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Journal papers and Book Chapters – peer-reviewed

M.V. Joshi, A. Jalobeanu: “MAP estimation for Multiresolution Fusion in Remotely Sensed Images using an IGMRF Prior Model” - IEEE Trans. on Geoscience and Remote Sensing (TGRS), accepted, Jul 2009
In this paper we propose a model based approach for the multiresolution fusion of satellite images. Given the high spatial resolution panchromatic (Pan) image and a low spatial and high spectral resolution multispectral (MS) image acquired over the same geographical area the problem is to generate a high spatial and high spectral resolution multispectral image. This is clearly an ill-posed problem and hence we need a proper regularization. We model each of the low spatial resolution MS images as the aliased and noisy versions of their corresponding high spatial resolution i.e., fused (to be estimated) MS images. A proper aliasing matrix is assumed to take care of the undersampling process. The high spatial resolution MS images to be estimated are then modeled as separate Inhomogeneous Gaussian Markov Random Fields (IGMRF) and a Maximum A Posteriori (MAP) estimation is used to obtain the fused image for each of the MS bands. The IGMRF parameters are estimated from the available high resolution Pan image and are used in the prior model for regularization purposes. Since the method does not directly operate on the Pan pixel values as most of the other methods do, the spectral distortion is minimum and the spatial properties are better preserved in the fused image as the IGMRF parameters are learned at every pixel. We demonstrate the effectiveness of our approach over some existing methods by conducting the experiments on synthetic data as well as on the images captured by the Quickbird satellite.
@article{ref75,
}
A. Jalobeanu, J.A. Gutiérrez, E. Slezak: “Multisource data fusion and super-resolution from astronomical images” - Statistical Methodology (STAMET), Special issue on Astrostatistics, 5(4), Jul 2008
Virtual Observatories give us access to huge amounts of image data that are often redundant. Our goal is to take advantage of this redundancy by combining images of the same field of view into a single object. To achieve this goal, we propose to develop a multi-source data fusion method that relies on probability and band-limited signal theory. The target object is an image to be inferred from a number of blurred and noisy sources, possibly from different sensors under various conditions (i.e. resolution, shift, orientation, blur, noise...). We aim at the recovery of a compound model "image+uncertainties" that best relates to the observations and contains a maximum of useful information from the initial data set. Thus, in some cases, spatial super-resolution may be required in order to preserve the information. We propose to use a Bayesian inference scheme to invert a forward model, which describes the image formation process for each observation, and takes into account some a priori knowledge (e.g. stars as point sources). This involves both automatic registration and resampling, which are ill-posed inverse problems that are addressed within a rigorous Bayesian framework. The originality of the work is in devising a new technique of multi-image data fusion that provides us with super-resolution, self-calibration and possibly model selection capabilities. This approach should outperform existing methods such as resample-and-add or drizzling since it can handle different instrument characteristics for each input image and compute uncertainty estimates as well. Moreover, it is designed to also work in a recursive way, so that the model can be updated when new data becomes available.
@article{ref69,
}
D.D. Fitzenz, A. Jalobeanu, S.H. Hickman: “Integrating Laboratory Creep Compaction Data With Numerical Fault Models: a Bayesian Framework” - Journal of Geophysical Research (JGR), AGU, 112(B08410), Aug 2007
We developed a robust Bayesian inversion scheme to plan and analyze laboratory creep compaction experiments. We chose a simple creep law that features the main parameters of interest when trying to identify rate-controlling mechanisms from experimental data. By integrating the chosen creep law or an approximation thereof, one can use all the data, either simultaneously or in overlapping subsets, thus making more complete use of the experiment data and propagating statistical variations in the data through to the final rate constants. Despite the non-linearity of the problem, with this technique one can retrieve accurate estimates of both the stress exponent and the activation energy, even when the porosity time series data are noisy. Whereas adding observation points and/or experiments reduces the uncertainty on all parameters, enlarging the range of temperature or effective stress significantly reduces the covariance between stress exponent and activation energy. We apply this methodology to hydrothermal creep compaction data on quartz to obtain a quantitative, semiempirical law for fault zone compaction in the interseismic period. Incorporating this law into a simple direct rupture model, we find marginal distributions of the time to failure that are robust with respect to errors in the initial fault zone porosity.
@article{ref68,
}
A. Jalobeanu, J. Zerubia, L. Blanc-Féraud: “Bayesian estimation of blur and noise in remote sensing imaging” - in Blind image deconvolution: theory and applications (CRC), P. Campisi and K. Egiazarian ed., Taylor & Francis / CRC Press, May 2007
We propose a Bayesian approach to infer the parameters of both blur and noise in remote sensing images. The modulation transfer function (MTF) of the imaging system, including atmosphere, optics and pixel-level sampling, is modeled by a parametric function with a small number of parameters. The noise is assumed to be white, additive and Gaussian. Both blur and noise processes are supposed to be stationary. To constrain this ill-posed inverse problem, the unknown scene is modeled by a scale-invariant stochastic process governed by a fractal exponent and a global energy term. The main novelty consists of treating all parameters as random variables whose mean is estimated within a fully Bayesian framework. The chosen approach can be summarized as the computation of the mean posterior marginal related to useful parameters only. This requires integrating the joint probability density function (PDF) with respect to all the nuisance parameters, which is achieved through Laplace approximations.
In this chapter we present two approaches; the former is straightforward, and the latter leads to a more efficient, simplified and optimized estimation algorithm. In addition, we investigate methods of uncertainty estimation and model assessment, in order to validate our approach on real images and to propose further improvements.
@inbook{ref48,
}
A.R. Hajian, S.M. Movit, D. Trofimov, B. Balick, Y. Terzian, K.H. Knuth, D. Granquist-Fraser, K. Huyser, A. Jalobeanu, D. McIntosh, A.E. Jaskot, S. Palen, N. Panagia: “An Atlas of [N II] and [O III] Images and Spectra of Planetary Nebulae” - Astrophysical Journal Supplement (APJSup), University of Chicago Press, 169, Nov 2006
As part of a multi-epoch observing program designed to acquire precise expansion distances to planetary nebulae, we have completed a longslit, spectroscopic survey of selected ob jects. Our overall strategy is to deduce the distance to each nebula by measuring the angular expansion rate of the nebular shell from multiepoch narrowband imagery, and the nebular expansion velocity from spatially resolved narrowband spectra. However, the nebular geometry must be properly considered in order to infer a distance from an observed tangential motion and radial velocity. For spherical nebulae, vexp is easy to determine from the observed spectra. For even slightly more complex ellipsoidal nebulae, uncertainties in the nebular morphology and kinematics can dominate the uncertainties in the resulting distance. In this paper, we present an atlas of Hubble Space Telescope images and groundbased, longslit, narrowband spectra centered on the 6584A line of [N II] and the 5007A line of [O III]. Almost all of the images were obtained by us for this pro ject as part of GO 8390 and 8773 (duplicated in GO 7501). The spectra were obtained for a variety of slit positions across each target (as shown on the images) in an effort to account for non-spherical nebular geometries in a robust manner. We have extended the Prolate Ellipsoidal Shell model of Aaquist and Kwok (1996) and Zhang and Kwok (1998) to generate synthetic images as wel l as longslit spectra. Using this model, we have derived basic parameters for the subsample of PNe which present ellipsoidal appearances and regular kinematic patterns. We find differences between our parameters for the target PNe as compared to those of Zhang and Kwok (1998), which we attribute to increased spatial resolution for our image data and the inclusion of kinematic data in the model fits. The data and analysis presented in this paper can be combined with detections of nebular angular expansion rates to determine precise distances to the PN targets.
@article{ref52,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “An adaptive Gaussian model for satellite image deblurring” - IEEE Trans. on Image Processing (TIP), IEEE SPS, 13(1), Jan 2004
The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spatially variant characteristics, we propose here to use an inhomogeneous model. We use the Maximum Likelihood Estimator (MLE) to estimate its parameters and we show that the MLE computed on the corrupted image is not suitable for image deconvolution, because it is not robust to noise. Then we show that the estimation is correct only if it is made from the original image. Since this image is unknown, we need to compute
an approximation of sufficiently good quality to provide useful estimation results.
Such an approximation is provided by a wavelet-based deconvolution algorithm. Thus, a hybrid method is first used to estimate the space-variant parameters from this image and then to compute the regularized solution. The obtained results on high resolution satellite images simultaneously exhibit sharp edges, correctly restored textures and a high SNR in homogeneous areas, since the proposed technique adapts to the local characteristics of the data.
@article{ref4,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “Satellite image deblurring using complex wavelet packets” - International Journal of Computer Vision (IJCV), Kluwer, 51(3), Feb 2003
The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. Direct inversion leads to unacceptable noise amplification. Usually, the problem is either regularized during the inversion process, or the noise is filtered after deconvolution and decomposition in the wavelet transform domain. Herein, we have developed the second solution, by thresholding the coefficients of a new complex wavelet packet transform; the thresholding functions are automatically estimated. The use of complex wavelet packets enables translational invariance and improves directional selectivity, while remaining of complexity O(N). The results obtained exhibit both correctly restored textures and a high SNR in homogeneous areas. Compared to previous algorithms, the proposed method is faster, rotationally invariant and better takes into account the directions of the details and textures of the image, improving restoration. The images deconvolved in this way can be used as they are (the restoration step proposed here can be inserted directly in the acquisition chain), and they can also provide a starting point for an adaptive regularization method, enabling one to obtain sharper edges.
@article{ref5,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “Hyperparameter estimation for satellite image restoration using a MCMC Maximum Likelihood method” - Pattern Recognition (PR), Elsevier, 35(2), Feb 2002
The satellite image deconvolution problem is ill-posed and must be regularized. Herein, we use an edge-preserving regularization model using a phi function, involving two hyperparameters. Our goal is to estimate the optimal parameters in order to automatically reconstruct images. We propose to use the maximum-likelihood estimator (MLE), applied to the observed image. We need sampling from prior and posterior distributions. Since the convolution prevents use of standard samplers, we have developed a modified Geman?Yang algorithm, using an auxiliary variable and a cosine transform. We present a Markov chain Monte Carlo maximum-likelihood (MCMCML) technique which is able to simultaneously achieve the estimation and the reconstruction.
@article{ref8,
}
J. Zerubia, A. Jalobeanu, Z. Kato: “Markov Random Fields in Image Processing. Application to Remote Sensing and Astrophysics” - in New avenues for astronomical data analysis (J. Phys. IV France), A. Bijaoui and J.P. Rozelot ed., EDP Sciences, Jan 2002
Early vision directly deals with raw pixel data involving image compression, restoration, edge detection, segmentation, texture analysis, motion detection, optical flow, etc. Most of these problems can be formulated within a general framework, called image labeling, where we associate a label to each pixel from a finite set. The meaning of this label depends on the problem that we are trying to solve. For image restoration, it means a grey-level; for edge detection, it means the presence or the direction of an edge; for image segmentation, it means a class (or region); etc. The problem here is how to choose a label for a pixel, which is optimal in a certain sense.
Our approach is probabilistic: at each pixel, we want to select the most likely labeling. To achieve this goal, we need to define some probability measure on the set of all possible labelings. In real scenes, neighboring pixels have usually similar intensities; edges are smooth and often straight. In a probabilistic framework, such regularities are well expressed by Markov Random Fields (MRF). Another reason for dealing with MRF models is of course the Hammersley-Clifford theorem which allows to define MRF through clique-potentials. In the labeling problem, this leads to the following Bayesian formulation: we are looking for the Maximum A Posteriori (MAP) estimate of the label field yielding to the minimization of a usually non-convex energy function. [...]
@inbook{ref9,
}

Conference papers – peer-reviewed

A. Jalobeanu: “Spatial Accuracy Assessment of Digital Elevation Models: A Probabilistic Approach” - American Society for Photogrammetry and Remote Sensing annual conference (ASPRS'09), Baltimore, MD, USA, Mar 2009
We propose a new method for the measurement of high resolution topography from an optical stereo pair. The main contribution is the ability to propagate errors from the imperfect observed data to the final result, providing all accuracy estimates required for the use of topography in planetary or Earth science applications. Indeed, digital elevation models (DEM) computed from images using state of the art methods usually lack quantitative error estimates. This can be a major issue when the result is used to measure actual physical parameters, such as slope or terrain roughness.
Thus, we propose a new algorithm to infer a dense bidimensional disparity map from two images, that also estimates the spatial distribution of errors. We use a probabilistic approach, which provides a rigorous way of estimating parameters and uncertainties. All the parameters are defined as random variables within a Bayesian framework. We start by building a forward model, which consists of warping the observed scene using B-Splines and using a spatially adaptive radiometric change map for robustness purposes. An a priori smoothness model is introduced in order to stabilize the solution. Solving the inverse problem to recover the disparity map requires to optimize a global non-convex energy function, which is difficult task. A deterministic optimization based on a multi-grid strategy, followed by a local energy analysis at the optimum, allows to recover the a posteriori probability density function (pdf) of the disparity, which encodes both the optimal solution and the related error map.
Finally, the disparity field is converted into a DEM through a geometric camera model. This model is either known initially, or calibrated using the estimated disparity map and extra data (existing low-resolution DEM or ground control points). Automatic calibration from uncertain disparity and topographic data allows for a comprehensive error propagation from the input data to the final elevation model.
@inproceedings{ref84,
}
M.V. Joshi, A. Jalobeanu: “A MAP estimation for Multiresolution Fusion in Remotely Sensed Images using an IGMRF Prior Model” - IEEE International Geoscience & Remote Sensing Symposium (IGARSS'08), Boston MA, USA, Jul 2008
In this paper we propose a model based approach for multi-resolution fusion of satellite images. Given the high spatial resolution panchromatic (Pan) image and a low spatial and high spectral resolution multi-spectral (MS) image acquired over the same geographical area, the problem is to generate a high spatial and high spectral resolution multi-spectral image. This is clearly an ill-posed problem, which requires a proper regularization. We model each of the low spatial resolution MS images as the aliased and noisy versions of their corresponding high spatial resolution images. A decimation (aliasing) matrix is estimated for each of the MS bands by using the available Pan and the MS image. The high spatial resolution MS images to be estimated are then modeled as separate Inhomogeneous Gaussian Markov Random Fields (IGMRFs) and the Maximum A Posteriori (MAP) estimation is used to obtain the fused images. The required IGMRF parameters representing the spatial correlation among high resolution MS pixels are estimated from the available high resolution Pan image and are used in the prior model during the regularization. Since the method does not directly operate on the Pan pixel values as most of the other methods do, the spectral distortion is minimum and the spatial properties are better preserved in the fused image as the IGMRF parameters are learnt at every pixel. We demonstrate the effectiveness of our approach by conducting experiments on synthetic data as well as on real images captured by the Quickbird satellite.
@inproceedings{ref81,
}
A. Jalobeanu, D.D. Fitzenz: “Inferring deformation fields from multidate satellite images” - IEEE International Geoscience & Remote Sensing Symposium (IGARSS'08), Boston MA, USA, Jun 2008
We focus on a geophysical application of image processing: the measurement of high resolution ground deformation from two optical satellite images taken at different dates. Disparity maps estimated from image pairs usually lack quantitative error estimates. This is a major issue for measuring physical parameters, such as ground deformation or topography variations. Thus, we propose a new method to infer the disparity map. We adopt a probabilistic approach, treating all parameters as random variables, which provides a rigorous framework for parameter estimation and uncertainty evaluation. We start by defining a generative model of the data given all model variables. This forward model consists of warping the scene using B-Splines and applying a spatially adaptive radiometric change map. Then we use Bayesian inference to invert and recover the a posteriori probability density function (pdf) of the disparity map. The method is validated on multidate SPOT 5 imagery related to the Bam earthquake (Iran), showing results compatible with INSAR measurements.
@inproceedings{ref80,
}
A. Jalobeanu, D.D. Fitzenz: “Robust disparity maps with uncertainties for 3D surface reconstruction or ground motion inference” - ISPRS Proc. of Photogrammetric Image Analysis (PIA'07), Munich, Germany, Sep 2007
Disparity maps estimated using computer vision-derived algorithms usually lack quantitative error estimates. This can be a major issue when the result is used to measure reliable physical parameters, such as topography for instance. Thus, we developed a new method to infer the dense disparity map from two images. We use a probabilistic approach in order to compute uncertainties as well. Within this framework, parameters are described in terms of random variables. We start by defining a generative model for both raw observed images given all model variables, including disparities. The forward model mainly consists of warping the scene using B-Splines and adding a radiometric change map. Then we use Bayesian inference to invert and recover the a posteriori probability density function (pdf) of the disparity map.
The main contributions are: The design of an efficient fractal model to take into account radiometric changes between images; A multigrid processing so as to speed up the optimization process; The use of raw data instead of orthorectified imagery; Efficient approximation schemes to integrate out unwanted parameters and compute uncertainties on the result. Three applications could benefit from this disparity inference method: DEM generation from a stereo pair (along or across track), automatic calibration of pushbroom cameras, and ground deformation estimation from two images at different dates.
@inproceedings{ref71,
}
A. Jalobeanu, J.A. Gutiérrez: “Inverse covariance simplification for efficient uncertainty management” - Proc. of 26th workshop on Bayesian Inference and Maximum Entropy methods (MaxEnt'07), Saratoga Springs, NY, USA, Jul 2007
When it comes to manipulating uncertain knowledge such as noisy observations of physical quantities, one may ask how to do it in a simple way. Processing corrupted signals or images always propagates the uncertainties from the data to the final results, whether these errors are explicitly computed or not. When such error estimates are provided, it is crucial to handle them in such a way that their interpretation, or their use in subsequent processing steps, remain user-friendly and computationally tractable. A few authors follow a Bayesian approach and provide uncertainties as an inverse covariance matrix. Despite its apparent sparsity, this matrix contains many small terms that carry little information. Methods have been developed to select the most significant entries, through the use of information-theoretic tools for instance. One has to find a Gaussian pdf that is close enough to the posterior pdf, and with a small number of non-zero coefficients in the inverse covariance matrix. We propose to restrict the search space to Markovian models (where only neighbors can interact), well-suited to signals or images. The originality of our approach is in conserving the covariances between neighbors while setting to zero the entries of the inverse covariance matrix for all other variables. This fully constrains the solution, and the computation is performed via a fast, alternate minimization scheme involving quadratic forms. The Markovian structure advantageously reduces the complexity of Bayesian updating (where the simplified pdf is used as a prior). Moreover, uncertainties exhibit the same temporal or spatial structure as the data.
@inproceedings{ref70,
}
A. Jalobeanu, E. Slezak, J.A. Gutiérrez: “Multisource data fusion and super-resolution from astronomical images” - Astronomical Data Analysis IV (ADA IV), Marseille, France, Sep 2006
Virtual Observatories give us access to huge amounts of image data that are often redundant. Our goal is to take advantage of this redundancy by combining images of the same field of view into a single object. To achieve this goal, we propose to develop a multi-source data fusion method that relies on probability and band-limited signal theory. The target object is an image to be inferred from a number of blurred and noisy sources, possibly from different sensors under various conditions (i.e. resolution, shift, orientation, blur, noise...). We aim at the recovery of a compound model "image+uncertainties" that best relates to the observations and contains a maximum of useful information from the initial data set. Thus, in some cases, spatial super-resolution may be required in order to preserve the information. We propose to use a Bayesian inference scheme to invert a forward model, which describes the image formation process for each observation, and takes into account some a priori knowledge (e.g. stars as point sources). This involves both automatic registration and resampling, which are ill-posed inverse problems that are addressed within a rigorous Bayesian framework. The originality of the work is in devising a new technique of multi-image data fusion that provides us with super-resolution, self-calibration and possibly model selection capabilities. This approach should outperform existing methods such as resample-and-add or drizzling since it can handle different instrument characteristics for each input image and compute uncertainty estimates as well. Moreover, it is designed to also work in a recursive way, so that the model can be updated when new data becomes available.
@inproceedings{ref60,
}
A. Jalobeanu, J.A. Gutiérrez: “Multisource data fusion for bandlimited signals: a Bayesian perspective” - Proc. of 25th workshop on Bayesian Inference and Maximum Entropy methods (MaxEnt'06), Paris, France, Aug 2006
We consider data fusion as the reconstruction of a single model from multiple data sources. The model is to be inferred from a number of blurred and noisy observations, possibly from different sensors under various conditions. It is all about recovering a compound object, signal+uncertainties, that best relates to the observations and contains all the useful information from the initial data set.
We wish to provide a flexible framework for bandlimited signal reconstruction from multiple data. In this paper, we focus on a general approach involving forward modeling (prior model, data acquisition) and Bayesian inference. The proposed method is valid for n-D objects (signals, images or volumes) with multidimensional spatial elements. For the sake of clarity, both formalism and test results will be shown in 1D for single band signals. The main originality lies in seeking an object with a prescribed bandwidth, hence our choice of a B-Spline representation. This ensures an optimal sampling in both signal and frequency spaces, and allows for a shift invariant processing.
The model resolution, the geometric distortions, the blur and the regularity of the sampling grid can be arbitrary for each sensor. The method is designed to handle realistic Gauss+Poisson noise.
We obtained promising results in reconstructing a super-resolved signal from two blurred and noisy shifted observations, using a Gaussian Markov chain as a prior. Practical applications are under development within the SpaceFusion project. For instance, in astronomical imaging, we aim at a sharp, well-sampled, noise-free and possibly super-resolved image. Virtual Observatories could benefit from such a way to combine large numbers of multispectral images from various sources. In planetary imaging or remote sensing, a 3D image formation model is needed; nevertheless, this can be addressed within the same framework.
@inproceedings{ref58,
}
A. Jalobeanu: “Multisource data fusion and super-resolution from astronomical images” - Statistical Challenges in Modern Astronomy IV (SCMA'IV), Penn State, PA, USA, Jun 2006
The goal is to combine multiple astronomical images of the same field of view into a single model, within the Virtual Observatory framework where the huge amounts of data often exhibit some redundancy. To achieve this goal, we propose to develop a multi-source data fusion method using probability theory. We want to infer an image from several blurred and noisy observations, possibly from different sensors and instruments under various conditions. We aim at the recovery of a compound object "image+uncertainties" that contains a maximum of useful information from the initial data set. In some cases, conserving information may require achieving super-resolution.
We propose to use a Bayesian inference scheme to invert a generative model that explains the image formation for each observation while taking into account a priori knowledge. Understanding the image formation process is crucial.
The originality of the work is in devising a new technique of multi-image data fusion that also addresses spatial super-resolution and recursive model updating. This involves both automatic registration and resampling, which are difficult inverse problems that are treated within a probabilistic framework. Our contribution outperforms state of the art methods in astronomy since it can handle different instrument characteristics for each input and provide uncertainty estimates as well.
@inproceedings{ref59,
}
D.D. Fitzenz, A. Jalobeanu, S.H. Hickman, N.H. Sleep: “Integrating Laboratory Compaction Data With Numerical Fault Models: a Bayesian Framework” - Proc. of 25th workshop on Bayesian Inference and Maximum Entropy methods (MaxEnt'05), San Jose, CA, USA, Aug 2005
When analyzing rock deformation experimental data, one deals with both uncertainty and complexity. Though each part of the problem might be simple, the relationships between them can form a complex system. This often leads to partial or only qualitative data analyses from the experimental rock mechanics community, which limits the impact of these studies in other communities (e.g., modelling). However, it is a perfect case study for graphical models.
We present here a Bayesian framework that can be used both to infer the parameters of a constitutive model from rock compaction data, and to simulate porosity reduction within direct fault models from a known (e.g. lab-derived) constitutive relationship, while keeping track of all the uncertainties. This latter step is crucial if we are to go toward process-based seismic hazard assessment. Indeed, the rate of effective stress build-up (namely due to fault compaction) as well as the recovery of fault strength determine how long it will take for different parts of the previously ruptured fault to reach failure again, thus controlling both the timing and the size of the next rupture. But deterministic models need to rigorously incorporate uncertainties it they are to be useful in creating probabilistic assessments of seismic hazard. It is therefore important to work within a framework able to assess model validity as well as use data uncertainties.
Our approach involves a hierarchical inference scheme using several steps of marginalization. Existing experimental data are rarely adequate to completely define a single constitutive relationship for given physical fault material parameters over temperature and effective confining pressures of relevance to actual fault zones. We therefore focus on one rather general, though experimentally derived, compaction law to illustrate how applying the proposed inference scheme on simulated data can help design compaction experiments to provide better constraints on creep parameters.
@inproceedings{ref3,
}
A. Jalobeanu: “Bayesian Vision for Shape Recovery” - Proc. of 24th workshop on Bayesian Inference and Maximum Entropy methods (MaxEnt'04), Garching-Munich, Germany, Jul 2004
We present a new Bayesian vision technique that aims at recovering a shape from two or more noisy observations taken under similar lighting conditions. The shape is parametrized by a piecewise linear height field, textured by a piecewise linear irradiance field, and we assume Gaussian Markovian priors for both shape vertices and irradiance variables. The modeled observation process, equivalent to rendering, is modeled by a non-affine projection (e.g. perspective projection) followed by a convolution with a piecewise linear point spread function, and contamination by additive Gaussian noise. We assume that the observation parameters are calibrated beforehand.
The major novelty of the proposed method consists of marginalizing out the irradiances considered as nuisance parameters, which is achieved by a hierarchy of approximations. This reduces the inference to minimizing an energy that only depends on the shape vertices, and therefore allows an efficient Iterated Conditional Mode (ICM) optimization scheme to be implemented. A Gaussian approximation of the posterior shape density is computed, thus providing estimates of both the geometry and its uncertainty. We illustrate the effectiveness of the new method by shape reconstruction results in a 2D case. A 3D version is currently under development and aims at recovering a surface from multiple images, reconstructing the topography by marginalizing out both albedo and shading.
@inproceedings{ref2,
}
A. Jalobeanu, F.O. Kuehnel, J.C. Stutz: “Modeling Images of Natural 3D Surfaces: Overview and Potential Applications” - Proc. of IEEE conf. on Computer Vision and Pattern Recognition, Graphical Model-Based Vision workshop (CVPR'04), Washington DC, USA, Jul 2004
Generative models of natural images have long been used in computer vision. However, since they only describe the statistics of 2D scenes, they fail to capture all the properties of the underlying 3D world. Even though such models are sufficient for many vision tasks, a 3D scene model is needed when it comes to inferring a 3D object or its characteristics. In this paper, we present such a generative model, incorporating both a multiscale surface prior model for surface geometry and reflectance, and an image formation process model based on realistic rendering, that accounts for the physics of image generation. We focus on the computation of the posterior model parameter densities, and on the critical aspects of the rendering. We also discuss how to efficiently invert the model within a Bayesian framework. We present a few potential applications, such as asteroid modeling and planetary topography recovery, illustrated by promising results on real images.
@inproceedings{ref1,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “Natural image modeling using complex wavelets” - Proc. of SPIE, Wavelets X (SPIE-5207), San Diego, CA, USA, Aug 2003
We propose to model satellite and aerial images using a probabilistic approach. We show how the properties of these images, such as scale invariance, rotational invariance and spatial adaptivity lead to a new general model which aims to describe a broad range of natural images. The complex wavelet transform initially proposed by Kingsbury is a simple way of taking into account all these characteristics. We build a statistical model around this transform, by defining an adaptive Gaussian model with interscale dependencies, global parameters, and hyperpriors controlling the behavior of these parameters.
This model has been successfully applied to denoising and deconvolution, for real images and simulations provided by the French Space Agency.
@inproceedings{ref6,
}
A. Jalobeanu: “Fractal 3-D modeling of asteroids using wavelets on arbitrary meshes” - 1st Symp. on Interdisciplinary Approaches in Fractal Analysis (IAFA'03), Bucharest, Romania, May 2003
In this work, we study the 3D geometry of the small bodies in our Solar System in order to derive a probabilistic model of such objects. Images taken by various spacecrafts seem to exhibit a fractal behaviour, which we propose to investigate by using a multiscale approach. The idea is to look for a scale-invariant model that could simply describe the statistics of the asteroid surfaces. In order to access the different scales, we need either a Fourier or a Wavelet transform that could be applied to the triangular mesh defining the object to analyze. Since the former transform could not be easily constructed on meshes (because of their irregularity), we use a wavelet transform instead. This analysis tool is designed to capture both scaling and spatial information on the object. The main novelty w.r.t. existing wavelet transforms on meshes consists of providing a local estimate of the scale. This way, we show that the suspected fractal properties are actually an efficient modeling tool, and we build a statistical model of asteroids. A possible application of this model is the dense 3D reconstruction from multiple images, which is an ill-posed inverse problem. Using the fractal approach as a prior model within a Bayesian framework should enable us to get an accurate estimate of the asteroid shape.
@inproceedings{ref7,
}
A. Jalobeanu, R.D. Nowak, J. Zerubia, M. Figueiredo: “Satellite and aerial image deconvolution using an EM method with complex wavelets” - IEEE International Conference on Image Processing (ICIP'02), Rochester, NY, USA, Oct 2002
In this paper, we present a new deconvolution method, able to deal with noninvertible blurring functions. To avoid noise amplification, a prior model of the image to be reconstructed is used within a Bayesian framework. We use a spatially adaptive prior, defined with a complex wavelet transform in order to preserve shift invariance and to better restore variously oriented features. The unknown image is estimated by an EM technique, whose E step is a Landweber update iteration, and the M step consists of denoising the image, which is achieved by wavelet coefficient thresholding. The new algorithm has been applied to high resolution satellite and aerial data, showing better performance than existing techniques when the blurring process is not invertible, like motion blur for instance.
@inproceedings{ref73,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “Estimation of blur and noise parameters in remote sensing” - Proc. of Int. Conf. on Acoustics, Speech and Signal Processing (ICASSP'02), Orlando, FLA, USA, May 2002
In this paper we propose a new algorithm to estimate the parameters of the noise related to the sensor and the impulse response of the optical system, from a blurred and noisy satellite or aerial image. The noise is supposed to be white, Gaussian and stationary. The blur kernel has a parametric form and is modeled in such a way as to take into account the physics of the system (the atmosphere, the optics and the sensor). The observed scene is described by a fractal model, taking into account the scale invariance properties of natural images.
The estimation is performed automatically by maximizing a marginalized likelihood, which is achieved by a deterministic algorithm whose complexity is limited to O(N), where N is the number of pixels.
@inproceedings{ref10,
}
A. Jalobeanu, N.G. Kingsbury, J. Zerubia: “Image deconvolution using Hidden Markov modeling of Complex Wavelet Packets” - IEEE International Conference on Image Processing (ICIP'01), Thessaloniki, Greece, Oct 2001
In this paper, we propose to use a hidden Markov tree modeling of the complex wavelet packet transform, to capture the inter-scale dependencies of natural images. First, the observed image, blurred and noisy, is deconvolved without regularization. Then its transform is denoised within a Bayesian framework using the proposed model, whose parameters are estimated by an EM technique. The total complexity of this new deblurring algorithm remains O(N).
@inproceedings{ref36,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “Estimation des paramètres instrumentaux en imagerie satellitaire et aérienne” - 17th GRETSI Symposium on Signal and Image Processing (GRETSI'01), Toulouse, France, Sep 2001
In this paper, a new method is proposed, enabling us to estimate the parameters of the noise of the sensor and the impulse response of the optical system, from a blurred and noisy satellite or aerial image. The blurring kernel is parametrized, and modeled taking into account the physics of the sensor; the natural scene is described by a fractal model. The estimation is performed automatically, by maximizing the joint likelihood, which is achieved by a deterministic algorithm.
@inproceedings{ref35,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “Estimation rapide du paramètre de régularisation en déconvolution d'images” - Congrès francophone de vision par ordinateur (ORASIS'01), Cahors, France, Jun 2001
La déconvolution des images satellitaires floues et bruitées est un problème inverse mal posé, qui peut être régularisé dans un cadre bayésien par l'utilisation d'un modèle a priori de la solution reconstruite. Des modèles basés sur une fonctionnelle de régularisation non quadratique ont été utilisés avec succès afin de restaurer des images exemptes de bruit tout en préservant les contours. Toutefois, ces modèles présentent des paramètres, dont la valeur influe très fortement sur la qualité de la solution obtenue. Nous avions déjà proposé une technique d'estimation de ces paramètres, toujours dans un cadre bayésien, qui donne de bons résultats mais qui nécessite un temps de calcul important, car il s'agit d'une méthode stochastique. Dans cet article, nous proposons une nouvelle méthode d'estimation du paramètre de régularisation, fondée sur une approximation gaussienne. Cette technique présente l'avantage d'être déterministe. De cette manière, l'estimation est rendue particulièrement rapide, quelle que soit la taille de l'image que l'on cherche à déconvoluer, car elle ne nécessite qu'une FFT et quelques opérations par pixel. L'estimateur que nous avons utilisé est le maximum de vraisemblance (MV) en données complètes. La technique proposée consiste à approcher les distributions a priori et a posteriori par une loi gaussienne, ce qui rend les fonctions de normalisation relatives à ces lois calculables analytiquement. Le paramètre estimé de cette manière correspond à une régularisation quadratique (qui ne préserve pas les contours), il est donc réajusté en conséquence afin de permettre l'utilisation d'une fonctionnelle non quadratique lors de la déconvolution. Les images déconvoluées de cette manière peuvent être utilisées telles quelles, lorsque la dégradation n'est pas trop importante. Elles peuvent également servir à l'estimation des paramètres adaptatifs dans un algorithme travaillant dans une base d'ondelettes, car elles présentent des bords francs et un bruit résiduel suffisamment faible.
@inproceedings{ref34,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “Estimation of adaptive parameters for satellite image deconvolution” - International Conference on Pattern Recognition (ICPR'00), Barcelona, Spain, Sep 2000
The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spatially variant characteristics, we propose to use an inhomogeneous model. We use the Maximum Likelihood Estimator (MLE) to estimate its parameters. We demonstrate that the MLE computed on the corrupted image is not suitable for image deconvolution, because it is not robust to noise. Then we show that the estimation is correct only if it is made from the original image. As this image is unknown, we need to compute an approximation of sufficiently good quality to provide useful estimation results. Such an approximation is provided by a wavelet-based deconvolution algorithm. Thus, an hybrid method is first used to estimate the space-variant parameters from this image and second to compute the regularized solution. The obtained results on high resolution satellite images simultaneously exhibit sharp edges, correctly restored textures and a high SNR in homogeneous areas, since the proposed technique adapts to the local characteristics of the data.
@inproceedings{ref54,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “Satellite image deconvolution using complex wavelet packets” - International Conference on Image Processing (ICIP'00), Vancouver, Canada, Sep 2000
The deconvolution of blurred and noisy satellite images is an ill-posed inverse problem. Donoho has proposed to deconvolve the image without regularization and to denoise the result in a wavelet basis by thresholding the transformed coefficients.
We have developed a new filtering method, consisting of using a complex wavelet packet basis. Herein, the thresholding functions associated to the proposed method are automatically estimated. The estimation is performed within a Bayesian framework, by modeling the subbands using Generalized Gaussian distributions, and by applying the Maximum A Posteriori (MAP) estimator on each coefficient.
Compared to real wavelet-packet-based algorithms, the proposed method is shift invariant, provides good directionality properties and remains of complexity O(N).
@inproceedings{ref53,
}

Abstracts, Posters, Preprints, Reports and Theses

A. Jalobeanu: “Impact of DEM uncertainties on flood maps: vulnerability of the Portuguese coast to sea level rise” - 6º Simpósio de Meteorologia e Geofísica da APMG, Aldeia dos Capuchos, Portugal, Mar 2009
Flood maps are usually computed by thresholding digital elevation models (DEM) without taking into account errors on the topography. Even if scientists wish to do so in the future, the only information about DEM uncertainty available now is a RMS error at best. Thus, we propose to use our recent work on uncertainty estimation, allowing us to reconstruct a DEM and the spatial distribution of errors as well. Indeed, relevant flood maps can be derived rigorously if the elevation data comes with error bars. Flood probability maps could be directly computed, either for predefined sea levels, or for uncertain sea level rise predictions coming from global climate change models. The Bayesian framework allows for a rigorous management of various error sources so as to produce physically meaningful vulnerability maps. We plan to apply this methodology to several test sites on the portuguese coast using high-resolution digital aerial imagery.
@misc{ref83,
}
A. Jalobeanu: “Probabilistic Digital Elevation Model Generation For Spatial Accuracy Assessment” - AGU Fall Meeting, San Francisco, CA, USA, Dec 2008
We propose a new method for the measurement of high resolution topography from a stereo pair. The main application area is the study of planetary surfaces.
Digital elevation models (DEM) computed from image pairs using state of the art algorithms usually lack quantitative error estimates. This can be a major issue when the result is used to measure actual physical parameters, such as slope or terrain roughness.
Thus, we propose a new method to infer a dense bidimensional disparity map from two images, that also estimates the spatial distribution of errors. We adopt a probabilistic approach, which provides a rigorous framework for parameter estimation and uncertainty evaluation. All the parameters are described in terms of random variables within a Bayesian framework. We start by defining a forward model, which mainly consists of warping the observed scene using B-Splines and using a spatially adaptive radiometric change map for robustness purposes. An a priori smoothness model is introduced in order to stabilize the solution. Solving the inverse problem to recover the disparity map requires to optimize a global non-convex energy function, which is difficult in practice due to multiple local optima. A deterministic optimization technique based on a multi-grid strategy, followed by a local energy analysis at the optimum, allows to recover the a posteriori probability density function (pdf) of the disparity, which encodes both the optimal solution and the related error map.
Finally, the disparity field is converted into a DEM through a geometric camera model. This camera model is either known initially, or calibrated automatically using the estimated disparity map and available measurements of the topography (existing low-resolution DEM or ground control points). Automatic calibration from uncertain disparity and topography measurements allows for efficient error propagation from the initial data to the generated elevation model.
Results from Mars Express HRSC data are presented. A pair of images (including the nadir view) at 30m resolution was used to obtain a DEM with a vertical accuracy better than 10m in well-textured areas. The lack of information in smooth regions naturally led to large uncertainty estimates.
@misc{ref82,
}
D.D. Fitzenz, A. Jalobeanu, S.H. Hickman: “Integrating Laboratory Compaction Data with Numerical Fault Models: a Bayesian Framework” - Gordon Res. Conference on Rock Deformation, Big Sky, MT, USA, Sep 2006
@misc{ref76,
}
D.D. Fitzenz, A. Jalobeanu, S.H. Hickman: “Integrating Laboratory Compaction Data With Numerical Fault Models: a Bayesian Framework” - European Geosciences Union General Assembly, Vienna, Austria, Apr 2006
When analyzing rock deformation experimental data, one deals with both uncertainty and complexity. This often leads to partial or only qualitative data analyses from the experimental rock mechanics community, which limits the impact of these studies in other communities (e.g., modelling). However, it is a perfect case study for graphical models. We present here a Bayesian framework that can be used both to infer the parameters of a constitutive model from rock compaction data, and to generate porosity reduction within direct fault models from a known (e.g. lab-derived) constitutive relationship, and still keep track of all the uncertainties. This latter step is crucial if we are to go toward process-based seismic hazard assessment. Indeed, the rate of effective stress build-up (namely due to fault compaction) as well as the recovery of fault strength determine how long it will take for different parts of the previously ruptured fault to reach failure again, thus controlling both the timing and the size of the next rupture. But deterministic models need a measure of their robustness to become process-based earthquake-rupture forecast models. It is therefore important to work within a framework able to assess model validity as well as use data uncertainties. Our approach involves a hierarchical inference scheme using several steps of marginalization. We focus on one rather general, though experimentally derived, model of a compaction law, with a stress exponent, an apparent activation energy, and a porosity term as main parameters. We will first describe the method and show how it can help define the number and the duration of the experiments, as well as the range of conditions that would lead to a good determination of the physical parameters. We will then present an application to the Niemeijer et al (EPSL2002) data on quartz. Finally we will show how such creep laws can be implemented in direct models of pore pressure evolution using graphical models as a guide to propagate the uncertainties.
@misc{ref66,
}
D.D. Fitzenz, A. Jalobeanu, S.H. Hickman: “Integrating Laboratory Compaction Data with Numerical Fault Models: a Bayesian Framework” - AGU Fall Meeting, San Francisco, CA, USA, Dec 2004
@misc{ref77,
}
A. Jalobeanu, L. Blanc-Féraud, J. Zerubia: “Digital image processing method in particular for satellite images” - Patent #20040234162, Washington, DC, USA, Nov 2004
The invention concerns processing of digital images, captured by detection of electromagnetic waves, such as satellite pictures. The inventive processing consists in applying a parameterable fractal modelling to Fourier transforms of the pixels of the image and comparing (fig) the thus modelled transforms (aijq, wo) to the initial transforms to bring the parameters (q,w0) closer to the fractal model, and if required, the parameters of a transfer function of the instrument which has captured the image.
@unpublished{ref11,
}
A. Jalobeanu: “Modèles, estimation bayésienne et algorithmes pour la déconvolution d'images satellitaires et aériennes” - University of Nice Sophia Antipolis PhD Thesis, France, Dec 2001
Satellite or aerial images are corrupted by the optical system and the sensor. To reconstruct a good quality image from a noisy and blurred observation, one needs to perform a deconvolution.
First, we recall the principles of the acquisition chain, from optics to the sensor (visible or infrared), enabling us to model the degradation of the image.
In order to reconstruct the image without amplifying the noise, while preserving edges and textures, it is necessary to impose constraints on the reconstructed solution, which consists of choosing a prior model. We study satellite and aerial image modeling, which can be done within both probabilistic and variational frameworks, and using both discrete and continuous models. We propose new statistical models that take into account the fractal properties of natural scenes and their non-stationarity, using multiscale and adaptive approaches.
Next we study different techniques for estimating the model parameters, describing the properties of the images to be reconstructed. These techniques are developed within a Bayesian framework, and can be solved using either stochastic, or deterministic algorithms, depending on the problem.
Finally, we propose new fully automatic reconstruction algorithms. First, we suppose that the degradations (blurring kernel and noise statistics) are known, and we try to reconstruct the unknown image. Second, we consider the case where these degradations are unknown. We perform a blind deconvolution, in two steps, the first step consisting of determining the instrumental parameters, and the second of deconvolving the image with fixed degradation parameters.
Tests have been performed on remote sensing data such as satellite images (SPOT 5 and Pléïades simulations) and high resolution visible and infrared aerial images.
@phdthesis{ref12,
}

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Astronomy & Astrophysics

Planetary Imaging (Small Bodies & Planets)

Remote Sensing (Earth Observation)

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Journal papers and Book Chapters – peer-reviewed

Conference papers – peer-reviewed

Abstracts, Posters, Preprints, Reports and Theses

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