding by proposing an original exact decoding procedure for it. Rank order coding was proposed by Thorpe . who stated that the order in which the retina cells are activated encodes for the visual stimulus. Based on this idea, the authors proposed in a rank order coder/decoder associated to a retinal model. Though, it appeared that the decoding procedure employed yields reconstruction errors that limit the model bit-cost/quality performances when used as an image codec. The attempts made in the literature to overcome this issue are time consuming and alter the coding procedure, or are lacking mathematical support and feasibility for standard size images. Here we solve this problem in an original fashion by using the frames theory, where a frame of a vector space designates an extension for the notion of basis. Our contribution is twofold. First, we prove that the analyzing filter bank considered is a frame, and then we define the corresponding dual frame that is necessary for the exact image reconstruction. Second, to deal with the problem of memory overhead, we design a recursive out-of-core blockwise algorithm for the computation of this dual frame. Our work provides a mathematical formalism for the retinal model under study and defines a simple and exact reverse transform for it with over than 265 dB of increase in the peak signal-to-noise ratio quality compared to . Furthermore, the framework presented here can be extended to several models of the visual cortical areas using redundant representations

Frames for Exact Inversion of the Rank Order Coder

Our goal is to revisit rank order coding by proposing an original exact decoding procedure for it. Rank order coding was proposed by Simon Thorpe et al. who stated that the retina represents the visual stimulus by the order in which its cells are activated. A classical rank order coder/decoder was then designed on this basis [1]. Though, it appeared that the decoding proce- dure employed yields reconstruction errors that limit the model Rate/Quality performances when used as an image codec. The attempts made in the litera- ture to overcome this issue are time consuming and alter the coding procedure, or are lacking mathematical support and feasibility for standard size images. Here we solve this problem in an original fashion by using the frames theory, where a frame of a vector space designates an extension for the notion of basis. First, we prove that the analyzing filter bank considered is a frame, and then we define the corresponding dual frame that is necessary for the exact image reconstruction. Second, to deal with the problem of memory overhead, we de- sign a recursive out-of-core blockwise algorithm for the computation of this dual frame. Our work provides a mathematical formalism for the retinal model under study and defines a simple and exact reverse transform for it with up to 270 dB of PSNR gain compared to [1]. Furthermore, the framework presented here can be extended to several models of the visual cortical areas using redundant representations.Notre objectif est de revisiter le codage d'images statiques par rang en proposant une procédure originale de décodage exact. Le codage par rang a été proposé par Simon Thorpe et al. qui a affirmé que la rétine représente le stimulus visuel par l'ordre selon lequel ses cellules sont activées. Un codeur par ordre classique ainsi que le décodeur ont ensuite été conçus se basant sur ces résultats [1]. Cependant, il s'avère que la procédure de décodage employé engendre des erreurs de reconstruction qui limitent les performances Débit / Qualité du modèle lorsqu'il est utilisé comme un codec d'images. Les tentatives proposées dans la littérature pour surmonter ce problème prennent du temps et modifie la procédure de codage, ou manquent d'apport mathématique et de faisabilité pour des images de tailles standards. Ici nous résolvons ce problème de façon originale en utilisant la théorie des "frames", où une frame d'un espace vectoriel désigne une extension de la notion de base. Tout d'abord, nous montrons que le banc de filtres d'analyse considéré est une frame, puis nous définissons la frame duale correspondante qui est nécessaire pour la reconstruction exacte de l'image. Deuxièmement, pour faire face au problème du débordement de mémoire, nous concevons un algorithme récursif, out-of-core, et opérant par blocs pour le calcul de cette frame duale. Notre travail fournit un formalisme mathématique pour le modèle de la rétine à l'étude et définit une inversion simple et exacte de la transformée bio-inspirée définie dans [1] avec un maximum de 270 dB de gain de PSNR par rapport au modèle originel. Par ailleurs, le travail présenté ici peut être étendu à plusieurs autres modèles de zones corticales visuelles utilisant des représentations redondantes

Streaming an image through the eye: The retina seen as a dithered scalable image coder

We propose the design of an original scalable image coder/decoder that is inspired from the mammalians retina. Our coder accounts for the time-dependent and also nondeterministic behavior of the actual retina. The present work brings two main contributions: As a first step, (i) we design a deterministic image coder mimicking most of the retinal processing stages and then (ii) we introduce a retinal noise in the coding process, that we model here as a dither signal, to gain interesting perceptual features. Regarding our first contribution, our main source of inspiration will be the biologically plausible model of the retina called Virtual Retina. The main novelty of this coder is to show that the time-dependent behavior of the retina cells could ensure, in an implicit way, scalability and bit allocation. Regarding our second contribution, we reconsider the inner layers of the retina. We emit a possible interpretation for the non-determinism observed by neurophysiologists in their output. For this sake, we model the retinal noise that occurs in these layers by a dither signal. The dithering process that we propose adds several interesting features to our image coder. The dither noise whitens the reconstruction error and decorrelates it from the input stimuli. Furthermore, integrating the dither noise in our coder allows a faster recognition of the fine details of the image during the decoding process. Our present paper goal is twofold. First, we aim at mimicking as closely as possible the retina for the design of a novel image coder while keeping encouraging performances. Second, we bring a new insight concerning the non-deterministic behavior of the retina.Comment: arXiv admin note: substantial text overlap with arXiv:1104.155

Dynamic Quantization using Spike Generation Mechanisms

This paper introduces a neuro-inspired co-ding/decoding mechanism of a constant real value by using a Spike Generation Mechanism (SGM) and a combination of two Spike Interpretation Mechanisms (SIM). One of the most efficient and widely used SGMs to encode a real value is the Leaky-Integrate and Fire (LIF) model which produces a spike train. The duration of the spike train is bounded by a given time constraint. Seeking for a simple solution of how to interpret the spike train and to reconstruct the input value, we combine two different kinds of SIMs, the time-SIM and the rate-SIM. The time-SIM allows a high quality interpretation of the neural code and the rate-SIM allows a simple decoding mechanism by couting the spikes. The resulting coding/decoding process, called the Dual-SIM Quantizer (Dual-SIMQ), is a non-uniform quantizer. It is shown that it coincides with a uniform scalar quantizer under certain assumptions. Finally, it is also shown that the time constraint can be used to control automatically the reconstruction accuracy of this time-dependent quantizer