A quantum computer directly manipulates information stored in the state of quantum mechanical systems. The available operations have many attractive features but also underly severe restrictions, which complicate the design of quantum algorithms. We present a divide-and-conquer approach to the design of various quantum algorithms. The class of algorithm includes many transforms which are well-known in classical signal processing applications. We show how fast quantum algorithms can be derived for the discrete Fourier transform, the Walsh-Hadamard transform, the Slant transform, and the Hartley transform. All these algorithms use at most O(log² N) operations to transform a state vector of a quantum computer of length N.

It is necessary to predict unknown higher-frequency components which are lost by sampling for enlarging digital images. Based on Laplacian pyramid representation, the prediction of unknown higher-frequency components is equivalent to the prediction of an unknown high-resolution Laplacian image. We have proposed the higher resolution method based on the Laplacian pyramid representation. However, the overshooting and undershooting are appeared near the step-edge regions of the higher resolution result. Particularly, these overshooting and undershooting of the color digital images are standed out as shifting color components and we call this artifact the edge effect. In this paper, we propose a new color image higher resolution method with the (epsilon) -filtering, in order to reduce the edge effect. Excellent higher resolution color images without edge effect are obtained by the proposed method.

The validity of feature correspondences plays an important role for feature-correspondence based motion estimation, which leads to the final goal of object tracking. Though different data association methods have been proposed, the problem of feature correspondence is, in general, ill-posed due to either the presences of multiple candidates within search regions or no candidates because of occlusion or other factors. Our research is inspired by how we evaluate the effectiveness of the feature correspondence and how the evaluation will affect motion estimation. The evaluation of template based feature correspondence is achieved by considering the feedback of the latest motion estimation from first visit of Kalman Filtering. Then motion estimation and feature correspondence are re-processed based on evaluation result, which constitutes the second and third visit of Kalman filtering. What makes our work different from others is also that instead of restricting the semantic object tracking in 2D domain, our framework is formulated to recover the 3D depth values of selected features during motion estimation process.

Granulometric features have been widely used for classification, segmentation and recently in estimation of parameters in shape models. In this paper we study the inference of clustering based on granulometric features for a collection of structuring probes in the context of random models. We use random Boolean models to represent grains of different shapes and structure. It is known that granulometric features are excellent descriptors of shape and structure of grains. Inference based on clustering these features helps to analyze the consistency of these features and clustering algorithms. This greatly aids in classifier design and feature selection. Features and the order of their addition play a role in reducing the inference errors. We study four different types of feature addition methods and the effect of replication in reducing the inference errors.

Edge detection is the first step for some boundary extraction and boundary representation algorithms. In this paper, a fuzzy switch approach is proposed. Different existing edge filters, such as Sobel filter, Prewitt filter, Roberts filter, Isotropic filter and Canny filter, are viewed as different expert systems. In order to capture the knowledge from these expert systems, a fuzzifier is employed, which normalizes the output of each edge filter to a matrix with the values of its elements being in between zero and one. By comparing the corresponding elements in these matrices, those with the highest values are with the highest fuzzy membership values of being at an edge point. A fuzzy engine can then be designed to select the highest fuzzy membership values. Then, a defuzzifier maps the selected membership value to a crisp point, which is either zero or one. Simulations were carried out using the Sobel filter, Prewitt filter, Roberts filter, Isotropic filter and Canny filter as the edge filters. It can be concluded from the simulations that the proposed algorithm captures the advantages of the expert filters.

This paper deals with the problem of accurate position, orientation and scale estimation (localization) of objects in images, in the context of the Laguerre-Gauss Transform (GLT) theory. The solution proposed here is based on the maximization of the Maximum Likelihood functional, expressed by means of the Laguerre-Gauss expansion of the object and of the observed image. The original computational complexity of the problem, which would imply maximization over a four dimensional parameter space, is drastically reduced taking advantage of properties of the GLT image representation system.

Equating objects based on shape similarity (for example scaled Euclidean transformations) is often desirable to solve the Automatic Target Recognition (ATR) problem. The Procrustes distance is a metric that captures the shape of an object independent of the following transformations: translation, rotation, and scale. The Procrustes metric assumes that all objects can be represented by a set of landmarks (i.e. points), that they have the same number of points, and that the points are ordered (i.e., the exact correspondence between the points is known from one object to the next). Although this correspondence is not known for many ATR problems, computationally feasible methods for examining all possible combinations are being explored. Additionally, most objects can be mapped to a shape space where translation, rotation, and scaling are removed, and distances between object points in this space can then form another useful metric. To establish a decision boundary in any classification problem, it is essential to know the a prior probabilities in the appropriate space. This paper analyzes basic objects (triangles) in two-dimensional space to assess how a known distribution in Euclidean space maps to the shape space. Any triangles whose three coordinate points are uniformly distributed within a two-dimensional box transforms to a bivariate independent normal distribution with mean (0,0) and standard deviations of 2 in Kendall shape space (two points of the triangle are mapped to {-1/2,0} and {1/2,0}). The Central Limit Theorem proves that the limit of sums of finite variance distributions approaches the normal distribution. This is a reasonable model of the relationship between the three Euclidean coordinates relative to the single Kendall shape space coordinate. This paper establishes the relationship between different objects in the shape space and the Procrustes distance, which is an established shape metric, between these objects. Ignoring reflections (because it is a special case), the Procrustes distance is isometric to the shape space coordinates. This result demonstrates that both Kendall coordinates and Procrustes distance are useful features for ATR.

Human face perception is the key to identify confirmation in security systems, video teleconference, picture telephony, and web navigation. Modeling of human faces and facial expressions for different persons can be dealt with by building a point distribution model (PDM) based on spatial (shape) information or a gray-level model (GLM) based on spectral (intensity) information. To avoid short-comings of the local modeling of PDM and GLM, we propose a new approach for recognizing human faces and discriminating expressions associated with them in color images. It is based on the Laplacian of Gaussian (LoG) edge detection, KL transformation, and auto-regressive moving average (ARMA) filtering. First, the KL transform is applied to the R, G, and B dimensions, and a facial image is described by its principal component. A LoG edge-detector is then used for line drawing schematic of a face. The resultant face silhouette is divided into 5 X 5 non-overlapping blocks, each of which is represented by the auto-regressive (AR) parameter vector a. The ensample average of a over the whole image is taken as the feature vector for the description of a facial pattern. Each face class is represented by such ensample average vector a. Efficacy of the ARMA model is evaluated by the non-metric similarity measure S equals a.b/a.b for two facial images whose feature vectors, and a and b, are the ensample average of their ARMA parameters. Our measurements show that the ARMA modeling is effective for discriminating facial features in color images, and has the potential of distinguishing the corresponding facial expressions.

Hadamard matrices have received much attention in recent years, owing to their numerous known and promising applications. The difficulties of construction of N equalsV 0(mod 4)-point Hadamard transforms are related to the existence of Hadamard matrices problem. In this paper algorithms for fast computation of N-point Williamson-Hadamard transform based on multiplicative theorems are presented. Comparative estimates revealing the efficiency of the proposed algorithms with respect to the known ones are given. The results of numerical examples are presented.

Discretizing planar curves yields many useful applications. We show that in order to sample a curve, one needs to impose a priori assumptions about the type of parameterization (coordinate system), which would provide a functional form for otherwise just a set of points on the plane. The choice of parameterization is dependent on the nature of typical objects one intends to work with, and thus depends on a particular application. We show the general approach to the problem of choosing a suitable parameterization based on the prevailing shape of objects of interest. Samples of a curve must incorporate the information about both the curve and the coordinate system (type of parameterization) that was used to produce them. The curve is then obtained from the samples by first reconstructing the coordinate system and finally the curve itself. Provided examples illustrate sufficiently general applicability of the proposed techniques.

Morphological granulometries and their moment features are used as shape descriptors. These features find application in classification, segmentation and estimation. Design of classifiers has been a primary goal of most pattern recognition problems. Small sample design is often a constraint when designing classifiers. We use a recently proposed small sample design method in which the sample observations are spread with a probability mass and the classifiers designed on the spread mass. The designed classifiers are more reliability for relative to the population. Two issues are addressed: design of granulometric classifiers using a small sample, and granulometric classification based on a very small number of features.

A new technique to detect, localize and classify corners in digital closed curves is proposed. The technique is based on correct estimation of support regions for each point. We compute multiscale curvature to detect and to localize corners. As a further step, with the aid of some local features, it's possible to classify corners into seven distinct types. Classification is performed using a set of rules, which describe corners according to preset semantic patterns. Compared with existing techniques, the proposed approach inscribes itself into the family of algorithms that try to explain the curve, instead of simple labeling. Moreover, our technique works in manner similar to what is believed are typical mechanisms of human perception.

Digital signal resampling is required in many digital signal and image processing applications. Among the digital convolution based signal resampling methods, sinc-interpolation is theoretically the best one since it does not distort the signal defined by its samples. Discrete sinc-interpolation is most frequently implemented by the 'signal spectrum zero padding method.' However, this method is very inefficient and inflexible. Sinc-interpolation badly suffers also from boundary effects. In the paper, a flexible and computationally efficient methods for boundary effects free discrete sinc-interpolation are presented in two modifications: frame (global) sinc-interpolation in DCT domain and sinc-interpolation in sliding widow (local). In sliding window interpolation, interpolation kernel is a windowed sinc-function. Windowed sinc-interpolation offers options not available with other interpolation methods: interpolation with simultaneous local adaptive signal denoising and adaptive interpolation with super resolution. The methods outperform other existing discrete signal interpolation methods in terms of the interpolation accuracy and flexibility of the interpolation kernel design. Their computational complexity is O[log(Size of the frame)] per output sample for frame interpolation and O(Window Size) per output sample for sliding window interpolation.

Debris flow causes lot of damages all over the world. The surface velocity of such a natural random flow is one of the important physical parameters that are considered in drawing a hazard map or constructing a sediment control dam. Gradient-based method along with a multiscale smoothing operation finds application in the two-dimensional velocity estimation of a debris flow from its video images. This paper investigates the performance of another optical flow determination technique - the cross-correlation method in the above application and compares the results with those obtained by the gradient-based method. A computer simulation with synthetic random moving images shows that the accuracy of the cross correlation method is higher than that of the gradient-based method.

A new method is presented for the localization of synthetic references (SRs) in digital images based on normalized correlation. An augmented search template is used, which consists not only of occupied pixel fractions of the SR, but also of derivatives of these fractions with respects to shifts along the image axes. Resulting correlation values are higher than those based on standard correlation, especially for small SRs and unfavorable subpixel displacements between template and scene. The augmented template is also used to determine the location of the SR to subpixel accuracy. The precision of this determination is affected less by systematic and random error than is the case for centroiding or sampled correlation interpolation, and can be estimated explicitly from the calculated correlation value. Numerical examples are given and the algorithm is demonstrated on data taken in wind-tunnel tests under different lighting conditions. In particular, the situation is considered in which imaged SRs display poor contrast, mixed contrast, or are affected by other experimental artifacts such as specular reflection and partial occlusion. In these cases, successful subpixel localization is accomplished by treating the template as a composite set of overlapping 3-by-3 subtemplates.

In many digital color-image systems, most notably digital cameras, raw data from the sensor is processed to produce a pleasing image. One of the main steps in this process is demosaicing, which is the process of interpolating the raw data into a full color image. The resulting image is in turn compressed to enable compact storage. Each of these two steps, namely the demosaicing and compression, creates its own artifacts on the final image. In this work we consider the two stages together, and design a demosaicing algorithm which takes into account the fact that the final image is to be compressed. Examples are given to demonstrate the above ideas.

Desirable features of any digital image resolution- enhancement algorithm include exact interpolation (for 'distortionless' or 'lossless' processing) adjustable resolution, adjustable smoothness, and ease of computation. A given low-order polynomial surface (linear, quadratic, cubic, etc.) optimally fit by least squares to a given local neighborhood of a pixel to be interpolated can enable all of these features. For example, if the surface is cubic, if a pixel and the 5-by-5 pixel array surrounding it are selected, and if interpolation of this pixel must yield a 4- by-4 array of sub-pixels, then the 10 coefficients that define the surface may be determined by the constrained least squares solution of 25 linear equations in 10 unknowns, where each equation sets the surface value at a pixel center equal to the pixel gray value and where the constraint is that the mean of the surface values at the sub-pixel centers equals the gray value of the interpolated pixel. Note that resolution is adjustable because the interpolating surface for each pixel may be subdivided arbitrarily, that smoothness is adjustable (within each pixel) because the polynomial order and number neighboring pixels may be selected, and that the most computationally demanding operation is solving a relatively small number of simultaneous linear equations for each pixel.

We propose a technique for generating the MPEG-7 descriptor in compressed image/video data. Image processing in the transform domain is a much interesting area recently because compressed image and video data are becoming widely available with the data format like MPEG or JPEG.. In general, processing in the transform domain requires smaller data quantities, and lower computation complexity than that in the spatial domain. In this paper, we propose a generation algorithm of the MPEG-7 metadata in the compressed domain. We have developed an algorithm to get the homogeneous texture descriptor in the compressed domain.

This paper presents results of the automatic counting of illuminated spheres, where the random Boolean model depends on certain distributions of parameters. The problem is to estimate the number of randomly sized spheres in a region of 3D space by taking a set of parallel slices and using the slice intersections with the spheres to form the estimate. The simulation software is developed in the framework of the MATLAB-based Graphical User Interface, which generates spheres and allows visualization of spheres as well as their 2 D projections onto slices, which themselves appear as ordinary images. The dynamic interface provides manipulation of all parameters of the model, including the sampling rate (number of slices), sphere-size, location and intensity distributions, overlapping of spheres, and parameters of noise. That allows us to analyze the illuminated sphere counting along different ranges of various model parameters with respect to the sampling rate, specially for cases when random spheres may intersect and noise may exist.

Removal of periodic and quasi-periodic patterns from photographs is an important problem. There are a lot of sources of this periodic noise, e.g. the resolution of the scanner used to scan the image affects the high frequency noise pattern in the acquired image and can produce moire patterns. It is also characteristic of gray scale images obtained from single-chip video cameras. Usually periodic and quasi-periodic noise results peaks in image spectrum amplitude. Considering this, processing in the frequency domain is a much better solution than spatial domain operations (blurring for example, which can hide the periodic patterns at the cost of the edge sharpness reduction). A new frequency domain filter for periodic and quasi-periodic noise reduction is introduced in this paper. This filter analyzes the image spectrum amplitude using a local window, checks every spectral coefficient whether it needs the filtering and if so, replaces it with the median taken from the local window. To detect the peaks in the spectrum amplitude, a ratio of the current amplitude value to median value is used. It is shown that this ratio is stable for the non-corrupted spectral coefficients independently of the frequencies they correspond to. So it is invariant to the position of the peaks in the spectrum amplitude. This kind of filtering completely eliminates periodic noise, and shows quite good results on quasi-periodic noise while completely preserves the image boundaries.

A typical problem in image processing is to evaluate the noise characteristics of an image at hand. It is often desirable to perform this operation automatically with appropriate accuracy, i.e. without errors due to user's subjective views. The proposed method is based on myriad operation at the final stage of the sequence of the traditional steps performed in blind evaluation of noise variance. Using it the accuracy of blind evaluation of noise variance can be considerably improved if the parameters of myriad operation are adjusted correctly. Recommendations concerning this adjustment are given. The proposed method is verified for both artificial and real images.

A new approach to impulsive noise filtering is considered in the paper. It is known that the median filter is a sliding window filter, with a window N X N. As it is known, the impulsive noise is a 'big' and unusual jump of brightness. So if the central pixel in the window is noisy, its value belongs to one of the ends of the variation representation of the local histogram. We analyze, where the value of central pixel of the window is positioned in the variation series. If it is positioned close to the boarders, we can assume that it is an impulsive corruption and it must be filtered. This kind of analysis could be used for the improvement of many filters: median, rank-order, cellular neural, etc. So, implementing such kind of preliminary noise detection, we achieve the good results. Filters became gentler and less destructive for the image, but steel very effective.

The most famous morphological filters are the morphological opening and closing, produced by superposition of morphological dilation and erosion implemented as Minkovsky addition and subtraction with structuring elements. And in practice the modern image processing uses no other morphological filters. However, it is possible to design some other and different morphological filters satisfying the Serra's definition of morphological filter and having some useful and meaningful properties. In the previous work the new 'selective morphology' (SM) was proposed based on 'monotonization' technique. SM allows designing special morphological operators different from operators of classic MM Serra. This paper describes the further results of this approach: It is proved, that the classic and selective morphological filters are corresponding bottom and top bounds for any other morphological filters of some kind. The required and enough conditions are determined those guarantee operators designed by 'monotonization' scheme to be morphological filters in Serra's sense. The new constructive scheme is proposed that makes it possible to design a wide range of alternative morphological filters between classic and selective morphological operators. Some examples of morphological filters design based on selective morphology are given. In particular, the morphological filter based on Hough Transform is described.

Digital Still Color Cameras sample the visible spectrum using an array of color filters overlaid on a CCD such that each pixel samples only one color band. The resulting mosaic of color samples is processed to produce a high resolution color image such that a value of a color band not sampled at a certain location is estimated from its neighbors. This is often referred to as 'demosaicking.' In this paper, we approach the process of demosaicking as a bilateral filtering process which is a combination of spatial domain filtering and filtering based on similarity measures. Bilateral filtering smooths images while preserving edges by means of nonlinear combinations of neighboring image pixel values. A bilateral filter can enforce similarity metrics (such as squared error or error in the CIELAB space) between neighbors while performing the typical filtering operations. We have implemented a variety of kernel combinations while performing demosaicking. This approach provides us with a means to denoise, sharpen and demosaic the image simultaneously. We thus have the ability to represent demosaicking algorithms as spatial convolutions. The proposed method along with a variety of existing demosaicking strategies are run on synthetic images and real-world images for comparative purposes.

We describe a novel approach to solve a problem of window size selection for median based filtering of noisy images. The approach is based on the intersection of confidence intervals (ICI) rule and results in algorithms that are simple in implementation. The ICI rule gives the adaptive varying bandwidths and enables the algorithm to be spatially adaptive in the sense that its quality is close to that which one could achieve if the smoothness of the estimated signal were known in advance. We propose and analyze a two-stage structure for the median based adaptive filter with different use of the ICI rule. At the first stage (segmentation), the ICI rule with the median filter is applied in order to find the adaptive window size for every pixel of the image. At the second stage (filtering), the image denoising is produced by a weighted median filter with varying window sizes obtained at the first stage. Two different approaches (with a single centered window and with combined four-quadrant windows), affecting the structure of the filters, have been considered in order to form the local neighborhood of the targeted pixel. Comparison of the developed algorithm with known techniques for noise removal shows the advantage of the new adaptive window size approach, both quantitatively and visually.

New weight functions called filters or masks, have been designed through nonparametric Local Polynomial Approximation methods (LPA) for both, de-Noising and edge detection tasks. These new masks, are combined with the nearest neighborhood interpolators. The produced modified nearest neighborhood interpolation filter structures are incorporated to a new and effective statistical strategy of bandwidth (window size) selection known as the Intersection of Confidence Intervals (ICI), rendering good performance and accuracy when dealing contaminated data. Nonparametric estimation methods (among them LPA) can be considered as being the driving force for the development of bandwidth selection methods (among them ICI).

Recently, the video images are introduced in the measurement and the monitoring system. The image sequences, which are obtained by these systems, are corrupted by additive noise. The restoration of the image sequences corrupted by additive noise is important to obtain the high quality image and the high compression. In this paper, we propose a restoration method for the image sequences corrupted by Gaussian noise. The conventional restoration methods are archived by spatio-temporal filtering after the motion estimation. The accuracy of the motion estimation of the conventional method is affected by the Gaussian noise. Therefore, the filtering performance after the motion estimation is not satisfied. In this paper, to overcome this defect without increasing the calculation time, we propose a spatio-temporal separable data-dependent weighted average filter with the motion estimation. The first process of the proposed method, we use the spatial filter for the corrupted image sequences. This process regards as the pre-filtering for motion estimation and realizes the robust motion estimation. The second process is the motion estimation process. Since the motion is estimated using the output of the first process, the accuracy of estimation is high. In the third process, the temporal filter is used to reduce the noise with the motion compensation. We demonstrate the performance of the proposed method through a lot of simulation results.

Removing noise from data is often the first step in data analysis. Denoising techniques should not only reduce the noise, but do so without blurring or changing the location of the edges. Many approaches have been proposed to accomplish this; in this paper, we focus on one such approach, namely the use of non-linear diffusion operators. This approach has been studied extensively from a theoretical viewpoint ever since the 1987 work of Perona and Malik showed that non-linear filters outperformed the more traditional linear Canny edge detector. We complement this theoretical work by investigating the performance of several isotropic diffusion operators on test images from scientific domains. We explore the effects of various parameters such as the choice of diffusivity function, explicit and implicit methods for the discretization of the PDE, and approaches for the spatial discretization of the non-linear operator etc. We also compare these schemes with simple spatial filters and the more complex wavelet-based shrinkage techniques. Our empirical results show that, with an appropriate choice of parameters, diffusion-based schemes can be as effective as competitive techniques.

In this paper we consider the problem of complementary DNA (cDNA) microarray image segmentation for the purpose of relative spot intensity measurement. Our aim is to find reliable background and target areas for the measurement. In contrast to global and local thresholding techniques, we investigate methods insensitive to changes in intensity scale. We combine characteristics of binary hit-or-miss transform and assumption of ordinal scale measurements, thus leading to a rank-based shape detector. We also provide a segmentation scheme based on the detector and a training approach and goodness criteria for the detector.

We propose a heuristic method for the reconstruction of x-ray penumbral images from a noisy coded source. The ill-posed noisy penumbral image reconstruction problem is modeled as an optimization problem where the reconstructed image can be obtained by minimizing the mean square error between the obtained penumbral image and the estimated penumbral image, and Laplacian values of the estimated image. The Laplacian operator is used here a smoothness constraint. Since with heuristic methods, complicated a priori constraints can be easily incorporated by the appropriate modification of the cost function, the proposed method is well suited to the solution of this ill-posed problem. The proposed method has also been applied to real laser-plasma experiments.

A new approach towards automating the interpretation of geological structures like horizons or faults in reflection seismic data images is presented. Horizons are strong reflection events which indicate boundaries between rock formations while faults are discrete fractures across which there is measurable displacement of rock layering. Horizon tracking across faults and thereby determining geologically valid correlations is an important but time consuming task although it has still not been automated satisfactorily. The difficulties of matching horizon segments across faults are due to those types of images which contain only a small amount of local information, furthermore partially disturbed by vague or noisy signals. In this paper we describe a model-based approach which reduces these uncertainties by introducing global features based on geological constraints. Two optimization methods have been examined: an exhaustive search algorithm which reliably delivers the optimal solution presuming correctness of the model and a more practicable strategy; viz, a genetic algorithm. Both methods successfully matched all selected horizons across normal faults in typical seismic data images.

Edge linking is an important task in a boundary extraction problem. In this paper, a fuzzy approach is proposed. The proposed system consists of a fuzzy edge detection module and a fuzzy edge linking module, respectively. The fuzzy edge detector gives a fuzzy membership matrix and an initial edge map. Once the initial edge map is obtained, the pairing of the start and end points of the edges as well as the linking of appropriate segments of edges in the map can be found using the fuzzy edge linking module, as follows: First, for any start point, the corresponding end point is found by searching for the shortest distance between the points. Second, for any start point as a reference point, we search for the greatest fuzzy membership value among its neighbors, and connect the reference point to that neighbor. Then with that neighbor as the new reference point, this step of searching is repeated until the end point is reached. After applying the above technique to all the pairs of start and end points, all the open boundaries will be connected. A simulation evaluation of the proposed technique was carried out on an image 'Cancer.' The simulation result shows an improvement on the outlines of the cancer cells. The proposed algorithm is simple and low cost, and can be implemented easily in some real-time applications.

The aim of this paper that is organized in two parts is to introduce the concept of parallel access of data in regular but not orthogonal grids. Although the orthogonal grid and the corresponding sampling methods are well-known for many years and well established in science and technology, there is a certain interest in 2- and 3-dimensional imaging to study triagonal and hexagonal grids. In the 2-dimensional case these grids are generated by tessellation of the plane using triangles and hexagons, respectively. They form very regular patterns and they have very nice properties according to the number of neighborhood pixels and distance values in electronic imaging. Moreover, it is known for a long time that the retina part of the human visual system can be modeled by a hexagonal packing structure of rods and cones. In this paper we study the connection and the influence of the necessary data structures, access patterns, and system architecture to model imaging algorithms with triagonal and hexagonal grids. In particular, we study the parallel access to straight lines and hexagonal 'circles.' We show a possible parallel memory architecture for the parallel conflict-free access to rows, straight lines and hexagonal 'circles.' The necessary fundamental notions are given in this first part.

Fractal geometry concerns the study of non-Euclidean geometrical figures generated by a recursive sequence of mathematical operations. These figures show self-similar features in the sense that their shape, at a certain scale, is equal to, or at least 'similar' to, the same shape of the figure at a different scale or resolution. This property of scale invariance often occurs also in some natural events. The basis of the method is the very comparison of the space covering of one of those geometrical constructions, the 'Sierpinski Carpet,' and the particles location and size distribution in the portion of surface acquired in the images. Fractal analysis method, consists in the study of the size distribution structure and disposition modalities. Such an approach was presented in this paper with reference to the characterization of airborne dust produced in working environment through the evaluation of particle size disposition and distribution over a surface. Such a behavior, in fact, was assumed to be strictly correlated with 1) material surface physical characteristics and 2) on the modalities by which the material is 'shot' on the dust sample holder (glass support). To get this goal, a 2D-Fractal extractor has been used, calibrated to different area thresholding values, as a result binary sample image changes, originating different fractal resolutions plotted for the residual background area (Richardson plot). Changing the lower size thresholding value of the 2D-Fractal extractor algorithm, means to change the starting point of fractal measurements; in such way, it has been looked for possible differences of powders in the lower dimensional classes. The rate by which the lowest part of the plot goes down to residual area equal to zero, together with fractal dimensions (low and high, depending on average material curve) and their precision (R²) of 'zero curve' (Richardson Plot with area thresholding value equal to zero, i.e. whole fractal distribution), can be used as criterions to classify the materials and working actions producing dust. For the intrinsic structure of the procedure and algorithms the proposed 2D Fractal Analysis, originally developed for particles, can be successfully applied to many others sectors as biology (cell and tissues), medical imaging, food industry, advanced materials characterization, nanoparticles, composite materials, alloys, etc.

In this paper a new algorithm for recognizing 2D objects is introduced. The proposed algorithm is based on searching for first three matched connected lines in both input and model objects, then left and right lines in both input and model objects are marked as matched lines as long as they have the same relations of distance ratio and angle to the last matched and connected lines. The process is repeated until there is no more three matched connected lines. The ratio_test is then performed to detect scattered matched points and lines. The new algorithm is invariant to translations, rotations, reflections and scale changes and has O(m.n) as its computational complexity.

We present in this paper a novel and effective system for removing blotches in old film sequences. In particular we propose a new very efficacious detection method: it is able to yield a high correct detection rate while minimizing, at the same time, the false alarm rate. Moreover, it is very efficient also in presence of slow motion, since it exploits both temporal and spatial features of the blotches. Adaptive Block Matching is used for the blotch correction step.

Let L_n² equals L² (R) X L² (R) X ... X L² (R)/n. It is shown how to construct a system of functions {(phi) _k (x)} equals {(phi) _k⁽¹) (x), (phi) _k⁽²) (x), ..., (phi) _k⁽ⁿ) (x)} from L_n² which satisfies the following conditions: (1) After normalization it forms a Riesz basis in L_n²; (2) For any given set of functions [f₁(x), f₂(x), ..., f_n(x)] (summation) L_n² the representations f_j(x) equals (Sigma) /k c_k (DOT) (phi) _k^(j) (x), x (summation) R, j equals 1,n, hold, where the coefficients c_k are defined from {(phi) _k (x)} and [f₁(x), f₂(x),..., f_n(x)].

In this work a connected approach for morphological contrast enhancement is proposed. The morphological contrast is based on the notion of toggle mappings. The notion of toggle mappings progressed in the way suggested by the Kramer and Bruckner (KB) algorithm. Since the KB algorithm uses the erosion and the dilation as patterns, some problems in this transformation are the oscillations and jumps produced when it is iterated. In our case, both transformations (erosion and dilation) were used in a separated way to built a family of filters, called morphological slope filters (MSF). This allows a better control of the output image. However, sometimes the MSF are sensible to some configurations of the blurred edge. This inconvenience can be attenuated using a connected approach of MSF. Since a connected operator does not split components of the level sets, then connected operators must act on the level of flat zones rather than on pixel level. The notion of flat zone allows the attenuation in sensibility of the MSF. The interest of the use of connected transformations in contrast enhancement is illustrated when a modified version of the KB algorithm is tested and by comparing idempotent toggles using flat zone and pixel notions.

In this paper, we describe our recent work attempting to improve the motion estimation and compensation performance in MPEG, without introducing any significant computing cost. To achieve low complexity, MPEG used fixed frame classification or allocation of I, B, P-frames to do the motion estimation and compensation. By introducing an adaptive mechanism to connect the frame content and previous record analysis with the arrangement of video frames, the classification inside the video stream can be determined according to the nature of its content in relation to those neighboring video frames. During this process, records of motion estimation and compensation for previous frames are taken into consideration to form a basis of analysis. As a result, a histogram of those major directions is formulated to allow information flow being analyzed before the frame is classified. Thresholds are then applied along the analyzed direction to video frames, and their classification of I, B, or P-frames is determined on the fly. Hence, the performance of motion estimation and compensation can be improved towards the whole compression system. Extensive experiments are carried out to support our work and the results reported show that our proposed method outperforms the existing MPEG-2 scheme, when assessed in mean-square-errors.

The tasks of digital elevation map reconstruction from isogram maps and the arising problems are considered. An iterative algorithm based on discrete cosine transform and histogram filtering with taking into account several nonlinear constraints is proposed. The algorithm efficiency and accuracy analysis for test and real data is carried out. The advantages of the proposed technique and the perspectives of further investigations are shown.

A new method for coding and lossless compression of gray scale images has been proposed. After coding of intensities, a prediction process is performed followed by the mapping of prediction residuals that are split into bit planes to which the compression technique is applied. The planes can be coded as uncompressed or compressed using a variable block- size segmentation and coding. The used coding and compression schemes include minterm coding, coordinate data coding, discrete multiple-valued input binary functions, basic Walsh, triangular, Reed-Muller weights and spectra and the reference row technique. Experimental results show that the described method has comparable compression ratios when compared with other compression techniques.

Reconstruction of a line in 3-D space using arbitrary perspective views involves the problem of obtaining the set of parameters representing the line. This is widely used for many applications of 3-D object recognition and machine inspection. A performance analysis of the reconstruction process in the presence of noise in the image planes is necessary in certain applications which require a large degree of accuracy. In this paper, a methodology, which is based on the concept of epipolar line, for the reconstruction of a 3-D line, from two arbitrary perspective views is given. In this problem the points in the second image plane, which correspond to points in the first image plane are found by using epipolar line method, by considering all the points in the first image plane. Then triangulation law is used to find the points in 3-D space. Using least square regression in 3-D, the parameters of a line in 3-D space are found. This least square regression problem is solved by two different methods. Simulation study results of this epipolar line based method, in presence of noise, as well as results of error analysis are given.

Local entropy estimates can be useful in segmentation of Particle Image Velocimeter (PIV) images. Image intensity combined with local entropy estimates forms basis for bubble detection. The acquired images are corrupted by additive noise with fixed density function. Local entropy estimate of the original image can be extracted from the noisy image if noise distribution is known a priori. A new approach to the problem of local entropy estimation in noisy images is presented. We presume that our original image is corrupted by additive i.i.d. noise from an ergodic source. The noise thus comes from a source that has a fixed density function, which can be approximated by taking histogram over the noise image. Now the histogram of the observed image, can be approximated by convolving the histogram of the original with the noise density (or its approximation). Now, in principle, it is possible extract the histogram of the original image by a blind deconvolution and removing the effect of noise. In many cases, it is also possible to utilize a priori information of the noise process. Local histogram deconvolutions with different window sizes and histogram bin numbers are performed. It is found that with careful implementation the resulting entropy estimates improve the estimates based on noisy image. We expect that the proposed method will prove to be useful with higher dimensional input data. With multidimensional data the number samples grows rapidly with the window size which improves significantly the density estimates.

A biometric identification system based on the user's hand-palm is presented. Two main approaches for feature extraction are explored: (a) geometrical (a set of geometrical measurements i.e. fingers' length, hand's area and perimeter are obtained from the user's hand), (b) by using the hand-palm contour with no further information. The large amount of data obtained by using the second approach leads us to a dimensionality reduction problem. We address this problems using three different solutions, contour down-sampling, PCA (Principal Component Analysis) and Wavelet decomposition. Two well known classification techniques, KNN (K-Nearest Neighbor) and NN (Neural Networks) are used to identify the users. Experimental results comparing each of these techniques are given.

With the advent of flip-chips, internal debug tools need to image the active regions of devices through their silicon substrates. Infrared (IR) optics can 'see' through silicon, but accurate navigation to a particular node is challenged because IR resolution is often lower than the feature size to be probed. To meet this accuracy requirement, we have developed an automated sub-resolution alignment of a device's computer-aided design (CAD) to its through silicon IR image. Automated image alignment is not straightforward because CAD and IR images differ significantly in magnification, rotation, intensity, and resolution, causing standard alignment algorithms to fail. The light diffraction of the optical system blurs and distorts the shape and size of features, causing both edge-based and intensity-based cross-correlation techniques to fail. The alignment methodology we present, consists of pre-processing (equalization) of the two images, followed by sub-resolution offset computation along with x-y confidence factors. We apply a modeled point spread function (PSF) of the optical system to the CAD image to increase its resemblance to the optical image. The application of the PSF is important in resolution-equalization, and becomes critical if 'ghosting' is present in the optical image. Using our alignment algorithm which combines image equalization, over-sampling, and cross-correlation, we demonstrate the ability to achieve 0.1 micron placement accuracy with a 1 micron resolution optical system.

As a rule, blur is a form of bandwidth reduction of an ideal image owing to the imperfect image formation process. It can be caused by relative motion between the camera and the original scene, or by an optical system that is out of focus. Today there are different techniques available for solving of the restoration problem including Fourier domain techniques, regularization methods, recursive and iterative filters to name a few. But without knowing at least approximate parameters of the blur, these filters show poor results. If incorrect blur model is chosen then the image will be rather distorted much more than restored. The original solution of the blur and blur parameters identification problem is presented in this paper. A neural network based on multi-valued neurons is used for the blur and blur parameters identification. It is shown that using simple single-layered neural network it is possible to identify the type of the distorting operator. Four types of blur are considered: defocus, rectangular, motion and Gaussian ones. The parameters of the corresponding operator are identified using a similar neural network. After a type of blur and its parameters identification the image can be restored using several kinds of methods. Some fundamentals of image restoration are also considered.

In this paper, we present an algorithm to estimate mean vehicle speed from un-calibrated roadside cameras. The algorithm presented creates a new virtual speed sensor that leverages the large numbers of low quality cameras already installed by transportation agencies. The calibration problem considered here is complicated by the ability of the operation staff to pan, tilt, and zoom the un-calibrated roadside cameras. It is in this framework that we present an algorithm that: (1) performs a simplified dynamic calibration and (2) estimates mean vehicle speed. In the work presented, we wish to estimate the mean vehicle speeds and we will demonstrate that a simplified, and perhaps less accurate form of calibration is adequate to make an accurate mean speed estimate. We use 10-second video sequences as training sets to dynamically calibrate the camera. Our proposed method detects moving vehicles in a set of consecutive frames. This information, together with a mean vehicle dimension, allows us to estimate a scaling factor for a one-dimensional transformation between motion in the image and motion in the earth coordinates. As a result, our algorithm requires the estimation of fewer camera calibration parameters. We validate our algorithm with both simulated data and real world traffic scenes.

In our previous literature, we proposed a class of nonlinear filters whose output is given by a linear combination of weighted medians (LCWM) of the input sequence. We showed that, unlike the median type filters having the lowpass response, the LCWM filters consisting of weighted median subfilters can not only suppress both Gaussian noise and impulsive noise effectively, but also offer various frequency characteristics including lowpass, bandpass, and highpass responses. In an attempt to improve the performance of LCWM filters, we propose an adaptive LCWM (ALCWM) filter which consists of directional weighted median subfilters with different geometric structures. The weighting factor of each subfilter is adaptively determined using the similarity between the directional subwindow and the local geometric image features of interest. It is shown experimentally that the ALCWM filter performs better than the aforementioned filters including the median and the LCWM filters in preserving more details.

We introduce a new approach to video compression based on the Discrete Cosine Transform (DCT) generalized to 3 dimensions. An efficient tool of 'Activity Map' further exploits the temporal redundancies of video sequences, providing a very-low bit-rate system. The result is a compression ratio of more than 150:1 with good quality of the reconstructed sequence, measured as more than 37 db (PSNR). Although the compression results are comparable with existing methods, such as MPEG or H.263, the complexity of the proposed approach is approximately 90% lower, making it suitable for hand-held systems such as cellular videophones.

This work extends the idea of spectral optimization for the design of Weighted Median filters and employ adaptive filtering that updates the coefficients of the FIR filter from which the weights of the median filters are derived. Mallows' theory of non-linear smoothers [1] has proven to be of great theoretical significance providing simple design guidelines for non-linear smoothers. It allows us to find a set of positive weights for a WM filter whose sample selection probabilities (SSP's) are as close as possible to a SSP set predetermined by Mallow's. Sample selection probabilities have been used as a basis for designing stack smoothers as they give a measure of the filter's detail preserving ability and give non-negative filter weights. We will extend this idea to design weighted median filters admitting negative weights. The new method first finds the linear FIR filter coefficients adaptively, which are then used to determine the weights of the median filter. WM filters can be designed to have band-pass, high-pass as well as low-pass frequency characteristics. Unlike the linear filters, however, the weighted median filters are robust in the presence of impulsive noise, as shown by the simulation results.

In this paper, we present a method to reduce blocking and ringing artifacts in low bit-rate block-based video coding. For each block, its DC value and DC values of the surrounding eight neighbor blocks are exploited to predict low frequency AC coefficients. Those predicted AC coefficients allow to infer spatial characteristics of a block before quantization stage in the encoding system. They are used to classify each block into either of two categories, low-activity and high-activity block. In the following post-processing stage, two kinds of low pass filters are adaptively applied according to the classified result on each block. It allows for strong low pass filtering in low-activity regions where the blocking artifacts are most noticeable, whereas it allows for weak low pass filtering in high-activity regions to reduce ringing noise as well as blocking artifacts without introducing undesired blur. In the former case, the blocking artifacts are reduced by one dimensional (1-D) horizontal and vertical low pass filters, and selective use of horizontal/vertical direction is adopted depending on the absolute values of the predicted AC coefficients. In the latter case, deblocking and deringing is conducted by a single filter, which makes the architecture simple. TMN8 decoder for H.263+ is used to test the proposed method. The experimental results show that the proposed algorithm is efficient and effective in reducing ringing artifacts as well as blocking artifacts from the low bit-rate block-based video coding.

This paper presents a new algorithm for the minimization of Boolean functions: the Partitioned Incremental Splitting of Intervals (PISI). This algorithm permits a high performance distributed implementation with a high speedup with relation to the original ISI algorithm, and an acceptable increase in the Boolean function representation complexity. Experimental results illustrate the main characteristics of the technique proposed.