Lattice Green functions and diffusion for modelling traffic routing in ad hoc networks

We describe basic properties of Markov chains on finite state spaces and their application to Green functions, partial differential equations, and their (approximate) solution using random walks on a graph. Attention is paid to the influence of boundary conditions (Dirichlet/von Neumann). We apply these ideas to the study of traffic propagation and distribution in ad hoc networks

Potts models and image labelling relaxation by random Markov fields

We show in this paper the deep relationship between classic models from Statistical Physics and Markovian Random Fields models used in image labelling. We present as an application a markovian relaxation method for enhancement and relaxation of previously classified images . An energy function is defined, which depends only on the labels and on their initial value . The main a priori pixel knowledge results from the confusion matrix of the reference samples used for initial classification . The energy to be minimized includes also terms ensuring simultaneous spatial label regularty, growth of some classes and disparition of some others. The method allows for example to reclassify previous rejection class pixels in their spatial environment . Last we present some results on Remote Sensing multispectral and geological ore images, comparing the performances of Iterated Conditional Modes (ICM) and Simulated Annealing (SA) . Very low CPU time was obtained due to the principle of the method, working on labels instead of gray levels .Nous montrons dans cet article la relation profonde entre certains modèles d'énergie provenant de la Physique Statistique utilisés et les modèles utilisés en champ de Markov pour l'étiquetage d'images. Nous présentons comme application une méthode markovienne de relaxation et d'amélioration d'images préclassifiées. On définit pour cela une fonction énergie ne dépendant que des labels et de leur valeur initiale, la connaissance a priori sur l'image provenant de la matrice de confusion déduite des échantillons de référence utilisés pour la classification initiale. La fonction à minimiser inclut divers termes assurant la régularité spatiale des labels, la croissance ou la disparition de certaines classe

A spatial regularization method preserving local photometry for Richardson-Lucy restoration

In this article we give a simple method of spatial regularization deriving from the Richardson-Lucy (RL) algorithm in order to overcome the problem of noise amplification during the image reconstruction process. It is very important in astronomy to regularize images while controlling their photometric behavior. We propose a new reconstruction method preserving both the global and local image photometric properties. A mathematical presentation is described here. This method was applied to an image of Titan -a satellite of Saturn -acquired in near infrared with the adaptive optics system ADONIS installed at the ESO 3.6 m telescope in La Silla (Chile). The local photometric results here are compared using contours normalized at the same intensity levels

Solar image segmentation by use of mean field fast annealing

We present a "continuous” analysis of a solar ${\rm H}_{\alpha}$ image in order to address the problem of image segmentation. Our approach is based on combinatorial optimization methods and in particular on Mean Field Fast Annealing (MFFA). Mean-field theory gives a deterministic nature to our algorithm while its efficiency is improved by a fast cooling schedule. We show how this method can be used to separate efficiently the regions of different solar activity giving a tool for a future automated recognition and classification of sunspots

Solar image segmentation by use of mean field fast annealing

We present a “continuous” analysis of a solar H-alpha image in order to address the problem of image segmentation. Our approach is based on combinatorial optimization methods and in particular on Mean Field Fast Annealing (MFFA). Mean-field theory gives a deterministic nature to our algorithm while its efficiency is improved by a fast cooling schedule. We show how this method call be used to separate efficiently the regions of different solar activity giving a tool for a future automated recognition and classification of sunspots

Image relaxation by use of the Potts model with a fast deterministic method

We demonstrate a close relationship between classical models from statistical physics and Markov randomfield models for image labeling purposes. A picture is taken of a real image or map, defined by a measure of intensity over a set of pixels. Possible class (or gray-level) values are assigned to spin values in Potts theory. We present a continuous analysis of image relaxation by mean-field theory and apply it by using standard and extended Potts models. Accurate relaxation results were obtained with a specific deterministic method called mean-field fast annealing. © 1997 Optical Society of America

Application de la renormalisation a l'analyse de textures markoviennes gaussiennes

Le problème de l'estimation des paramètres associés aux champs markoviens est souvent abordé soit conjointement à un problème de restauration, ou de segmentation, soit directement dans le cadre d'approximations à partir du pseudo-maximum de vraisemblance. Ces méthodes se révèlent inappropriées dans le cadre de l'analyse de textures où une discrimination fine nécessite une estimation précise des paramètres caractéristiques du modèle markovien. Dans cet article, nous proposons une méthode pour l'estimation exacte des paramètres d'un modèle markovien gaussien 4-connexe reposant sur la théorie de la renormalisation. Tout d'abord, nous démontrons de façon analytique le caractère gaussien de la texture décimée, puis nous donnons les estimateurs conjoints, associés aux textures initiale et décimée permettant alors d'estimer les paramètres caractéristiques de la texture originale. Précision et robustesse des estimations sont établies à partir d'images de synthèse de textures stationnaires ou non

Building Block Extraction and Classification by means of Markov Random Fields using Aerial Imagery and LiDAR Data

Building detection has been a prominent area in the area of image classification. Most of the research effort is adapted to the specific application requirements and available datasets. Our dataset includes aerial orthophotos (with spatial resolution 20cm), a DSM generated from LiDAR (with spatial resolution 1m and elevation resolution 20 cm) and DTM (spatial resolution 2m) from an area of Athens, Greece. Our aim is to classify these data by means of Markov Random Fields (MRFs) in a Bayesian framework for building block extraction and perform a comparative analysis with other supervised classification techniques namely Feed Forward Neural Net (FFNN), Cascade-Correlation Neural Network (CCNN), Learning Vector Quantization (LVQ) and Support Vector Machines (SVM). We evaluated the performance of each method using a subset of the test area. We present the classified images, and statistical measures (confusion matrix, kappa coefficient and overall accuracy). Our results demonstrate that the MRFs and FFNN perform better than the other methods

Markov Random Fields based probabilistic relaying for multihop networks

In this paper, we demonstrate how a Markov Random Field (MRF) based framework can be used for multihop networks analysis and design. In fields such as image processing it has been shown that MRFs is a powerful tool to analyse distributed systems with strong spacial interactions, which is also a defining characteristic of multihop networks. In this work we focus on using MRFs to model traffic intensity of sensor networks using shortest path routing. Later we propose a probabilistic relaying mechanism to recreate a traffic pattern similar to that observed in a network using shortest path routing. The objective is to emulate the shortest path performance without complex routing protocols and associated overheads. Using a simulation study we then show that the proposed mechanism achieves 95% of the throughput of shortest path, without using a routing protocol