contextual estimators of mixing probabilities for markov chain random fields abstract this paper discusses the estimation of proportions of classes from an image classification methods are compared with likelihood methods and the importance of contextual information is discussed the joint distribution of classes at neighbouring sites is modelled by a markov chain random field the class attributes are estimated from training sets and unclassified observations the effect of biased class means is reduced with a stochastic model of the bias contextual likelihood methods yield better results than non contextual methods

estimation of generalized multisensor hidden markov chains and unsupervised image segmentation this paper attacks the problem of generalized multisensor mixture estimation a distribution mixture is said to be generalized when the exact nature of components is not known but each of them belongs to a finite known set of families of distributions estimating such a mixture entails a supplementary difficulty one must label for each class and each sensor the exact nature of the corresponding distribution such generalized mixtures have been studied assuming that the components lie in the pearson system we propose a more general procedure with applications to estimating generalized multisensor hidden markov chains our proposed method is applied to the problem of unsupervised image segmentation the method proposed allows one to 1 identify the conditional distribution for each class and each sensor 2 estimate the unknown parameters in this distribution 3 estimate priors and 4 estimate the true class image

enhanced gradient for training restricted boltzmann machines restricted boltzmann machines rbms are often used as building blocks in greedy learning of deep networks however training this simple model can be laborious traditional learning algorithms often converge only with the right choice of metaparameters that specify for example learning rate scheduling and the scale of the initial weights they are also sensitive to specific data representation an equivalent rbm can be obtained by flipping some bits and changing the weights and biases accordingly but traditional learning rules are not invariant to such transformations without careful tuning of these training settings traditional algorithms can easily get stuck or even diverge in this letter we present an enhanced gradient that is derived to be invariant to bit flipping transformations we experimentally show that the enhanced gradient yields more stable training of rbms both when used with a fixed learning rate and an adaptive one

parametric inference for imperfectly observed gibbsian fields this paper presents a maximum likelihood estimation method for imperfectly observed gibbsian fields on a finite lattice this method is an adaptation of the algorithm given in younes 28 presentation of the new algorithm is followed by a theorem about the limit of the second derivative of the likelihood when the lattice increases which is related to convergence of the method some practical remarks about the implementation of the procedure are eventually given

hyperparameter estimation for satellite image restoration using a mcmc maximum likelihood method abstract the satellite image deconvolution problem is ill posed and must be regularized herein we use an edge preserving regularization model using a 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

an edge theorem for polytopes of polynomials which can drop in degree abstract a new version of the edge theorem for robust stability of polynomials that can drop in degree is given the proof is of elementary nature and a counterexample is given to show that the original edge theorem of bartlett hollot and lin does not hold for the general case of arbitrary degree dropping

estimation of generalized mixtures and its application in image segmentation we introduce the notion of a generalized mixture and propose some methods for estimating it along with applications to unsupervised statistical image segmentation a distribution mixture is said to be generalized when the exact nature of the components is not known but each belongs to a finite known set of families of distributions for instance we can consider a mixture of three distributions each being exponential or gaussian the problem of estimating such a mixture contains thus a new difficulty we have to label each of three components there are eight possibilities we show that the classical mixture estimation algorithms expectation maximization em stochastic em sem and iterative conditional estimation ice can be adapted to such situations once as we dispose of a method of recognition of each component separately that is when we know that a sample proceeds from one family of the set considered we have a decision rule for what family it belongs to considering the pearson system which is a set of eight families the decision rule above is defined by the use of skewness and kurtosis the different algorithms so obtained are then applied to the problem of unsupervised bayesian image segmentation we propose the adaptive versions of sem em and ice in the case of blind i e pixel by pixel segmentation global segmentation methods require modeling by hidden random markov fields and we propose adaptations of two traditional parameter estimation algorithms gibbsian em gem and ice allowing the estimation of generalized mixtures corresponding to pearson s system the efficiency of different methods is compared via numerical studies and the results of unsupervised segmentation of three real radar images by different methods are presented

method of robust stability analysis with highly structured uncertainties this paper presents a method of analyzing the stability of linear time invariant interconnected systems with uncertainties each subsystem is single input single output and its vector locus lies inside a polygon at each frequency it is shown that the convex closure of the image of the cartesian product of these polygons under the mapping phi det i fh agrees with the convex closure of the image of the vertices of these polygons under the mapping from this result the image can be estimated by a finite dumber of calculations a sufficient stability condition is obtained by applying this result to the multivariable nyquist stability criterion

estimation of generalized mixture in the case of correlated sensors this paper deals with unsupervised bayesian classification of multidimensional data we propose an extension of a previous method of generalized mixture estimation to the correlated sensors case the method proposed is valid in the independent data case as well as in the hidden markov chain or field model case with known applications in signal processing particularly speech or image processing the efficiency of the method proposed is shown via some simulations concerning hidden markov fields with application to unsupervised image segmentation

thermodynamics and statistical analysis of gaussian random fields gaussian fields are considered as gibbsian fields thermodynamic functions are calculated for them and the variational principle is proved as an application we get an approximation of log likelihood and an information theoretic interpretation of the asymptotic behaviour of the maximum likelihood estimator for gaussian markov fields

noise contrastive estimation of unnormalized statistical models with applications to natural image statistics we consider the task of estimating from observed data a probabilistic model that is parameterized by a finite number of parameters in particular we are considering the situation where the model probability density function is unnormalized that is the model is only specified up to the partition function the partition function normalizes a model so that it integrates to one for any choice of the parameters however it is often impossible to obtain it in closed form gibbs distributions markov and multi layer networks are examples of models where analytical normalization is often impossible maximum likelihood estimation can then not be used without resorting to numerical approximations which are often computationally expensive we propose here a new objective function for the estimation of both normalized and unnormalized models the basic idea is to perform nonlinear logistic regression to discriminate between the observed data and some artificially generated noise with this approach the normalizing partition function can be estimated like any other parameter we prove that the new estimation method leads to a consistent convergent estimator of the parameters for large noise sample sizes the new estimator is furthermore shown to behave like the maximum likelihood estimator in the estimation of unnormalized models there is a trade off between statistical and computational performance we show that the new method strikes a competitive trade off in comparison to other estimation methods for unnormalized models as an application to real data we estimate novel two layer models of natural image statistics with spline nonlinearities

a stochastic method for bayesian estimation of hidden markov random field models with application to a color model we propose a new stochastic algorithm for computing useful bayesian estimators of hidden markov random field hmrf models that we call exploration selection estimation ese procedure the algorithm is based on an optimization algorithm of o francois called the exploration selection e s algorithm the novelty consists of using the a posteriori distribution of the hmrf as exploration distribution in the e s algorithm the ese procedure computes the estimation of the likelihood parameters and the optimal number of region classes according to global constraints as well as the segmentation of the image in our formulation the total number of region classes is fixed but classes are allowed or disallowed dynamically this framework replaces the mechanism of the split and merge of regions that can be used in the context of image segmentation the procedure is applied to the estimation of a hmrf color model for images whose likelihood is based on multivariate distributions with each component following a beta distribution meanwhile a method for computing the maximum likelihood estimators of beta distributions is presented experimental results performed on 100 natural images are reported we also include a proof of convergence of the e s algorithm in the case of nonsymmetric exploration graphs

exact solutions via equivalence transformations of variable coefficient fifth order kdv equations abstract in this paper a family of variable coefficient fifth order kdv equations has been considered by using an infinitesimal method based on the determination of the equivalence group differential invariants and invariant equations are obtained invariants provide an alternative way to find equations from the family which may be equivalent to a specific subclass of the same family and the invertible transformation which maps both equivalent equations here differential invariants are applied to obtain exact solutions

parameter estimation for a stationary process on a d dimensional lattice summary we study asymptotic properties of various estimation procedures for a general stationary regular process on a d dimensional lattice differences between d 1 time series and d 2 spatial processes are pointed out we suppose that the process is observed on a set pn with cn points which tends to infinity with the same speed in all directions the relative edge effect is of order cn lid increasing with d this effect is without statistical importance if d 1 but is important if d 2 we give a lcn consistent asymptotically normal estimator of the underlying parameter the procedure being constructed by a modification of whittle s approximation to the log likelihood in the gaussian case this procedure is asymptotically efficient

the shape boltzmann machine a strong model of object shape a good model of object shape is essential in applications such as segmentation detection inpainting and graphics for example when performing segmentation local constraints on the shapes can help where object boundaries are noisy or unclear and global constraints can resolve ambiguities where background clutter looks similar to parts of the objects in general the stronger the model of shape the more performance is improved in this paper we use a type of deep boltzmann machine salakhutdinov and hinton international conference on artificial intelligence and statistics 2009 that we call a shape boltzmann machine sbm for the task of modeling foreground background binary and parts based categorical shape images we show that the sbm characterizes a strong model of shape in that samples from the model look realistic and it can generalize to generate samples that differ from training examples we find that the sbm learns distributions that are qualitatively and quantitatively better than existing models for this task

comparison theorems for gibbs measures the dobrushin comparison theorem is a powerful tool to bound the difference between the marginals of high dimensional probability distributions in terms of their local specifications originally introduced to prove uniqueness and decay of correlations of gibbs measures it has been widely used in statistical mechanics as well as in the analysis of algorithms on random fields and interacting markov chains however the classical comparison theorem requires validity of the dobrushin uniqueness criterion essentially restricting its applicability in most models to a small subset of the natural parameter space in this paper we develop generalized dobrushin comparison theorems in terms of influences between blocks of sites in the spirit of dobrushin shlosman and weitz that substantially extend the range of applicability of the classical comparison theorem our proofs are based on the analysis of an associated family of markov chains we develop in detail an application of our main results to the analysis of sequential monte carlo algorithms for filtering in high dimension

efficient recursions for general factorisable models let n s valued categorical variables be jointly distributed according to a distribution known only up to an unknown normalising constant for an unnormalised joint likelihood expressible as a product of factors we give an algebraic recursion which can be used for computing the normalising constant and other summations a saving in computation is achieved when each factor contains a lagged subset of the components combining in the joint distribution with maximum computational efficiency as the subsets attain their minimum size if each subset contains at most r 1 of the n components in the joint distribution we term this a lag r model whose normalising constant can be computed using a forward recursion in o sr 1 computations as opposed to o sn for the direct computation we show how a lag r model represents a markov random field and allows a neighbourhood structure to be related to the unnormalised joint likelihood we illustrate the method by showing how the normalising constant of the ising or autologistic model can be computed

truncation artifact reduction in magnetic resonance imaging by markov random field methods a new statistical method is proposed for reduction of truncation artifacts when reconstructing a function by a finite number of its fourier series coefficients following the bayesian approach it is possible to take into account both the errors induced by the truncation of the fourier series and some specific characteristics of the function a suitable markov random field is used for modeling these characteristics furthermore in applications like magnetic resonance imaging where these coefficients are the measured data the experimental random noise in the data can also be taken into account monte carlo markov chain methods are used to make statistical inference parameter selection in the bayesian model is also addressed and a solution for selecting the parameters automatically is proposed the method is applied successfully to both simulated and real magnetic resonance images

fundamental solution in classical elasticity via lie group method abstract in this paper we show that the fundamental solution kelvin s matrix of three dimensional classical elasticity can be obtained by using the lie symmetry method

stochastic relaxation gibbs distributions and the bayesian restoration of images we make an analogy between images and statistical mechanics systems pixel gray levels and the presence and orientation of edges are viewed as states of atoms or molecules in a lattice like physical system the assignment of an energy function in the physical system determines its gibbs distribution because of the gibbs distribution markov random field mrf equivalence this assignment also determines an mrf image model the energy function is a more convenient and natural mechanism for embodying picture attributes than are the local characteristics of the mrf for a range of degradation mechanisms including blurring nonlinear deformations and multiplicative or additive noise the posterior distribution is an mrf with a structure akin to the image model by the analogy the posterior distribution defines another imaginary physical system gradual temperature reduction in the physical system isolates low energy states annealing or what is the same thing the most probable states under the gibbs distribution the analogous operation under the posterior distribution yields the maximum a posteriori map estimate of the image given the degraded observations the result is a highly parallel relaxation algorithm for map estimation we establish convergence properties of the algorithm and we experiment with some simple pictures for which good restorations are obtained at low signal to noise ratios

stochastic approximation algorithms for partition function estimation of gibbs random fields we present an analysis of previously proposed monte carlo algorithms for estimating the partition function of a gibbs random field we show that this problem reduces to estimating one or more expectations of suitable functionals of the gibbs states with respect to properly chosen gibbs distributions as expected the resulting estimators are consistent certain generalizations are also provided we study computational complexity with respect to grid size and show that monte carlo partition function estimation algorithms can be classified into two categories e type algorithms that are of exponential complexity and p type algorithms that are of polynomial complexity turing reducible to the problem of sampling from the gibbs distribution e type algorithms require estimating a single expectation whereas p type algorithms require estimating a number of expectations with respect to gibbs distributions which are chosen to be sufficiently close to each other in the latter case the required number of expectations is of polynomial order with respect to grid size we compare computational complexity by using both theoretical results and simulation experiments we determine the most efficient e type and p type algorithms and conclude that p type algorithms are more appropriate for partition function estimation we finally suggest a practical and efficient p type algorithm for this task

a simulation based estimator for hidden markov random fields an estimator for estimating the parameters of a markov random field x from inaccurate observations is introduced the author considers first a markov gibbs random field x x sub i j on a lattice l i j i 1 2 n j 1 2 m the marginal distributions of x sub i j x sub i u j v u v 1 0 1 are first estimated from an image then random fields x are simulated with the probability of x sub i u j v b nearly equal to the estimate of p x sub i j x sub i u b a simulation method similar to the gibbs sampler is used the parameters of the markov random field model are estimated from the x s with the pseudolikelihood method

an adaptive gaussian model for satellite image deblurring 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 we then 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

the k m n equation with generalized evolution term studied by symmetry reductions and qualitative analysis abstract in this paper we obtain symmetry reductions of the k m n equation with generalized evolution term the reduction to ordinary differential equations comes from an optimal system of subalgebras some of these equations admit symmetries which lead to further reductions and one of them comes out suitable for qualitative analysis its dynamical behavior is fully described and conservative quantities are stated

theoremes de convergence presque sure pour une classe d algorithmes stochastiques a pas decroissant the paper studies the pathwise asymptotic behaviour of stochastic algorithms of the following general form theta n 1 theta n gamma n 1 f theta n y n 1 the hypotheses allowing discontinuities on the adaptation termf the process y n n 0 is a markov chain controlled by n for each fixed the markov chain y n n 0 is essentially of positive recurrent type

on the statistical analysis of dirty pictures may 7th 1986 professor a f m smith in the chair summary a continuous two dimensional region is partitioned into a fine rectangular array of sites or pixels each pixel having a particular colour belonging to a prescribed finite set the true colouring of the region is unknown but associated with each pixel there is a possibly multivariate record which conveys imperfect information about its colour according to a known statistical model the aim is to reconstruct the true scene with the additional knowledge that pixels close together tend to have the same or similar colours in this paper it is assumed that the local characteristics of the true scene can be represented by a nondegenerate markov random field such information can be combined with the records by bayes theorem and the true scene can be estimated according to standard criteria however the computational burden is enormous and the reconstruction may reflect undesirable largescale properties of the random field thus a simple iterative method of reconstruction is proposed which does not depend on these large scale characteristics the method is illustrated by computer simulations in which the original scene is not directly related to the assumed random field some complications including parameter estimation are discussed potential applications are mentioned briefly

lie and noether symmetries for a class of fourth order emden fowler equations a group classification of a fourth order ordinary differential equation is carried out the noether symmetries are considered and some first integrals are established solutions for special lane emden systems are also obtained from the invariant solutions of the investigated equation

estimation of fuzzy gaussian mixture and unsupervised statistical image segmentation this paper addresses the estimation of fuzzy gaussian distribution mixture with applications to unsupervised statistical fuzzy image segmentation in a general way the fuzzy approach enriches the current statistical models by adding a fuzzy class which has several interpretations in signal processing one such interpretation in image segmentation is the simultaneous appearance of several thematic classes on the same site we introduce a new procedure for estimating of fuzzy mixtures which is an adaptation of the iterative conditional estimation ice algorithm to the fuzzy framework we first describe the blind estimation i e without taking into account any spatial information valid in any context of independent noisy observations then we introduce in a manner analogous to classical hard segmentation the spatial information by two different approaches contextual segmentation and adaptive blind segmentation in the first case the spatial information is taken into account at the segmentation step level and in the second case it is taken into account at the parameter estimation step level the results obtained with the iterative conditional estimation algorithm are compared to those obtained with expectation maximization em and the stochastic em algorithms on both parameter estimation and unsupervised segmentation levels via simulations the methods proposed appear as complementary to the fuzzy c means algorithms

hierarchical reconstruction using geometry and sinogram restoration the authors describe and demonstrate a hierarchical reconstruction algorithm for use in noisy and limited angle or sparse angle tomography the algorithm estimates an object s mass center of mass and convex hull from the available projections and uses this information along with fundamental mathematical constraints to estimate a full set of smoothed projections the mass and center of mass estimates are made using a least squares estimator derived from the principles of consistency of the radon transform the convex hull estimate is produced by first estimating the positions of support lines of the object from each available projection and then estimating the overall convex hull using prior shape information estimating the position of two support lines from a single projection is accomplished using a generalized likelihood ratio technique for estimating jumps in linear systems results for simulated objects in a variety of measurement situations are shown and several possible extensions to this work are discussed

uniform lan condition of planar gibbsian point processes and optimality of maximum likelihood estimators of soft core potential functions a parametric model of planar point patterns in a bounded region is constructed using grand canonical gibbsian point processes with soft core potential functions a simple and explicit condition that this model becomes a uniform locally asymptotic normal ulan family will be given from this result we can conclude that the maximum likelihood estimator of the potential function is asymptotically efficient for a wide class of loss functions

polytopes of polynomials with zeros in a prescribed set in the publication by a c bartlett c v holot and h lin proc amer contr conf minneapolis mn 1987 a fundamental result is established on the zero locations of a family of polynomials it is shown that the zeros of a polytope p of nth order real polynomials are contained in a simply connected set d if and only if the zeros of all polynomials along the edges of p are contained in d the present authors are motivated by the fact that the requirement of simple connectedness of d may be too restrictive and applications such as dominant pole assignment and filter design where the separation of zeros is required they extend the edge criterion of bartlett et al to handle any set d whose complement d sup c has the following property every point d in d sup c lies on some continuous path which remains within d sup c and is unbounded this requirement is typically verified by inspection and allows for a large class of disconnected sets

lie symmetries and equivalence transformations for the barenblatt gilman model in this paper we have considered the barenblatt gilman equation which models the nonequilibrium countercurrent capillary impregnation the equation of this model is a third order equation and the unknown function concerns to the effective water saturation we have applied the classical method to get the lie group classification with respect to unknown function and we have constructed the equivalence transformations we have also obtained the invariant solutions for some forms of the equation including travelling wave solutions based on the jacobi elliptic sine function

on the estimation of noisy binary markov random fields possolo technical report no 77 department of statistics gn 22 university of washington seattle 1986 and derin and elliott ieee trans pattern analysis mach intell pami 9 39 55 1987 proposed for the estimation of binary and more general m ary markov random fields the logit method based on histogramming an image the authors applied the method to noise free markov random fields for estimation of noisy images one might recursively implement the logit method within an iterative restoration algorithm such as the iterated conditional modes icm method of besag j r statist soc b48 259 302 1986 by alternating parameter estimation and restoration it is noted that failure to smooth zero histogram counts for the purposes of estimation can cause icm to cycle indefinitely

exact calculation of the multiloop stability margin a mapping theorem by l a zadeh and c a desoer 1963 serves as the basis for an algorithm that computes the stability margin k sub m of diagonally perturbed multivariable feedback systems without conservatism the stability margin determination not only verifies system stability but also quantifies how much further the plan uncertainties can be extended before instability occurs the essence of the computational approach is the realization that the true image of a given domain can be approximated with arbitrary accuracy by first subdividing the domain into the requisite number of subdomains and then forming the union of the convex hulls of their images the technique is illustrated in an example with a plant model having three uncertainties in general the method is applicable to either siso or mimo lti systems whose uncertainties can be modeled with noninteracting coefficients in the open loop transfer function representations

decay of correlations under dobrushin s uniqueness condition and its applications an estimate on the correlation of functionals of gibbs fields satisfying dobrushin s uniqueness condition is given as a consequence a result of gross saying that the truncated pair correlation function decays in the same weighted summability sense as the potential can be extended to the whole dobrushin uniqueness region applications to the central limit theorem and the second derivative of the pressure are also given

a cumulant expansion technique for simultaneous markov random field image restoration and hyperparameter estimation we investigate hyperparameter estimation for incomplete data in markov random field image restoration assuming linear dependence of energies with respect to hyperparameters framework we use a cumulant expansion technique widely known in statistical physics and signal processing new insight is given on maximum likelihood estimation of hyperparameters of the prior regularization and contour probability distribution functions pdfs for an explicit joint boundary pixel process aimed to preserve discontinuities in particular the case where the prior regularization potential is an homogeneous function of pixels is fully analyzed a generalized stochastic gradient gsg algorithm with a fast sampling technique is devised aiming to achieve simultaneous hyperparameter estimation and pixel restoration image restoration performances of posterior mean performed during gsg convergence and of simulated annealing performed after gsg convergence are compared experimentally results and perspectives are given

combining monte carlo and mean field like methods for inference in hidden markov random fields issues involving missing data are typical settings where exact inference is not tractable as soon as nontrivial interactions occur between the missing variables approximations are required and most of them are based either on simulation methods or on deterministic variational methods while variational methods provide fast and reasonable approximate estimates in many scenarios simulation methods offer more consideration of important theoretical issues such as accuracy of the approximation and convergence of the algorithms but at a much higher computational cost in this work we propose a new class of algorithms that combine the main features and advantages of both simulation and deterministic methods and consider applications to inference in hidden markov random fields hmrfs these algorithms can be viewed as stochastic perturbations of variational expectation maximization vem algorithms which are not tractable for hmrf we focus more specifically on one of these perturbations and we prove their almost sure convergence to the same limit set as the limit set of vem in addition experiments on synthetic and real world images show that the algorithm performance is very close and sometimes better than that of other existing simulation based and variational em like algorithms

lie symmetries for lie systems a lie system is a nonautonomous system of first order differential equations admitting a superposition rule i e a map expressing its general solution in terms of a generic family of particular solutions and some constants using that a lie system can be considered as a curve in a finite dimensional lie algebra of vector fields a so called vessiot guldberg lie algebra we associate every lie system with a lie algebra of lie point symmetries induced by the vessiot guldberg lie algebra this enables us to derive lie symmetries of relevant physical systems described by first and higher order systems of differential equations by means of lie systems in an easier way than by standard methods a generalization of our results to partial differential equations is introduced among other applications lie symmetries for several new and known generalizations of the real riccati equation are studied

fuzzy markov random fields versus chains for multispectral image segmentation this paper deals with a comparison of recent statistical models based on fuzzy markov random fields and chains for multispectral image segmentation the fuzzy scheme takes into account discrete and continuous classes which model the imprecision of the hidden data in this framework we assume the dependence between bands and we express the general model for the covariance matrix a fuzzy markov chain model is developed in an unsupervised way this method is compared with the fuzzy markovian field model previously proposed by one of the authors the segmentation task is processed with bayesian tools such as the well known mpm mode of posterior marginals criterion our goal is to compare the robustness and rapidity for both methods fuzzy markov fields versus fuzzy markov chains indeed such fuzzy based procedures seem to be a good answer e g for astronomical observations when the patterns present diffuse structures moreover these approaches allow us to process missing data in one or several spectral bands which correspond to specific situations in astronomy to validate both models we perform and compare the segmentation on synthetic images and raw multispectral astronomical data