In this paper, we have derived analytic expressions for the phase correlation of downsampled images. We have shown that for downsampled images the signal power in the phase correlation is not concentrated in a single peak, but rather in several coherent peaks mostly adjacent to each other. These coherent peaks correspond to the polyphase transform of a filtered unit impulse centered at the point of registration. The analytic results provide a closed-form solution to subpixel translation estimation, and are used for detailed error analysis. Excellent results have been obtained for subpixel translation estimation of images of different nature and across different spectral bands.

With the rapid development of remote sensing, digital image processing has become an important tool for the quantitative and statistical analysis of remotely sensed images. These images most often contain complex natural scenes. The robust interpretation of such images requires the use of different sources of information about the scenes under consideration. This paper presents an integrated approach to robust analysis of SPOT images with the aid of map information as well as a priori knowledge about the contextual information of images. Markov random field theory and the Bayes formula are used to formulate the image analysis problem as a problem of optimization of an objective function, which in turn permits the application of various existing optimization algorithms to solve the problem. To increase the robustness of the result, several techniques are proposed to effectively use map information and image contextual information. The first one is concerned with the estimation of the parameters in the objective function with the help of these two sources of information. The second one is the integration of map information in Bayes image modeling using a Markov random field. The third one is a new optimization algorithm which takes into account map information and image contextual information by means of a feedback control scheme. The last technique proposed to increase the robustness of the result is concerned with the fusion of several (intermediate) analysis results by again using map knowledge and image contextual information for the estimation of the reliability of these results.

Recent developments in statistics now allow maximum likelihood estimators for the parameters of Markov random fields (MRFs) to be constructed. We detail the theory required, and present an algorithm that is easily implemented and practical in terms of computation time. We demonstrate this algorithm on three MRF models--the standard Potts model, an inhomogeneous variation of the Potts model, and a long-range interaction model, better adapted to modeling real-world images. We estimate the parameters from a synthetic and a real image, and then resynthesize the models to demonstrate which features of the image have been captured by the model. Segmentations are computed based on the estimated parameters and conclusions drawn.

In this paper we introduce a method of isolating and extracting a certain class of local singular behaviours of signals/images which in turn leads to a method of pointwise noise estimation and suppression. The underlying motivation is to decompose functions directly in terms of components which would naturally represent different orders of regular or singular behaviours defined by the local Holder exponents. We have shown that such a decomposition can lead to a factorization of the spectrum of the singular portion of the signal in terms of the spectrum of the original signal and that of a denoising filter.

In this paper, we present a complete system for the recognition and localization of a three-dimensional (3-D) model from a sequence of monocular images with known motion. The originality of this system is twofold. First, it uses a purely 3-D approach, starting from the 3-D reconstruction of the scene and ending by the 3-D matching of the model. Second, unlike most monocular systems, we do not use token tracking to match successive images. Rather, subpixel contour matching is used to recover more precisely complete 3-D contours. In contrast with the token tracking approaches, which yield a representation of the 3-D scene based on disconnected segments or points, this approach provides us with a denser and higher level representation of the scene. The reconstructed contours are fused along successive images using a simple result derived from the Kalman filter theory. The fusion process increases the localization precision and the robustness of the 3-D reconstruction. Finally, corners are extracted from the 3-D contours. They are used to generate hypotheses of the model position, using a hypothesize-and-verify algorithm that is described in detail. This algorithm yields a robust recognition and precise localization of the model in the scene. Results are presented on infrared image sequences with different resolutions, demonstrating the precision of the localization as well as the robustness and the low computational complexity of the algorithms.

A method of registering images at subpixel accuracy has been proposed, which does not resort to interpolation. The method is based on the phase correlation method and is remarkably robust to correlated noise and uniform variations of luminance. We have shown that the cross power spectrum of two images, containing subpixel shifts, is a polyphase decomposition of a Dirac delta function. By estimating the sum of polyphase components one can then determine sub-pixel shifts along each axis.

Using a probabilistic interpretation of an n dimensional extension of Papoulis's Generalized Sampling Theorem, an iterative algorithm has been devised for 3D reconstruction of a Lambertian surface at subpixel accuracy. The problem has been formulated as an optimization one in a Bayesian framework. The latter allows for introducing a priori information on the solution, using Markov Random Fields (MRF). The estimated 3D features of the surface are the albedo and the height which are obtained simultaneously using a set of low resolution images. keywords: 3D Super resolution, Generalized Sampling Expansion, Low level image processing, Markov Random Fields (MRF).

This paper deals with the problem of unsupervised Bayesian segmentation of images modeled by Markov random fields (MRF). If the model parameters are known then we have various methods to solve the segmentation problem (simulated annealing, ICM, etc...). However, when they are not known, the problem becomes more difficult. One has to estimate the hidden label field parameters from the available image only. Our approach consists of a recent iterative method of estimation, called iterative conditional estimation (ICE), applied to a monogrid Markovian image segmentation model. The method has been tested on synthetic and real satellite images.

The paper deals with the problem of unsupervised classification of images modeled by Markov random fields (MRF). If the model parameters are known then we have various methods to solve the segmentation problem (simulated annealing, ICM, etc...). However, when they are not known, the problem becomes more difficult. One has to estimate the hidden label field parameters from the only observable image. Our approach consists of extending a recent iterative method of estimation, called iterative conditional estimation (ICE) to a hierarchical Markovian model. The idea resembles the estimation-maximization (EM) algorithm as we recursively look at the maximum a posteriori (MAP) estimate of the label field given the estimated parameters then we look at the maximum likelihood (ML) estimate of the parameters given a tentative labeling obtained at the previous step. We propose unsupervised image classification algorithms using a hierarchical model. The only parameter supposed to be known is the number of regions, all the other parameters are estimated. The presented algorithms have been implemented on a Connection Machine CM200. Comparative tests have been done on noisy synthetic and real images (remote sensing).>

This paper introduces a new general purpose algorithm that allows the optimal geometric match between contours to be determined, that is the transformation yielding a minimal deformation is obtained. The algorithm relies only on the geometric properties of the contours and does not call for any other constraint, so that it is particularly suitable when no parameterization of title deformation is available or desirable. Contour deformation is explicitly incorporated in the computation, allowing for a thorough use of all geometric information available. Moreover, no discretization is involved in the computation, resulting in two main advantages: first, the algorithm is robust to differences in the segmentation of contours and allows the matching of polygonal approximations of contours with very little loss of precision, second, subpixel precision matching can be achieved.>

Using a set of low resolution images it is possible to reconstruct high resolution information by merging low resolution data on a finer grid. A 3D super-resolution algorithm is proposed, based on a probabilistic interpretation of the n-dimensional version of Papoulis' (1977) generalized sampling theorem. The algorithm is devised for recovering the albedo and the height map of a Lambertian surface in a Bayesian framework, using Markov random fields for modeling the a priori knowledge.

Deterministic pseudo-annealing (DPA) is a new deterministic optimization method for finding the maximum a posteriori (MAP) labeling in a Markov random field, in which the probability of a tentative labeling is extended to a merit function on continuous labelings. This function is made convex by changing its definition domain. This unambiguous maximization problem is solved, and the solution is followed down to the original domain, yielding a good, if suboptimal, solution to the original labeling assignment problem. The performance of DPA is analyzed on randomly weighted graphs.

Given a set of low resolution camera images, it is possible to reconstruct high resolution luminance and depth information, specially if the relative displacements of the image frames are known. We propose iterative algorithms for recovering hash resolution albedo and depth maps that require no a priori knowledge of the scene, and therefore do not depend on other methods, as regards boundary and initial conditions. The problem of surface reconstruction has been formulated as one of expectation maximization (EM) and has been tackled in a probabilistic framework using Markov random fields (MRF). As for the depth map, our method directly recovers surface heights without refering to surface orientations, while increasing the resolution by camera jittering. Conventional statistical models have been coupled with geometrical techniques to construct a general model of the world and the imaging process.>

This paper presents a subpixel contour matching algorithm using a novel dynamic programming scheme. Unlike classical dynamic programming methods, where a discrete path is searched for across a graph, our approach allows the optimal continuous path to be determined. The matching is obtained as a piecewise parametric function, and no discretization is involved, nor any parameterized deformation assumed. As a side result, a measure of the deformation of the matched contours is obtained, yielding information on the quality of the match. The algorithm has been tested with different types of images, demonstrating its ability to deal with chains of contour segments as well as chains of contour edges, since the discretization of the contours does not limit the precision of the matches anymore.>

Deals with a form of knowledge of land use relating to mixture percentages. The authors present a method for the determination of mixture percentages in pixels of a multispectral satellite scene (Landsat TM or SPOT XS). This method is applied to images after correction for topographic and atmospheric effects. They continue with a description of the linear analysis of the satellite scene and capture of the reference spectra, pure units of the percentages calculation. This process is validated first by comparison with ground truth, and then with a comparison with classic land use classifications. An entropy coefficient has been calculated for each pixel.

Describes an algorithm which restores images of incomplete contours using a Markovian model. In order to complete the boundaries, a criterion is defined and introduced in an energy function, which has to be optimized. A deterministic relaxation algorithm ICM ("iterated conditional mode") is implemented to minimize this energy function. It generates a configuration in which the contours are reconstructed. Several examples of real image restoration have been tested on a SIMD computer (Connection Machine CM 200). This algorithm allows one to fill up large gaps and to get a better contour grouping.

A new technique for urban area detection in satellite images by integrating geographic map knowledge is presented. Satellite images are modeled by Markov random fields and digitized maps are used as a priori knowledge of the scene under analysis. An iterative scheme is proposed to increase the robustness of scene labeling algorithms by means of a feedback control. Experimental results on urban area detection in SPOT images show the effectiveness of the technique.

As it is well known, optimization of the energy function of Markov random fields is very expensive. Hierarchical models have usually much more communication per pixel than monogrid ones. This is why classical annealing schemes are too slow, even on a parallel machine, to minimize the energy associated with such a model. However, taking benefit of the pyramidal structure of the model, we can define a new annealing scheme: the multitemperature annealing (MTA), which consists of associating higher temperatures to coarser levels, in order to be less sensitive to local minima at coarser grids. The convergence to the global optimum is proved by a generalisation of the annealing theorem of Geman and Geman (1984). We have applied the algorithm to image classification and tested it on synthetic and real images.

Matching is recognized as the most difficult step in stereo vision. Many algorithms have been proposed but none of them is robust enough. The primary reason for this is that one of the most useful cues, namely shape similarity, is not appropriately exploited. Making full use of shape similarity for disambiguation requires determining an appropriate criterion and an adequate implementation. We show that a disparity gradient (DG) limit as small as 0.2 can be used to ensure shape similarity and permits the majority of scene surfaces to be correctly handled. This DG limit is a compromise between the quantity of matches and the quality of matching. The implementation of a DG limit is made effective by explicitly taking into account uncertainty in image point positions. A very effcient voting scheme is proposed. Many tests have been performed, mostly on complex real scenes, but none of the parameters has been adjusted. The results are satisfactory both in terms of the quantity of matches and the correctness of these in normal circumstances. 1

The authors consider multiscale Markov random field (MRF) models. It is well known that multigrid methods can improve significantly the convergence rate and the quality of the final results of iterative relaxation techniques. A hierarchical model is proposed, which consists of a label pyramid and a whole observation field. The parameters of the coarse grid can be derived by simple computation from the finest grid. In the label pyramid, a new local interaction is introduced between two neighbor grids. This model gives a relaxation algorithm which can be run in parallel on the entire pyramid. The model allows propagation of local interactions more efficiently, giving estimates closer to the global optimum for deterministic as well as for stochastic relaxation schemes. It can also be seen as a way to incorporate cliques with far apart sites for a reasonable price.>

A pseudo-stochastic variation of the Metropolis dynamics for combinatorial optimization in image classification using Markov random fields is presented. At high temperature, the behavior of the algorithm is similar to the stochastic ones. However, if the temperature is less than a certain threshold, it becomes deterministic. The length of the pseudo-stochastic phase is controlled by a constant threshold used in the modified dynamics. The algorithm yields an approximate but usually good solution to the optimization problem. The algorithm runs on a connection machine. It is applied to the standard pixel classification problem; objective and subjective comparisons with other algorithms have been made.>

Proposes deterministic psuedo annealing (DPA), a variation of simulated annealing. The method is an extension of relaxation labeling, a once popular framework for a variety of computer vision problems. The authors present its application to textured image segmentation. The basic idea is to introduce weighted labelings, which assign a weighted combination of labels to any site, and then to build a merit function of all the weighted labels. This function, a polynomial with non-negative coefficients, is an extension to a compact domain of R/sup N/ of an application defined on the finite (but very large) set of labelings; its only extrema under suitable constraints correspond to discrete labelings. DPA consists of changing the constraints, and thus the domain, so as to convexify this function, find its unique global maximum, and then track down the solution until the original constraints are restored, thus obtaining usually good discrete labeling.>

A new iterative algorithm for edge intensity image enhancement is proposed. It uses local cooperation-inhibition processes to produce an edge image in which the most relevant contours have reached maximal activation, and small gaps and junctions have been filled in. Implementation on a massively parallel machine has provided high speed performances, and results of experimentations with real scene images are presented. The algorithm is robust in complex edge image context, and is perfectly stable under any number of iterations.>

Multiscale Analysis of surfaces allows a hierarchical representation of their composing features. To represent a surface at a given scale, structures that are insignificant at that scale have to be eliminated. A typical example for this approach is cartography. However, the aims of cartographers reach beyond simply gradually eliminating the structures; in the majority of cases, the nature of geomorphological structures which compose the surface have to be preserved across all scales. Thus a global smoothing of the surface is not suitable to solve the present problem, since that would cause inevitably morphological modifications of certain important structures. In fact, the points to be preserved across scale variations are to be chosen interactively by the user. The authors present a surface model which allows them to perform a Multiscale Analysis which takes the importance of local structures into consideration, i.e. structures which are inherent to the relief morphology. From that discrete model we extract a context-dependent Multiscale Analysis Operator which can be isotropic or anisotropic and can be expressed in different forms.>

The high resolution of SPOT images, particularly in the panchromatic mode, is exploited to extract a part of these thin networks in a reliable and partially automatic fashion. The method relies on the extraction of ridges and valleys followed by a linking step, which yields a reliably localized but still broken network. Average grey levels and orientations of these linear pieces of structures are then used to search the original image again in order to complete them. Results for different areas in the southwest of France are given.>

We approach the problem of labeling a set of objects from a quantitative standpoint. We define a world model in terms of transition probabilities and propose a definition of a class of global criteria that combine both ambiguity and consistency. A projected gradient algorithm is developed to minimize the criterion. We show that the minimization procedure can be implemented in a highly parallel manner. Results are shown on several examples and comparisons are made with relaxation labeling techniques.

This paper describes an algorithm which builds a ``Peano scanning,'' i.e., the reciprocal mapping, from [0, 1]n to [0, 1], of the well-known ``Peano curve.'' This Peano scanning is applied to a set of points in [0, 1]n and gives a one-dimensional image of it. Several applications of this technique have already been developed and are presented in this paper.