Nonlinear signal processing elements are increasingly needed in current signal processing systems. Stack filters form a large class of nonlinear filters, which have found a range of applications, giving excellent results in the area of noise filtering. Naturally, the development of fast procedures for the optimization of stack filters is one of the major aims in the research in the field. In this paper we study optimization of stack filters with a simplified scenario: the ideal signal is constant and the noise distribution is known. The objective of the optimization method presented in this paper is to find the stack filter producing optimal noise attenuation and satisfying given constraints. The constraints may limit the search into a set of stack filters with some common statistical description or they may describe certain structures which must be preserved or deleted. The objective of this paper is to illustrate that design of nonlinear filters is possible while using suitable signal and noise models.

Novel robust filtering algorithms applicable to image processing are introduced. They were derived using robust M-type point estimators and the restriction technique of the well-known KNN filter. The derived filters effectively remove impulse noise and preserve edge and fine details. The proposed filters provide excellent visual quality of the processed simulated images and good quantitative quality in the MSE sense in comparison to the standard median filter. Recommendations to obtain best processing results by proper selection of derived filter parameters are given. Two derived filters are suitable for impulse noise reduction in any image processing applications. One can use the RM-KNN filters at the first stage of image enhancement followed by any detail-preserving techniques such as the Sigma filter at the second stage.

The ways to improve the computational efficiency of the Frost filter and make it robust in respect to spikes are considered. A hard-switching adaptive procedure is proposed and the aspects of proper selection of linear filter parameters and threshold values are discussed. Then the idea of subsequent application of FTR- median hybrid filter is put forward. Quantitative and visual simulation results are presented for different p.d.f.s of multiplicative noise to compare the properties and to demonstrate the advantages of proposed modifications. Real synthetic aperture radar and artificial image processing results are demonstrated.

A binary granulometry is formed as a union of parameterized openings. It induces a reconstructive granulometry by passing image components it does not fully eliminate. Reconstructive granulometries have historically been formed as unions of reconstructive parameterized openings. The theory has been extended to the new class of logical structure filters (LSF). These are unions of intersections of both reconstructive and complementary reconstructive openings. Reconstructive granulometries form the special class of disjunctive LSFs. This paper covers adaptive methods to design parameterized LSFs. A systematic formulation of adaptive transitions is given and applications are provided.

A signature of a binary image contains, for each of a set of parallel lines, the total number of 1s (as opposed to 0s) along that line. We have been studying the recognition of binary images from these signatures. Typically a very large number of binary images would satisfy three signatures. To overcome this difficulty, we have investigated the possibility of modeling the class of binary images of a particular application area as a Markov random field (MRF) and using a stochastic algorithm which seeks to optimize a functional which, in addition to a penalty term for the violation of the signatures, contains a regularization term indicating the likelihood provided by the MRF. We have found that for some MRFs (specified by small regions of the image, which are either uniform or contain edges or corners), the method works remarkably well: binary image randomly selected from the MRF were recovered within one location in nearly all cases we have tried. The time-consuming nature of the stochastic algorithm is ameliorated by a preprocessing step which discovers locations at which the value is the same in all images having the given signatures; this reduces the search space considerably. We discuss, in particular, a linear-programming approach to finding such `invariant' locations.

Deterministic and stochastic methods such as MPM and MAP have been extensively used for successfully solving problems related to image segmentation, restoration, texture analysis and motion estimation. Within this framework, Markov random field (MRF) is the most popular and powerful model used for describing and analyzing images. Nevertheless the question that arises is to know if MRF is able to model real images. In this paper we address the classification of real images into two model families, namely MRF and non-MRF families. Within this mathematical statistical framework, we propose a novel method based on parameter estimation techniques and hypothesis verification. The main steps of the approach are: (1) Estimating transition probabilities of MRF for various partitions of the image. This stage depends on following parameters: number of gray levels denoted by k, number of components in the partition denoted by L and number of the considered partitions denoted by R. We established that L depends on k, the neighborhood system and the size of the initial image. (2) Testing the homogeneity hypothesis over the set of all the transition matrix estimators. When R equals 1, a one-way analysis of variance is applied. When R >= 1, the dependence on the two factors L and R leads to a two-way analysis of the variances. Such a procedure was applied to different simulated images with the presence of exact MRF among them and to real images. Performances on the non supervised classification into MRF and non-MRF families are discussed in terms of accuracy and robustness. Application of the developed procedure to the lossy compression is presented in details.

We are concerned with the problem of image segmentation in which each pixel is assigned to one of a predefined finite number of classes. In Bayesian image analysis, this requires fusing together local predictions for the class labels with a prior model of segmentations. Markov Random Fields (MRFs) have been used to incorporate some of this prior knowledge, but this not entirely satisfactory as inference in MRFs is NP-hard. The multiscale quadtree model of Bouman and Shapiro (1994) is an attractive alternative, as this is a tree-structured belief network in which inference can be carried out in linear time (Pearl 1988). It is an hierarchical model where the bottom-level nodes are pixels, and higher levels correspond to downsampled versions of the image. The conditional-probability tables (CPTs) in the belief network encode the knowledge of how the levels interact. In this paper we discuss two methods of learning the CPTs given training data, using (a) maximum likelihood and the EM algorithm and (b) conditional maximum likelihood (CML). Segmentation obtained using networks trained by CML show a statistically-significant improvement in performance on synthetic images. We also demonstrate the methods on a real-world outdoor- scene segmentation task.

This paper presents a generic method for addressing the issue of 3D model-based head pose estimation. The method proposed relies on the downhill simplex optimization method and on the combination of motion and texture features. A proper initialization based on a block matching procedure associated with 3D/2D matching depending on texture and optical flow information leads to an accurate recovery of the pose parameters. By using a 3D head model, the procedure takes into account the motion of the entire head and not a set of characteristic parts. Similarly, unlike feature-based methods, the whole head is tracked and no constraint by some features vanishing from view is needed. We show that the accuracy of the pose estimation is increased when considering a 3D head-like synthesized surface by using a limited Fourier expansion instead of ellipsoidal head model. We demonstrate that this method is stable over extended sequences including large head motions, occultations, various head postures and lighting variations. The method proposed is generally enough to be applied to other tracking domains.

A new image matching method is proposed based on delauney triangulation of this paper. The first step of this method is making the delauney triangle segmentations of the 2 reference images; second, covering each paired triangle with the parallel lines or the polar lines; thirdly, matching the image points using the epipolar geometry constraint. The method gets rid of the classic time-consuming dense matching technique, effectively resolves the problem of match missing caused by the line lengthening and shortening, and greatly improves the speed and accuracy of matching.

A new optimization method for image registration has been proposed. Registration using Simulated Annealing converges to global minima/maxima as opposed to the previously wildly used algorithms that get trapped in local minima. The performance of this algorithm is tested against two other well-known optimization algorithms, Powell and Down Hill Simplex using two different methods. First, the algorithms are tested against famous De jong Test Suites and second, they are tested against Two-Cube Phantom. Our data shows that simulated annealing is the only algorithm that will always converges to the global minima with the cost of more function evaluation.

We present the intuitive interpretation of affine epipolar geometry for the orthographic, scaled orthographic, and paraperspective projection models in terms of the factorization method for the generalized affine projection (GAP) model proposed by Fujiki and Kurata (1997). Using the GAP model introduced by Mundy and Zisserman (1992), each affine projection model can be resolved into the orthographic projection model by the introduction of virtual image planes, then the affine epipolar geometry can be simply obtained from the estimation of the factorization method. We show some experiments using synthetic data and real images and also demonstrate to reconstruct the dense 3D structure of the object.

The theory converted from x-ray projection data to the hologram directly by combining the computer tomography (CT) with the computer generated hologram (CGH), is proposed. The purpose of this study is to offer the theory for realizing the all- electronic and high-speed seeing through 3D visualization system, which is for the application to medical diagnosis and non- destructive testing. First, the CT is expressed using the pseudo- inverse matrix which is obtained by the singular value decomposition. CGH is expressed in the matrix style. Next, `projection to hologram conversion' (PTHC) matrix is calculated by the multiplication of phase matrix of CGH with pseudo-inverse matrix of the CT. Finally, the projection vector is converted to the hologram vector directly, by multiplication of the PTHC matrix with the projection vector. Incorporating holographic analog computation into CT reconstruction, it becomes possible that the calculation amount is drastically reduced. We demonstrate the CT cross section which is reconstituted by He-Ne laser in the 3D space from the real x-ray projection data acquired by x-ray television equipment, using our direct conversion technique.

The theory of Unified Focus and Defocus Analysis (UFDA) was presented by us earlier and it was extended to use both classical optimization technique and regularization approach for 3D scene recovery. In this paper we present a computational algorithm for UFDA which uses variable number of images in an optimal fashion. UFDA is based on modeling the sensing of defocused images in a camera system. This approach unifies Image Focus Analysis (IFA) and Image Defocus Analysis (IDA), which form two extremes in a range of possible methods useful in 3D shape and focused image recovery. The proposed computational algorithm consists of two main steps. In the first step, an initial solution is obtained by a combination of IFA, IDA, and interpolation. In the second step, the initial solution is refined by minimizing the error between the observed image data and the image data estimated using a given solution and the image formation model. A classical gradient descent or a regularization technique is used for error minimization. Our experiments indicate that the most difficult part of the algorithm is to obtain a reasonable solution for the focused image when only a few image frames are available. We employ several methods to address this part of the problem. The algorithm has been implemented and experimental results are presented.

This paper presents a low bit rate videophone system for deaf people communicating by means of sign language. Classic video conferencing systems have focused on head and shoulders sequences which are not well-suited for sign language video transmission since hearing impaired people also use their hands and arms to communicate. To address the above-mentioned functionality, we have developed a two-step content-based video coding system based on: (1) A segmentation step. Four or five video objects (VO) are extracted using a cooperative approach between color-based and morphological segmentation. (2) VO coding are achieved by using a standardized MPEG-4 video toolbox. Results of encoded sign language video sequences, presented for three target bit rates (32 kbits/s, 48 kbits/s and 64 kbits/s), demonstrate the efficiency of the approach presented in this paper.

Image processing is properly viewed as modeling and estimation in two dimensions. Image are often projections of higher dimensional phenomena onto a 2D grid. The scope of phenomena that can be imaged is unbounded, thus a wealth of image models is required. In addition, models should be constructed according to rigorous mathematics from first principles. One such approach is random- set modeling. The fit between random sets and our intuitive notion of image formation is natural, but poses difficult mathematical and statistical problems. We review the foundation of the random set approach in the continuous and discrete setting and present several highlights in estimation and filtering for binary images.

Robust statistical estimators have found wide application in image processing and computer vision because conventional estimation methods fail to work when outliers from the assumed image model are present in real image data. In this paper, the method of partial robust estimates is described in which the final estimate of model parameters is made by the concept of maximum a posteriori probability or by the adaptive linear combination depending on the image contents. The underlying image model consists of a polynomial regression representation of the image intensity function and a structural model of local objects on non-homogeneous background. The developed estimation procedures have been tested on radiographic images in applications to detail-preserving smoothing and detection of local objects of interest. The obtained results and theoretical investigation confirm the model adequacy to real image data and robustness of the developed estimators of the model parameters.

We suggest a new approach to assess discrepancies between grey- scale images. Such numerical discrepancy measures are usually called error metrics, since they provide a numerical assessment of the dissimilarity between two images. The suggested approach is based on the idea that each upper semicontinuous grey-scale image f corresponds to a random closed set F_U equals {x: f(x) >= U} which appear if the image is thresholded as a randomly chosen level U. Then distance between distributions of random sets (which generalize the concept of probability metric distances for random variables) serve as error metrics for grey- scale images. These metrics generalize the famous constructs like uniform distance between distributions of random variables and Monge-Kantorovich metric for distribution functions. However, instead of distribution functions of random variables, their definitions refer to capacity functionals of the corresponding random closed sets. Several general mathematical constructions for such metrics are presented, compared and examined from both theoretical and practical viewpoints. Among wide range of applications of error metrics in image processing we concentrate on their use to assess performance of image restoration algorithms and in Bayesian image reconstruction. In the latter case we focus on one particular error metric and show how it can be used in the context of Bayesian image restoration, where the `true' image is unknown, but is assumed to have a certain prior distribution.

There are many statistical models for Synthetic Aperture Radar (SAR) images. Among them, the multiplicative model is based on the assumption that the observed random field Z is the result of the product of two independent and unobserved random fields: X and Y. The random field X models the backscatter, and thus depends only on the type of area each pixel belongs to. On the other hand, the random field Y takes into account that SAR images are the result of a coherent imaging system that produces the well known phenomenon called speckle, and that they are generated by performing an average of n statistically independent images - looks- in order to reduce the speckle effect. There are various ways of modeling the random fields X and Y. Recently Frery et. al. proposed the distributions (Gamma) ^1/2 ((alpha) ,(gamma) ) and (Gamma) ^1/2(n,n) for of X and Y respectively. This resulted in a new distribution for Z: the G⁰_A((alpha) ,(gamma) ,n) distribution. Here, the parameters (alpha) and (gamma) depend on the ground truth of each pixel and the parameter n is the number of looks used to generate the image. The advantage of this distribution over the ones used in the past is that it models very well extremely heterogenous areas like cities, as well as moderately heterogeneous areas like forests, and homogeneous areas like pastures. As the ground truth can be characterized by the parameters (alpha) and (gamma) , their estimation for each pixel generates parameter maps that can be used as the input for classical classification methods. In this work, different parameter estimation procedures are used and compared on synthetic and real SAR images, and then, supervised and unsupervised classifications are performed and evaluated.

The multiplicative model has been widely used to explain the statistical properties of SAR images. In it, the model for the image Z is a 2D random field, that is regarded as the result of the product of X, the backscatter that depends on the physical characteristics of the sensed area, and Y, the speckle that depends on the number of looks used to generate the image Z. The most famous distribution for SAR images based on the multiplicative model is the K distribution (Jackeman et al). Recently Frery et al. proposed an alternative distribution, the G⁰_A((alpha) ,(gamma) ,n) distribution which models very well extremely heterogenous areas (cities) as well as moderately heterogeneous areas (forest) and homogeneous areas (crop fields). The ground truth at each pixel can be characterized by the statistical parameters (alpha) and (gamma) , while n is constant for all of the pixels. The purpose of estimating these parameters for every pixel is twofold: first, it can be used to perform a segmentation process and, second, it can be used for gray level restoration. In this work we follow a Markov random field approach and propose an energy function derived from the statistical model adopted: G⁰_A((alpha) ,(gamma) ,n). Edge- preservation is taken into account implicitly in the energy function.

We present in this paper a method to estimate movement in digital video sequences from a 3D representation model based on polynomial transforms. This transform allows to obtain representations of the video sequence at multiple spatiotemporal resolutions. Our approach analyzes the video sequence locally by means of spatiotemporal windows. It allows to recover the true flow in regions free of the aperture problem as well as given an estimate of the normal component of motion for oriented patterns detected within each window. Different window sizes in space and time are allowed for an efficient analysis of all types of motion.

The optimal binary window filter is the binary conditional expectation of the pixel value in the ideal image given the set of observations in the window. This filter is typically designed from pairs of ideal and observation images, and the filter used in practice is the resulting estimate of the optimal filter, not the optimal filter itself. For large windows, design is hampered by the exponentially growing number of window observations. This paper discusses two types of prior information that can facilitate design for large windows: design by adapting a given (prior) filter known to work fairly well, and Bayesian design resulting from assuming the conditional probabilities determining the optimal filter satisfy prior distributions reflecting the possible states of nature. A second problem is that a filter must be applied in imaging environments different from the one in which it is designed. This results in the robustness problem: how well does a filter designed for one environment perform in a changed environment? This problem is studied by considering the ideal and observed images to be determined by distributions whose parameters are random and possess prior distributions. Then, based on these prior distributions determining the design conditions, we can evaluate filter performance across the various states. Moreover, a global filter can be designed that tends to maintain performance across states, albeit, at the cost of some increase in error relative to specific states.

This paper presents theory and experiment to perform a pattern recognition task. The task is to detect a mine in visual imagery, using a training algorithm. The marginal statistics for the data windows around potential targets are collected using a lexicode approach. Theoretical results supporting the lexicode's ability to perform such a task are presented. Preprocessing of the data is performed prior to the application of the lexicode. Discussion is given on the theoretical foundations and the preprocessing of the data, with future research activities outlined.

Segmentation algorithms are usually qualified of supervised or non-supervised according to the amount of external information needed during the procedure. This article will list several examples of Markovian supervised or non supervised segmentation algorithms in order to present several modeling possibilities and ways to improve the initial models. Following a Bayesian approach, the energies are usually divided in two terms: the interaction term and the regularization term. After introducing the two basical models, we will compare the two energies, discuss more precisely of the different terms and more precisely, of the interaction term. Then the neighborhood systems will be considered as well as their possible dependency on the observations. We will also present general ways to use some edge information in the segmentation energies and a more general segmentation approach allowing the use of `non-classified' labels. Finally, various hierarchical approaches can be used in order to alleviate the optimization task and for different kind of energies. We are not mainly interested here in ways to improve the optimization procedure but rather in the definition of new models for non supervised segmentation. They will combine different primitives and the usual segmentation energies.

Skew detection is one the first operations to be applied to scanned documents when converting data to a digital format. Its aim is to align an image before further processing because text segmentation and recognition methods require properly aligned next lines. Here we represent a new method of skew detection based on the principal component analysis and multi-resolution processing. A combination of these two approaches allows us to increase correctness of skew detection when finding an arbitrary skew angle from 0 to 179 degrees with low-resolution images of 25 - 50 dots per inch (dpi). The obtained results advantageously differentiate our technique from the methods determining a skew at a single resolution under conditions above.

The purpose of our work is the microcalcifications detection on digital mammograms. In order to do so, we model the grey levels of digital mammograms by the sum of a surface trend (bicubic spline function) and an additive noise or texture. We also introduce a robust estimation method in order to overcome the bias introduced by the microcalcifications. After the estimation we consider the subtraction image values as noise. If the noise is not correlated, we adjust its distribution probability by the Pearson's system of densities. It allows us to threshold accurately the images of subtraction and therefore to detect the microcalcifications. If the noise is correlated, a unilateral autoregressive process is used and its coefficients are again estimated by the least squares method. We then consider non overlapping windows on the residues image. In each window the texture residue is computed and compared with an a priori threshold. This provides correct localization of the microcalcifications clusters. However this technique is definitely more time consuming that then automatic threshold assuming uncorrelated noise and does not lead to significantly better results. As a conclusion, even if the assumption of uncorrelated noise is not correct, the automatic thresholding based on the Pearson's system performs quite well on most of our images.

In this paper an approach is described for segmenting medical images. We use active contour model, also known as snakes, and we propose an energy minimization procedure based on Genetic Algorithms (GA). The widely recognized power of deformable models stems from their ability to segment anatomic structures by exploiting constraints derived from the image data together with a priori knowledge about the location, size, and shape of these structures. The application of snakes to extract region of interest is, however, not without limitations. As is well known, there may be a number of problems associated with this approach such as initialization, existence of multiple minima, and the selection of elasticity parameters. We propose the use of GA to overcome these limits. GAs offer a global search procedure that has shown its robustness in many tasks, and they are not limited by restrictive assumptions as derivatives of the goal function. GAs operate on a coding of the parameters (the positions of the snake) and their fitness function is the total snake energy. We employ a modified version of the image energy which consider both the magnitude and the direction of the gradient and the Laplacian of Gaussian. Experimental results on medical images are reported. Images used in this work are ocular fundus images, snakes result very useful in the segmentation of the Foveal Avascular Zone. The experiments performed with ocular fundus images show that the proposed method is promising in the early detection of the diabetic retinopathy.

2D images cannot convey information on object depth and location relative to the surfaces. The medical community is increasingly using 3D visualization techniques to view data from CT scans, MRI etc. 3D images provide more information on depth and location in the spatial domain to help surgeons making better diagnoses of the problem. 3D images can be constructed from 2D images using 3D scalar algorithms. With recent advances in communication techniques, it is possible for doctors to diagnose and plan treatment of a patient who lives at a remote location. It is made possible by transmitting relevant data of the patient via telephone lines. If this information is to be reconstructed in 3D, then 2D images must be transmitted. However 2D dataset storage occupies a lot of memory. In addition, visualization algorithms are slow. We describe in this paper a scheme which reduces the data transfer time by only transmitting information that the doctor wants. Compression is achieved by reducing the amount of data transfer. This is possible by using the 3D wavelet transform applied to 3D datasets. Since the wavelet transform is localized in frequency and spatial domain, we transmit detail only in the region where the doctor needs it. Since only ROM (Region of Interest) is reconstructed in detail, we need to render only ROI in detail, thus we can reduce the rendering time.