N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, no. 5, pp. 465--475, 1997.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....of multi dimensional laws. II. HIDDEN MARKOV CHAIN MODEL In the context of HMC model, the remotely sensed data is considered as a noisy observation from which the segmentation has to be found. The 2D observation is first transformed into a 1D chain through a Hilbert Peano scan on the image [10]. When the observation is an hyperspectral data cube, the Hilbert Peano scan is applied spatially in order to yield a chain that contains each pixel y (i.e. each spectral signature) along the scan. A. Overview of the scalar case It is considered that observations y, which are the pixels of the ....

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chain and unsupervised image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, no. 5, pp. 465--475, May 1997.

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N. Giordana and W. Pieczynski, Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation, IEEE Trans. on PAMI, Vol. 19, No. 5, pp. 465-475, 1997.

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N. Giordana and W. Pieczynski, Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 5, pp. 465-475, 1997.

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N. Giordana and W. Pieczynski, Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 5, pp. 465-475, 1997.

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N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, pp. 465--475, 1997.

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N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chain and unsupervised image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, no. 5, pp. 465--475, May 1997.

....= # , # . III. HIDDEN MARKO V CHAIN MONj In the context of HMC model, the remote sensing data is considered as a noisy observation from which the segmentation has to be found. The 2D observation is first transformed into a 1D chain through a Hilbert Peano scan on the image [5]. When this observation is of vector value, the Hilbert Peano scan is applied spatially in order to yield a chain that contains each pixel (i. L 1 , # L 1 , # ) along the scan. A. Overview of the scalar case It is considered that observations y, which are the pixels of the ....

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chain and unsupervised image segmentation," IEEE Trans. PatternAnal. MachineIntell. , vol. 19, no. 5, pp. 465--475, May 1997.

....posteriori (MAP) or the maximum posterior marginal (MPM) However, the computing time is often prohibitive with this approach. A substantially quicker alternative is to use a hidden Markov chain (HMC) model, which can be adapted to two dimensional analysis through a Hilbert Peano scan of the image [1, 2, 3, 4]. In the case of unsupervised classification, the statistical properties of the different classes are unknown and must be estimated. For each of the Markov models cited above, we can estimate characteristic parameters with iterative methods such as estimation maximisation (EM) 5] stochastic ....

....estimation (ICE) 7, 8] Classical mixture estimation consists in identifying the parameters of a set of Gaussian distributions corresponding to the different classes. In generalised mixture estimation we are not limited to Gaussian distributions, but to a finite set of distribution families [9, 4]. For each class we thus seek both the correct distribution family and the parameters that best describe its samples. In a recent study [10] we compared analysis schemes based on HMRF and HMC models on simulated synthetic aperture radar (SAR) images. We limited ourselves to the ICE estimation ....

[Article contains additional citation context not shown here]

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 5, pp. 465--475, 1997.

No context found.

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 5, pp. 465-475, 1997.

....4 8:9 76 9= III. HIDDEN MARKOV CHAIN MODEL In the context of HMC model, the remote sensing data is considered as a noisy observation from which the segmentation has to be found. The 2D observation is first transformed into a 1D chain through a Hilbert Peano scan on the image [5]. When this observation is of vector value, the Hilbert Peano scan is applied spatially in order to yield a chain that contains each pixel (i.e. 2 3 4 6 4 8;9 9A ) along the scan. A. Overview of the scalar case It is considered that observations , which are the pixels of ....

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chain and unsupervised image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, no. 5, pp. 465--475, May 1997.

....the vector Y = III. HIDDEN MARKOV CHAIN MODEL In the context of HMC model, the remote sensing data is considered as a noisy observation from which the segmentation has to be found. The 2D observation is first transformed into a 1D chain through a Hilbert Peano scan on the image [5]. When this observation is of vector value, the Hilbert Peano scan is applied spatially in order to yield a chain that contains each pixel (i.e. along the scan. A. Overview of the scalar case It is considered that observations y, which are the pixels of the image, are the noisy ....

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chain and unsupervised image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, no. 5, pp. 465--475, May 1997.

....the maximum posterior marginal (MPM) 3] 10] However, the computing time is considerable and often prohibitive with this approach. A substantially quicker alternative is to use Markov chains, which can be adapted to two dimensional (2 D) analysis through a Hilbert Peano scan of the image [11] [14]. In the case of unsupervised classification, the statistical properties of the different classes are unknown and must be estimated. For each of the Markov models cited above, we can estimate characteristic parameters with iterative methods such as expectation maximization (EM) 15] 17] ....

....to the different classes of the image. The weighted sum (or mixture) of the distributions of the different classes should approach the overall distribution of the image. In generalized mixture estimation, we are not limited to Gaussian distributions, but to a finite set of distribution families [14], 21] For each class we thus seek both the distribution family and the parameters that best describe its samples. In this paper, we consider some distribution families that are well adapted to single or multilook amplitude radar images and to classes with or without texture [2] By texture, we ....

[Article contains additional citation context not shown here]

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, pp. 465--475, May 1997.

....posteriori (MAP) or the maximum posterior marginal (MPM) However, the computing time is often prohibitive with this approach. A substantially quicker alternative is to use a hidden Markov chain (HMC) model, which can be adapted to two dimensional analysis through a Hilbert Peano scan of the image [1, 2, 3, 4]. In the case of unsupervised classification, the statistical properties of the different classes are unknown and must be estimated. For each of the Markov models cited above, we can estimate characteristic parameters with iterative methods such as estimation maximisation (EM) 5] stochastic ....

....estimation (ICE) 7, 8] Classical mixture estimation consists in identifying the parameters of a set of Gaussian distributions corresponding to the different classes. In generalised mixture estimation we are not limited to Gaussian distributions, but to a finite set of distribution families [9, 4]. For each class we thus seek both the correct distribution family and the parameters that best describe its samples. In a recent study [10] we compared analysis schemes based on HMRF and HMC models on simulated synthetic aperture radar (SAR) images. We limited ourselves to the ICE estimation ....

[Article contains additional citation context not shown here]

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 5, pp. 465--475, 1997.

No context found.

Giordana, N. and Pieczynski, W. "Estimation of generalized multisensor hidden markov chains and unsupervised imge segmentation". IEEE Trans. on PAMI, vol 19, n. 5, pp 465-475, 1997.

.... a Posteriori (MAP) once we have adopted some model for the class process like, for instance, Markov field [6, 11] These methods can be made unsupervised by estimating the model parameters by some general methods like Stochastic Gradient (SG, 16] or Iterative Conditional Estimation (ICE, [8, 9]) When the nature of the noise is not known exactly, it is still possible to estimate the model using some recent extension of ICE [8] Finally, considering the multisensor case with sensors neither independent nor Gaussian, one can still estimate the model parameters by a further recent ....

.... be made unsupervised by estimating the model parameters by some general methods like Stochastic Gradient (SG, 16] or Iterative Conditional Estimation (ICE, 8, 9] When the nature of the noise is not known exactly, it is still possible to estimate the model using some recent extension of ICE [8]. Finally, considering the multisensor case with sensors neither independent nor Gaussian, one can still estimate the model parameters by a further recent extension ICE [12] On the other hand, the Dempster Shafer theory of evidence can provide some interesting extension of the classical ....

[Article contains additional citation context not shown here]

N. Giordana and W. Pieczynski, Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation, IEEE Transactions on PAMI, Vol. 19, No. 5, pp. 465-475, 1997.

....of PMRF could be the verification of the existing conditions uniformly with respect to X . The second problem is the parameter estimation one. One could view applying the general Iterative Condition Estimation (ICE [Pie92] which gives satisfying results in some classical situations [DMP97] [GiP97], SaP97] Using ICE requests considering an estimator from complete data ( X,Y ) one possible way of seeking such an estimator could be considering the stochastic gradient [You88] applied to ( X,Y ) instead of X . Acknowledgment. We thank Alain Hillion, Directeur Scientifique de l cole ....

N. Giordana and W. Pieczynski, Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 5, pp. 465-475, 1997.

....Bayesian sensor, in pixel by pixel way as well as in the Markovian one. The first series of experiments, described in the Section V A, is concerned with some hand drawn images. Section V B is devoted to the unsupervised fusion using an original variant of the generalized mixture estimation [9] [14], and in the last Section V C, we present some results of real world images segmentation. A. Simulated Images Let be a set of three classes and the power set of . We will consider two cases. In the first one, the evidential sensor is a consonant one, which means that the mass function defined by ....

....we have to determine , and concerning the Bayesian sensor, and , and concerning the Evidential one. Estimating these functions from the observations is the mixture estimation problem and we propose to solve it by applying a new variant of a recent method of generalized mixture estimation [14]. A mixture is called generalized when the form of each component is not known; however, it belongs to a given set of forms. For instance, if each of the densities , and can be Normal or exponential, we have eight possibilities of classical mixtures and the additional difficulty is to determine ....

[Article contains additional citation context not shown here]

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, pp. 465--475, May 1997.

....proposed [9, 21, 22, 31] We choose here to describe the socalled Iterative Conditional estimation (ICE) which is fairly general and flexible method. Firstly proposed in [22] ICE has been successfully used in different applications of hidden Markov models to different image processing problems [10, 13, 14, 19, 20]. Furthermore, first applications of ICE to Pairwise Markov Chains (PMC) and Pairwise Markov Fields have also given promising results [7, 8, 29] ICE resembles EM and some relationships are specified in [6] So, we briefly discuss how the particular ICE method used in [2, 19] can be adapted to the ....

N. Giordana and W. Pieczynski, Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation, IEEE Trans. on PAMI, Vol. 19, No. 5, pp. 465-475, 1997.

No context found.

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation," IEEE Trans. on PAMI 19(5), pp. 465--475, 1997.

....of X according to its posterior distribution are feasible, we may propose the use of Iterative Conditional Estimation (ICE, 9] for parameter estimation. This method has given good results, even in more complex situations where the form of the noise corresponding to each class is not known, [14, 15], or still in hierarchical models, 18, 20] To apply ICE, one needs an estimator from complete data (X; Y ) and the choice of the stochastic gradient [8] with the difference that it would be applied to (X; Y ) instead of X, for this estimator could be a good one. In fact, the use of the ....

Giordana N., Pieczynski W. : Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation. IEEE Trans. PAMI, 19(5), 465-475.

....n ) Different methods of such a statistical classification exist once the distribution P ( X , Y ) of (X,Y) is known. When P ( X , Y ) is not known, one has to identify it from Y = y , the only data available. The aim of our paper is to generalize to correlated sensors the method proposed in [8]. Let us first consider the case of one sensor. When P ( X , Y ) depends on an unknown parameter q , the problem is to estimate q from Y . This problem, which is known as the mixture estimation problem, is a very general and important one [17] The pioneering method of mixture estimation is the ....

....or Iterated Conditional Mode (ICM [1] 2 All these methods are easily generalizable to the multi sensor case when the noise is Gaussian. When the noise is not Gaussian and the sensors are independent, one may use the ICE General Mixture (ICE GEMI) algorithm, valid in the following context [8]. We have k classes, and so we have to find the k probability densities f 1 , f k on R m . Because of the independence, each of these densities f i is written f i (y 1 1 , y 1 2 , y 1 m ) f i 1 (y 1 1 ) f i 2 (y 1 2 ) f i m (y 1 m ) 1.1) ICE GEMI allows one to find ....

N. Giordana and W. Pieczynski, Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation, IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 5, pp. 465-475, 1997.

No context found.

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation," IEEE Trans. Pattern Anal. Machine Intell., vol. 19, no. 5, pp. 465--475, 1997.

No context found.

N. Giordana and W. Pieczynski, "Estimation of Generalized Multisensor Hidden Markov Chains and Unsupervised Image Segmentation," IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 5, pp. 465-475, May 1997.

No context found.

N. Giordana, W. Pieczynski, Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation, IEEE Trans. Pattern Anal. Mach. Intell. vol. 19 (5) (1997) 465--475.

No context found.

N. Giordana and W. Pieczynski, "Estimation of generalized multisensor hidden Markov chains and unsupervised image segmentation", IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. 19, No. 5, pp. 465-475, 1997.

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