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This paper focuses on the classification of multichannel images. The proposed supervised Bayesian classification method applied to histological (medical) optical images and to remote sensing (optical and synthetic aperture radar) imagery consists of two steps. The first step introduces the joint statistical modeling of the coregistered input images. For each class and each input channel, the class-conditional marginal probability density functions are estimated by finite mixtures of well-chosen parametric families. For optical imagery, the normal distribution is a well-known model. For radar imagery, we have selected generalized gamma, log-normal, Nakagami and Weibull distributions. Next, the multivariate d-dimensional Clayton copula, where d can be interpreted as the number of input channels, is applied to estimate multivariate joint class-conditional statistics. As a second step, we plug the estimated joint probability density functions into a hierarchical Markovian model based on a quadtree structure. Multiscale features are extracted by discrete wavelet transforms, or by using input multiresolution data. To obtain the classification map, we integrate an exact estimator of the marginal posterior mode.

Object extraction from images is one of the most important tasks in remote sensing image analysis. For accurate extraction from very high resolution (VHR) images, object geometry needs to be taken into account. A method for incorporating strong yet flexible prior shape information into a marked point process model for the extraction of multiple objects of complex shape is presented. To control the computational complexity, the objects considered are defined using the image data and the prior shape information. To estimate the optimal configuration of objects, the process is sampled using a Markov chain based on a stochastic birth-and-death process on the space of multiple objects. The authors present several experimental results on the extraction of tree crowns from VHR aerial images.

We propose an alternate minimization algorithm for estimating the point-spread function (PSF) of a confocal laser scanning microscope and the specimen fluorescence distribution. A three-dimensional separable Gaussian model is used to restrict the PSF solution space and a constraint on the specimen is used so as to favor the stabilization and convergence of the algorithm. The results obtained from the simulation show that the PSF can be estimated to a high degree of accuracy, and those on real data show better deconvolution as compared to a full theoretical PSF model.

We comprehensively study the least-squares Gaussian approximations of the diffraction-limited 2D-3D paraxial-nonparaxial point-spread functions (PSFs) of the wide field fluorescence microscope (WFFM), the laser scanning confocal microscope (LSCM), and the disk scanning confocal microscope (DSCM). The PSFs are expressed using the Debye integral. Under an L^∞ constraint imposing peak matching, optimal and near-optimal Gaussian parameters are derived for the PSFs. With an L^1 constraint imposing energy conservation, an optimal Gaussian parameter is derived for the 2D paraxial WFFM PSF. We found that (1) the 2D approximations are all very accurate; (2) no accurate Gaussian approximation exists for 3D WFFM PSFs; and (3) with typical pinhole sizes, the 3D approximations are accurate for the DSCM and nearly perfect for the LSCM. All the Gaussian parameters derived in this study are in explicit analytical form, allowing their direct use in practical applications.

We present a supervised classification model based on a variational approach. This model is devoted to find an optimal partition composed of homogeneous classes with regular interfaces. The originality of the proposed approach concerns the definition of a partition by the use of level sets. Each set of regions and boundaries associated to a class is defined by a unique level set function. We use as many level sets as different classes and all these level sets are moving together thanks to forces which interact in order to get an optimal partition. We show how these forces can be defined through the minimization of a unique fonctional. The coupled Partial Differential Equations (PDE) related to the minimization of the functional are considered through a dynamical scheme. Given an initial interface set (zero level set), the different terms of the PDE's are governing the motion of interfaces such that, at convergence, we get an optimal partition as defined above. Each interface is guided by internal forces (regularity of the interface), and external ones (data term, no vacuum, no regions overlapping). Several experiments were conducted on both synthetic and real images.

Markovian approaches to early vision processes need a huge amount of computing power. These algorithms can usually be implemented on parallel computing structures. Herein, we show that the Markovian labeling approach can be implemented in fully parallel cellular network architectures, using simple functions and data representations. This makes possible to implement our model in parallel imaging VLSI chips.

Given a set of low resolution camera images of a Lambertian surface, it is possible to reconstruct high resolution luminance and height information, when the relative displacements of the image frames are known. We have proposed iterative algorithms for recovering high resolution albedo with the knowledge of high resolution height and vice versa. The problem of surface reconstruction has been tackled in a Bayesian framework and has been formulated as one of minimizing an error function. Markov Random Fields (MRF) have been employed to characterize the a priori constraints on the solution space. As for the surface height, we have attempted a direct computation without refering to surface orientations, while increasing the resolution by camera jittering.

In this paper, we are interested in massively parallel multiscale relaxation algorithms applied to image classification. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. First, we present a classical multiscale model which consists of a label pyramid and a whole observation field. The potential functions of coarser grids are derived by simple computations. The optimization problem is first solved at the higher scale by a parallel relaxation algorithm; then the next lower scale is initialized by a projection of the result. Second, we propose a hierarchical Markov random field model based on this classical model. We introduce new interactions between neighbor levels in the pyramid. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price. This model results in a relaxation algorithm with a new annealing scheme: the multitemperature annealing (MTA) scheme, which consists of associating higher temperatures to higher levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalization of the annealing theorem of S. Geman and D. Geman (IEEE Trans. Pattern Anal. Mach. Intell.6, 1984, 721–741).

We propose an information-theoretic variational filter for image denoising. It is a result of minimizing a functional subject to some noise constraints, and takes a hybrid form of a negentropy variational integral for small gradient magnitudes and a total variational integral for large gradient magnitudes. The core idea behind this approach is to use geometric insight in helping to construct regularizing functionals and avoiding a subjective choice of a prior in maximum a posteriori estimation. Illustrative experimental results demonstrate a much improved performance of the approach in the presence of Gaussian and heavy-tailed noise.