Results 1  10
of
16
Hidden Markov measure field models for image segmentation
 IEEE Transactions on Pattern Analysis and Machine Intelligence
, 2003
"... Abstract—Parametric image segmentation consists of finding a label field that defines a partition of an image into a set of nonoverlapping regions and the parameters of the models that describe the variation of some property within each region. A new Bayesian formulation for the solution of this pro ..."
Abstract

Cited by 36 (1 self)
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Abstract—Parametric image segmentation consists of finding a label field that defines a partition of an image into a set of nonoverlapping regions and the parameters of the models that describe the variation of some property within each region. A new Bayesian formulation for the solution of this problem is presented, based on the key idea of using a doubly stochastic prior model for the label field, which allows one to find exact optimal estimators for both this field and the model parameters by the minimization of a differentiable function. An efficient minimization algorithm and comparisons with existing methods on synthetic images are presented, as well as examples of realistic applications to the segmentation of Magnetic Resonance volumes and to motion segmentation. Index Terms—Markov random fields, segmentation, motion. 1
Satellite image deconvolution using complex wavelet packets
 In Proc. of ICIP
, 2000
"... The deconvolution of blurred and noisy satellite images is an illposed 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 ..."
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Cited by 12 (6 self)
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The deconvolution of blurred and noisy satellite images is an illposed 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 waveletpacketbased algorithms, the proposed method is shift invariant, provides good directionality properties and remains of complexity O(N). Y=HX+NwhereHX=h?X 1.
An adaptive Gaussian model for Satellite image deblurring
"... The deconvolution of blurred and noisy satellite images is an illposed 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 inhomogene ..."
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Cited by 7 (1 self)
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The deconvolution of blurred and noisy satellite images is an illposed 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 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 su#ciently good quality to provide useful estimation results.
Satellite Image Deblurring Using Complex Wavelet Packets
 Int. J. Comput. Vis
, 2003
"... The deconvolution of blurred and noisy satellite images is an illposed 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 ..."
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Cited by 5 (2 self)
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The deconvolution of blurred and noisy satellite images is an illposed 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
Adaptive Parameter Estimation for Satellite Image Deconvolution
, 2000
"... The deconvolution of blurred and noisy satellite images is an illposed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Homogeneous regularization models do not provide sufficiently satisfactory results, since real satelli ..."
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Cited by 5 (1 self)
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The deconvolution of blurred and noisy satellite images is an illposed inverse problem, which can be regularized within a Bayesian context by using an a priori model of the reconstructed solution. Homogeneous regularization models do not provide sufficiently satisfactory results, since real satellite data show spatially variant characteristics. We propose
Estimation of adaptive parameters for satellite image deconvolution
 INRIA Research Report
, 2000
"... from CNRS sults: it is necessary to regularize the solution by introducing a priori constraints [1]. The regularization constraint is The deconvolution of blurred and noisy satellite images a roughness penalty on the solution. The regularized soluis an illposed inverse problem, which can be regula ..."
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Cited by 3 (2 self)
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from CNRS sults: it is necessary to regularize the solution by introducing a priori constraints [1]. The regularization constraint is The deconvolution of blurred and noisy satellite images a roughness penalty on the solution. The regularized soluis an illposed inverse problem, which can be regularized tionXis then computed by minimizing the energy: within a Bayesian context by using an a priori model of the reconstructed solution. Since real satellite data show spa(2) tially variant characteristics, we propose to use an inhomogeneous model. We use the Maximum Likelihood Estima It is equivalent to computing the Maximum A Posteriori tor (MLE) to estimate its parameters. We demonstrate that (MAP) within a Bayesian framework, by assuming thatX the MLE computed on the corrupted image is not suitable is a Markov Random Field (MRF) and follows the prior disfor image deconvolution, because it is not robust to noise. tributionP(X)=Z�1 (X)=Xijbxij(DxX)2ij+byij(DyX)2ij Xe�(X). is defined by: Then we show that the estimation is correct only if it is made from the original image. As this image is unknown, we need (3) to compute an approximation of sufficiently good quality to provide useful estimation results. Such an approximation is provided by a waveletbased wherebxijandbyijare the adaptive parameters, w.r.t. deconvolution algorithm. Thus, an hybrid method is first columns and lines, andDx;Dyare first order difference used to estimate the spacevariant parameters from this im operators. The variablesbare analogous to continuous line age and second to compute the regularized solution. The process [1], as a low value ofbcorresponds to an edge loobtained results on high resolution satellite images simultacated between two pixels. neously exhibit sharp edges, correctly restored textures and We have chosen to model the unknown image by an Ina high SNR in homogeneous areas, since the proposed techhomogeneous Gaussian MRF (IGMRF) [5], since real imnique adapts to the local characteristics of the data. ages cannot be efficiently described by homogeneous models, even by using nonlinearity through'functions. The
Waveletbased hyperparameter estimation for solving inverse problems
, 2012
"... We consider the problem of image restoration/reconstruction where the acquisition system is modeled by a linear operator with additive Gaussian noise. A variational approach is adopted for image inversion in order to compute a restored/reconstructed image, consisting in minimizing a convex criterion ..."
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Cited by 1 (0 self)
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We consider the problem of image restoration/reconstruction where the acquisition system is modeled by a linear operator with additive Gaussian noise. A variational approach is adopted for image inversion in order to compute a restored/reconstructed image, consisting in minimizing a convex criterion composed of two parts: a data fidelity term (e.g. quadratic) and a regularization term (e.g. ℓ 1norm) expressed in the wavelet domain. The purpose of this paper is to estimate the regularization hyperparameters (one per subband) based on a Maximum Likelihood (ML) estimator, only knowing the observed data. A difficult task in such estimation is to compute the expectation according to the a posteriori probability as there is no analytical form. This expectation must be approximated numerically by sampling the distribution. However, sampling the a posteriori distribution is a difficult task because of pixel interactions introduced by the linear operator (image acquisition) in the same time as the wavelet transform (regularization). Moreover, the possible different nature (ℓ 2, ℓ 1norm...) of the fidelity and regularization terms does not allow to easily process them simultaneously. We show that both operators can be separated using an auxiliary (hidden) variable and splitting the a posteriori probability in two parts which are sampled alternately using MCMC (Gibbs sampling and MetropolisHastings). We show the equivalence between both formulations of the a posteriori distribution. Then a gradient method is used to estimate the hyperparameters. Simulation results demonstrate the good performance and behavior of the proposed approach. 1
Alain Abergel Professeur de l’Université ParisSud 11 Coencadrant JeanFrançois Giovannelli Professeur de l’Université Bordeaux 1 Directeur de thèse
"... Inversion bayésienne myope et nonsupervisée pour l’imagerie surrésolue. Application à l’instrument SPIRE de l’observatoire spatial Herschel. ..."
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Inversion bayésienne myope et nonsupervisée pour l’imagerie surrésolue. Application à l’instrument SPIRE de l’observatoire spatial Herschel.
en Ingeniería y Tecnología Posgrado en Ingeniería de Sistemas
, 901
"... A novel formalism for Bayesian learning in the context of complex inference models is proposed. The method is based on the estimation of the marginal posterior densities via Stationary Fokker–Planck sampling. Bayesian inference is performed in classification and regression examples with a computatio ..."
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A novel formalism for Bayesian learning in the context of complex inference models is proposed. The method is based on the estimation of the marginal posterior densities via Stationary Fokker–Planck sampling. Bayesian inference is performed in classification and regression examples with a computation cost that grows slowly with the model’s dimension. 1
Posgrado en Ingeniería de Sistemas
, 901
"... A novel formalism for Bayesian learning in the context of complex inference models is proposed. The method is based on the use of Stationary Fokker–Planck (SFP) sampling in order to sample from the posterior density. The SFP procedure admits the construction of approximate analytical expressions for ..."
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A novel formalism for Bayesian learning in the context of complex inference models is proposed. The method is based on the use of Stationary Fokker–Planck (SFP) sampling in order to sample from the posterior density. The SFP procedure admits the construction of approximate analytical expressions for the marginals of the posterior. Off–line and on–line Bayesian inference and Maximum Likelihood Estimation from the posterior is performed in classification and regression examples. The computation cost of SFP, measured in terms of loss function evaluations, grows linearly with the inference model’s dimension. 1