Simultaneous Image Restoration and Hyperparameter Estimation for Incomplete Data by a Cumulant Analysis

: The purpose of this report is first to show the main properties of Gibbs distributions considered as exponential statistics on finite spaces, as well as their sampling and annealing properties. Moreover, the definition and use of their cumulant expansions enables to exhibit other important properties of such distributions. Last, we tackle the problem of hyperparameter estimation in an incomplete data frame for image restoration purposes. A detailed analysis of several joint restoration-estimation methods using generalized stochastic gradient algorithms is presented, requiring infinite, continuous configuration spaces. Using once again cumulant analysis and its relationship with Statistical Physics allows us to propose new algorithms and to extend them to an explicit boundary frame. Key-words: exponential statistics, Gibbs distributions, hyperparameters, restoration, estimation, stochastic gradient. (Rsum : tsvp) * E-mail: [email protected]. This work was done while the author was..

Application of Projection Learning to the Detection of Urban Areas in SPOT Satellite Images

: We introduce a novel learning algorithm for neural networks, with the major feature of being rapid when compared to classical learning algorithms, offering misclassification rates of 5% and less after only a few iterations, i.e. 20-30 seconds of learning, depending on the task, if a suitable preprocessing has been done. The algorithm is based on considering a neural network as a base in function space, base onto which the function to be learned is projected. We thus call our algorithm projection learning. We present the algorithm, show the application to the detection of inhabited areas in satellite images, discuss the various preprocessors used, compare to other approaches used, and outline further directions of research Key-words: Learning in computer vision, segmentation and perceptual grouping, neural networks, texture analysis, pixel-based classification, low-level processing, feedforward networks, satellite image analysis (R'esum'e : tsvp) [email protected] giraudon@soph..

Modelling Image Redundancy

: C.E. Shannon in his Information Theory defined a rate of information transmission of a transmitter-receiver couple. We use this concept to define three models of image redundancy. First we apply information theory to a simple model considering an image as a set of isolated pixels. Then we introduce a Markov Random Field model to take into account the neighbourhood of a pixel. We show that we have to determine some parameters of the MRF in order to obtain sufficient statistics from common satellite images, and we propose a measure based on a generalized Ising model. Our third model considers the correspondence between grey level vectors of cliques. We introduce a distance in the grey level space to solve the problem of insufficient statistics. Finally, results for the proposed definitions are presented for some synthetic and a large variety of SPOT XS1, XS2 and XS3 image triples and are compared to the classical correlation coefficient measure. Key-words: Image redundancy, entropy, m..

Towards Robust Analysis of Satellite Images Using Map Information - Application to Urban Area Detection

With the rapid development in remote sensing, digital image processing becomes an important tool for quantitative and statistical analysis of remotely sensed images. These images contain most often complex natural scenes. Robust interpretation of such images requires the use of different sources of information about the scenes under consideration. This paper presents an integrated approach to the robust analysis of remotely sensed images by using multi-spectral SPOT image data, as well as map knowledge and contextual information. Several techniques are proposed for the effective use of map information for urban area detection in SPOT images. The first one is concerned with the modeling of SPOT images and map information using Markov random fields, which in turn permits application of various existing energy minimization algorithms for solving image analysis problems. The second one is on a new iterative optimization algorithm which automatically adjusts the optimal valures of the paramet..

Direct Search Generalized Simplex Algorithm for Optimizing Non-linear Functions

: Multivariable optimisation techniques have long been used in all fields for improving the design and performance of systems. Yet the number of well known algorithms that can effectively be used under realistic conditions is usually limited due to many practical considerations such as the limit of applicability to certain classes of problems, the time and computational cost of them under conditions of the problem and more importantly, the efficiency of these algorithms under noisy conditions, which is indeed the case in almost all practical problems. Variants of simplex algorithm have been named since 60's as efficient algorithms in noisy situations. However, no theoretical results have been stablished as regards their convergence and computational efficiency. In this report, we have generalized the simplex method and have addressed theoretical aspects concerning the convergence of the algorithm. Key-words: simplex method, search algorithms, optimization. (R'esum'e : tsvp) hshekar@s..