Marc Sigelle

Image Restoration with Discrete Constrained Total Variation Part I: Fast and Exact Optimization

This paper deals with the total variation minimization problem in image restoration for convex data fidelity functionals. We propose a new and fast algorithm which computes an exact solution in the discrete framework. Our method relies on the decomposition of an image into its level sets. It maps the original problems into independent binary Markov Random Field optimization problems at each level. Exact solutions of these binary problems are found thanks to minimum cost cut techniques in graphs. These binary solutions are proved to be monotone increasing with levels and yield thus an exact solution of the discrete original problem. Furthermore we show that minimization of total variation under L1 data fidelity term yields a self-dual contrast invariant filter. Finally we present some results.

Unsupervised classification of radar images using hidden Markov chains and hidden Markov random fields

Due to the enormous quantity of radar images acquired by satellites and through shuttle missions, there is an evident need for efficient automatic analysis tools. This paper describes unsupervised classification of radar images in the framework of hidden Markov models and generalized mixture estimation. Hidden Markov chain models, applied to a Hilbert-Peano scan of the image, constitute a fast and robust alternative to hidden Markov random field models for spatial regularization of image analysis problems, even though the latter provide a finer and more intuitive modeling of spatial relationships. We here compare the two approaches and show that they can be combined in a way that conserves their respective advantages. We also describe how the distribution families and parameters of classes with constant or textured radar reflectivity can be determined through generalized mixture estimation. Sample results obtained on real and simulated radar images are presented.

SAR Image Regularization With Fast Approximate Discrete Minimization

Synthetic aperture radar (SAR) images, like other coherent imaging modalities, suffer from speckle noise. The presence of this noise makes the automatic interpretation of images a challenging task and noise reduction is often a prerequisite for successful use of classical image processing algorithms. Numerous approaches have been proposed to filter speckle noise. Markov random field (MRF) modelization provides a convenient way to express both data fidelity constraints and desirable properties of the filtered image. In this context, total variation minimization has been extensively used to constrain the oscillations in the regularized image while preserving its edges. Speckle noise follows heavy-tailed distributions, and the MRF formulation leads to a minimization problem involving nonconvex log-likelihood terms. Such a minimization can be performed efficiently by computing minimum cuts on weighted graphs. Due to memory constraints, exact minimization, although theoretically possible, is not achievable on large images required by remote sensing applications. The computational burden of the state-of-the-art algorithm for approximate minimization (namely the alpha -expansion) is too heavy specially when considering joint regularization of several images. We show that a satisfying solution can be reached, in few iterations, by performing a graph-cut-based combinatorial exploration of large trial moves. This algorithm is applied to joint regularization of the amplitude and interferometric phase in urban area SAR images.

Image Restoration with Discrete Constrained Total Variation Part II: Levelable Functions, Convex Priors and Non-Convex Cases

In Part II of this paper we extend the results obtained in Part I for total variation minimization in image restoration towards the following directions: first we investigate the decomposability property of energies on levels, which leads us to introduce the concept of levelable regularization functions (which TV is the paradigm of). We show that convex levelable posterior energies can be minimized exactly using the level-independant cut optimization scheme seen in Part I. Next we extend this graph cut scheme to the case of non-convex levelable energies.We present convincing restoration results for images corrupted with impulsive noise. We also provide a minimum-cost based algorithm which computes a global minimizer for Markov Random Field with convex priors. Last we show that non-levelable models with convex local conditional posterior energies such as the class of generalized Gaussian models can be exactly minimized with a generalized coupled Simulated Annealing.

Estimating Gaussian Markov random field parameters in a nonstationary framework: application to remote sensing imaging

In this paper, we tackle the problem of estimating textural parameters. We do not consider the problem of texture synthesis, but the problem of extracting textural features for tasks such as image segmentation. We take into account nonstationarities occurring in the local mean. We focus on Gaussian Markov random fields for which two estimation methods are proposed, and applied in a nonstationary framework. The first one consists of extracting conditional probabilities and performing a least square approximation. This method is applied to a nonstationary framework, dealing with the piecewise constant local mean. This framework is adapted to practical tasks when discriminating several textures on a single image. The blurring effect affecting edges between two different textures is thus reduced. The second proposed method is based on renormalization theory. Statistics involved only concern variances of Gaussian laws, leading to Cramer-Rao estimators. This method is thus especially robust with respect to the size of sampling. Moreover, nonstationarities of the local mean do not affect results. We then demonstrate that the estimated parameters allow texture discrimination for remote sensing data. The first proposed estimation method is applied to extract urban areas from SPOT images. Since discontinuities of the local mean are taken into account, we obtain an accurate urban areas delineation. Finally, we apply the renormalization based on method to segment ice in polar regions from AVHRR data.

Hierarchical Markov random field models applied to image analysis: a review

The need for hierarchical statistical tools for modeling and processing image data, as well as the success of Markov random fields (MRFs) in image processing, have recently given rise to a significant research activity on hierarchical MRFs and their application to image analysis problems. Important contributions, relying on different models and optimization procedures, have thus been recorded in the literature. This paper presents a synthetic overview of available models and algorithms, as well as an attempt to clarify the vocabulary in this field. We propose to classify hierarchical MRF-based approaches as explicit and implicit methods, with appropriate subclasses. Each of these major classes is defined in the paper, and several specific examples of each class of approach are described.

Recognition of degraded characters using dynamic Bayesian networks

In this paper, we investigate the application of dynamic Bayesian networks (DBNs) to the recognition of degraded characters. DBNs are an extension of one-dimensional hidden Markov models (HMMs) which can handle several observation and state sequences. In our study, characters are represented by the coupling of two HMM architectures into a single DBN model. The interacting HMMs are a vertical HMM and a horizontal HMM whose observable outputs are the image columns and image rows, respectively. Various couplings are proposed where interactions are achieved through the causal influence between state variables. We compare non-coupled and coupled models on two tasks: the recognition of artificially degraded handwritten digits and the recognition of real degraded old printed characters. Our models show that coupled architectures perform more accurately on degraded characters than basic HMMs, the linear combination of independent HMM scores, as well as discriminative methods such as support vector machines (SVMs).

Joint Regularization of Phase and Amplitude of InSAR Data: Application to 3-D Reconstruction

Interferometric synthetic aperture radar (SAR) images suffer from a strong noise, and their regularization is often a prerequisite for successful use of their information. Independently of the unwrapping problem, interferometric phase denoising is a difficult task due to shadows and discontinuities. In this paper, we propose to jointly filter phase and amplitude data in a Markovian framework. The regularization term is expressed by the minimization of the total variation and may combine different information (phase, amplitude, optical data). First, a fast and approximate optimization algorithm for vectorial data is briefly presented. Then, two applications are described. The first one is a direct application of this algorithm for 3-D reconstruction in urban areas with very high resolution images. The second one is an adaptation of this framework to the fusion of SAR and optical data. Results on aerial SAR images are presented.

Optimal Relay Placement in Cellular Networks

In this paper, we address the problem of optimally placing relay nodes in a cellular network with the aim of maximizing cell capacity. In order to accurately model interference, we use a dynamic framework, in which users arrive at random time instants and locations, download a file and leave the system. A fixed point equation is solved to account for the interactions between stations. We also propose an extension of a fluid model to relay based cellular networks. This allows us to obtain quick approximations of the Signal to Interference plus Noise Ratio (SINR) that are very close to 3GPP LTE-A guideline results in terms of SINR distribution. We then use these formulas to develop a dedicated Simulated Annealing (SA) algorithm, which adapts dynamically the temperature to energy variations and uses a combination of coarse and fine grids to accelerate the search for an optimized solution. Simulations results are provided for both in-band and out-of-band relays. They show how relays should be placed in a cell in order to increase the capacity in case of uniform and non-uniform traffic. The crucial impact of the backhaul link is analyzed for in-band relays. Insights are given on the influence of shadowing.

Fast SAR image restoration, segmentation, and detection of high-reflectance regions

An iterative filter that can be used for speckle reduction and restoration of synthetic aperture radar (SAR) images is presented here. This method can be considered as a first step in the extraction of other important information. The second step is the detection of high-reflectance regions and continues with the segmentation of the total image. We have worked in three-look simulated and real European Remote Sensing 1 satellite amplitude images. The iterative filter is based on a membrane model Markov random field approximation optimized by a synchronous local iterative method. The final form of restoration gives a total sum-preserving regularization for the pixel values of our image. The high-reflectance regions are defined as the brightest regions of the restored image. After the separation of this extreme class, we give a fast segmentation method using the histogram of the restored image.