The present paper introduces a method for automatically designing optimal binary filters by beginning with a prior filter and then altering this filter in the presence of sample pairs of ideal and degraded image realizations. The technique includes as a special case the method of differencing used for digital documents, and when an appropriate prior filter is used, can significantly improve the precision of filter estimation. Besides outlining design from prior filters and providing examples, the paper provides expressions for error of estimation.

A new concept of a mixed median filter that generalizes the traditional median filter is considered. These kinds of median filters unite the various filters using in signal and image processing, including the weighted median filters, order statistic filters, dilation and erosion of functions by the set. By means of the mixed median filters, the corresponding minimizing conditions for the order statistics are given. The threshold decomposition properties of the mixed median filter is considered to show that unlike stack filters the firsts are determined by different Boolean functions at the threshold levels. Representation of the mixed median filter and its basis statistical properties are studied.

Here we propose adaptive nonlinear filters based on calculation and analysis of two or three order statistics in a scanning window. They are designed for processing images corrupted by severe speckle noise with non-symmetrical. (Rayleigh or one-side exponential) distribution laws; impulsive noise can be also present. The proposed filtering algorithms provide trade-off between impulsive noise can be also present. The proposed filtering algorithms provide trade-off between efficient speckle noise suppression, robustness, good edge/detail preservation, low computational complexity, preservation of average level for homogeneous regions of images. Quantitative evaluations of the characteristics of the proposed filter are presented as well as the results of the application to real synthetic aperture radar and ultrasound medical images.

An FFT-ordered L-filter (FFT-LF) has been previously proposed as an alternative to the L-filter. FFT-LF filter is defined as a linear combination of 'FFT-ordered' inputs which can be considered as outputs of a bank of stack filters formed according to an FFT-like flowchart. It has been shown that FFT-LF's efficiently remove mixed noise. They possess good characteristics of performance and are simple in implementation. The idea of this paper is based on using FFT-LF in adaptive LMS filtering framework. This allows to incorporate advantages of both transform-domain adaptive LMS (TD-LMS) filters and adaptive L-filters into a unified design. We propose a new adaptive filter structure, called adaptive FFT-LF filter which consists of two stages: preprocessing and the LMS algorithm. Many different adaptive filters, in particular, TD-LMS, adaptive L-filters can be realized based on the proposed structure. The range of these filters is efficiently implemented on a unified device.

This paper illustrates the design of a nonlinear filter for edge-enhancing smoothing of multiplicative noise using a morphology-based filter structure. This filter is called the minimum coefficient of variation (MCV) filter. The coefficient of variation is the ratio of the standard deviation of a random process to its mean. For an image corrupted only by stationary multiplicative noise, the coefficient of variation is theoretically constant at every point. Estimates of the coefficient of variation indicate whether a region is approximately constant beneath the multiplicative noise or whether it contains significant image features. Regions containing edges or other image features yield higher estimates of the coefficient of variation than areas that are roughly constant. The MCV filter uses a morphological structure to direct low-pass filtering to act only over regions determined to be most nearly constant by measuring the coefficient of variation. Examples of the sue of the MCV filter are given on synthetic aperture radar (SAR) images of the earth. SAR images are corrupted by speckle, a predominantly multiplicative noise process. Therefore, the MCV filter is a good choice for reducing speckle without blurring edges. The MCV filter is useful for preprocessing in image analysis applications such as coastline detection in SAR images.

The proposed filter consists of a set of linear separable Boolean functions (LSBF) from which, each time, only one is selected to perform the actual filtering. The selection depends on the pixel values in a subset V of the filter window W. The paper shows that in terms of performance, the introduced filter is bounded between the V-windowed Boolean filter and the W-windowed Boolean filter. The advantage of the proposed filter is that it can be used with very large windows which permits to overcome the limits of the other binary image filtering methods. The paper proves that the new filter can be designed by training each LSBF independently. SEveral design methods for LSBF are analyzed and a new efficient and reliable training algorithm is developed. The experimental results compare the performance of the new filter against the Boolean filter and LSBF for various windows. The new LSBF training algorithm is also compared with the design method used by Lee and Lee for linear separable threshold Boolean filters.

In this paper, a structure-adaptive approach to the nonlinear image filtering is described. The adaptive procedure is based on selection of the most homogenous neighborhood region from several possible structuring regions by the principle of maximum a posteriori probability. Then, an optimal evaluation of the pixel value is performed involving pixels from the determined neighborhood region. Trimmed mean filters are used for the robust evaluation of local properties during estimation of object and background intensities when the noise has a mixed conditional distribution, e.g. normal distribution with outliers.

Mathematical morphology (MM) can be defined in terms of complete lattices. Thus, MM is useful for the processing of binary images or of single-valued intensity images - images for which a partial ordering, hence a lattice structure, is apparent. The lattice structure of an intensity image is manifest through set inclusion with ordering on intensity. It is always possible to define majorants and minorants for collections of sets that are intensities with spatial support. Not all the components of a color image can be ordered trivially. In particular, hue is angle-valued. Consequently, MM has not been as useful for color image processing because it has not been clear how to define set inclusion for angle-valued images. This paper contains definitions for erosion, dilation, opening, and closing for angle-valued images using hue as the exemplar. The fundamental idea is to define a structuring element (SE) with a given hue or hues. From each image neighborhood of the SE, the erosion operation returns the hue value that is closest to the hue of the corresponding SE member. Examples of the effects of the operators on a color noise field are shown. Histograms demonstrate the effects of the operators on the hue distributions.

Performing morphological operations such as dilation and erosion of binary images, using very long line structuring elements is computationally expensive when performed brute- force following the definitions. In this paper, we present a two-pass algorithm that runs at constant time for obtaining dilations, irrespective of the lengths and orientations of the line structuring elements. We use the concept of orientation error between the continuous line and its discrete counterpart in generating the basic digital line structuring element used in obtaining what we call the dilation transform. To obtain any dilation, we just threshold the dilation transform with a value that is the length of the desired line structuring element. We implemented the algorithm in general image processing system environment on a sun sparc station 10, and tested them on a set of 240 X 250 sized salt and pepper noise images with probability of a pixel being a 1-pixel set to 0.25, for orientations (theta) (epsilon) [ (pi) /2, 3(pi) /2 ] of the normals of the continuous lines, of which the digital line structuring elements are a discretization, and their lengths in the range 5 to 145 pixels. We achieved a speed up of about 50 over the conventional methods when the structuring elements had lengths of 145 pixels. The algorithm ran at a constant time of 200ms. We required only one minimum operation per result pixel.

In this paper, we show that gray scale dilation, erosion and consequently hit-miss transform, are solutions to a regularization problem. The theory is an extension to the fact that maximum and minimum operators are Green's functions. These morphological operators are used successfully in a morphological shared-weight neural network designed for automatic target recognition and handwritten digit recognition.

An algorithm for shape description is proposed in this paper. A sequence of shapes, called morphological shape signature, is generated by application of the morphological signature transform (MST), in the first step of the method. After the shape transformation process is completed a simple shape descriptor is applied to each shape from the obtained shape signature. The original MST algorithm uses erosion for iterative morphological shape processing. The original MST is modified so that both erosion and dilation are used. The method is tested on the problem of shape matching and experimental results have demonstrated that proposed method has better recognition performance.

In this article we describe a new approach of brooking stationary detection in a noisy signal. We consider the signal corrupted by an additive stationary noise, whose form of the density of probability is none. This new approach leans on the detection and the analysis of the transitions of the signal. The extraction of transition in the signal associates, to each sample in the transition, a constant value equal to the surface of the signal in the transition. The application of this operator to the gradient of the signal gives us the value of the transitions dynamics in the signal. The dynamics transitions density probability modelization by a parametric curve allows us to deduce the level of noise in the signal. It is from the level of noise that we determine a threshold on the height of the transitions. Then we consider the transitions smaller than the threshold as transitions of the noise and the transitions higher than the threshold as the variations of the signal without noise. THis technique of rupture detection is entirely automatic and self adapted to the level of noise in the signal. We present the study and the implementation of this global approach for the detection of roof and step edges in range images. We detect roof and step edge in the image with the signals of transition extracted in two orthogonal directions.

We have recently proposed an objective measure of edge sharpness or acutance of a region of interest (ROI) in the image. As acutance is related to image sharpness, one possible approach to image enhancement is to apply enhancement techniques in such a way as to increase the acutance of the ROI. Then, we may expect the perceived sharpness of the ROI to be increased as a result. A new image sharpening method designed on the basis of acutance is proposed in this paper. In this method, 1D operators are applied to sets of pixels along the normals at each boundary pixel of an ROI. It is shown that the method can improve sharpness without creating significant artifacts.

Segmentation of images is an important aspect of image recognition. While grayscale image segmentation has become quite a mature field, much less work has been done with regard to color image segmentation. Until recently, this was predominantly due to the lack of available computing power and color display hardware that is required to manipulate true color images (24-bit). TOday, it is not uncommon to find a standard desktop computer system with a true-color 24-bit display, at least 8 million bytes of memory, and 2 gigabytes of hard disk storage. Segmentation of color images is not as simple as segmenting each of the three RGB color components separately. The difficulty of using the RGB color space is that it doesn't closely model the psychological understanding of color. A better color model, which closely follows that of human visual perception is the hue, saturation, intensity model. This color model separates the color components in terms of chromatic and achromatic information. Strickland et al. was able to show the importance of color in the extraction of edge features form an image. His method enhances the edges that are detectable in the luminance image with information from the saturation image. Segmentation of both the saturation and intensity components is easily accomplished with any gray scale segmentation algorithm, since these spaces are linear. The modulus 2(pi) nature of the hue color component makes its segmentation difficult. For example, a hue of 0 and 2(pi) yields the same color tint. Instead of applying separate image segmentation to each of the hue, saturation, and intensity components, a better method is to segment the chromatic component separately from the intensity component because of the importance that the chromatic information plays in the segmentation of color images. This paper presents a method of using the gray scale K-means algorithm to segment 24-bit color images. Additionally, this paper will show the importance the hue component plays in the segmentation of color images.

3D images are becoming more popular in the medical field. In order to extract desired objects with uncertainties in 3D images, we proposed a novel method to detect fuzzy boundaries with the aid of fuzzy connectivity relation derived from the theory of fuzzy digital topology. A seed point is interactively selected which is definitely inside the desired object, and is assigned an appropriate membership according to the statistic characteristics in its neighborhood, which is called 'seed region'. Memberships of the other points in the image depend not only on their similarity of greylevel to the seed region, but also on their similarity to adjacent voxels. The later may be calculated from a point to the seed region on the basis of a newly defined concept of fuzzy connectivity. After such transformation, a fuzzy boundary is generated corresponding to a characteristic edge point that is selected by experiences or according to the requirement of practical applications. Furthermore, we may take use of skeleton extraction to optimize this boundary. Boundaries extracted like this are ensured to be Jordan. Experiments on some ultrasonic images show satisfying results with smoothed, connective and optimal boundaries.

This work addresses a catchment basins merging algorithm developed to automate the segmentation of microscopic images, which is directly derived from the traditional non- hierarchical watershed algorithm. The proposed merging algorithm, based on digital topology concepts, employs regional criteria to merge the non-significant minima. It can be classified as a region growing method by flooding simulation, working at the scale of the main structures. The shape of the structures is absolutely irrelevant to the merging process. As a characteristic of the flooding simulation methods, the gray level image is viewed as a relief where each gray level is assigned a height. In the proposed method the relief is always flooded from all its local minima which are progressively detected and merged as the flooding takes place. The catchment basins merging process is guided by two parameters: a depth criterion and an area criterion. This solution suppresses the characteristic over-segmentation of the traditional watershed enabling the direct segmentation of the original image without the need of a previous pre-processing step. Due to the automatic detection of all local minima there is not need of the explicit marker extraction step often required by other flooding simulation methods. It is shown that this solution produces excellent segmentation results allowing the characterization of several materials from their microscopic images.

The filtering performance of the soft morphological filters in decomposition schemes is studied. Optimal soft morphological filters for the filtering of the decomposition bands are sought and their properties are analyzed. The performance and properties of the optimal filters found are compared to those of the corresponding optimal composite soft morphological filters. Also, the applicability of different decomposition methods, especially those related to soft morphological filters, is studied.

A unified framework for grey value and texture segmentation has been developed. It makes use of a special graph structure (feature similarity graph - FSG) which is based on a feature similarity criterion and a feature smoothing procedure applied in each layer of the network. The feature similarity criterion reflects the fact that not the features themselves but their differences are responsible for segmentation. Furthermore, it takes also into account that the separability of regions depends on the feature variation inside the regions. The segments are the connected components of the FSG. Therefore, the method can be understood as a clustering or grouping procedure of features. Starting with grey value segmentation one obtains segments which, for textured images, represent texture elements or parts of texels and background, respectively. The texels can be described by certain features, namely position, orientation, size, grey value or color, and shape descriptors. Studying position, orientation and size, spatial frequency phenomena and important observations made by investigators of human perception can be explained. The method also gives an explanation of the old Gestalt laws of proximity and similarity. Therefore, it can serve as a model for pre-attentive vision. On the other side, as a highly parallel method with local, regional and global processing ability it might be an approach for future technical vision systems. But to demonstrate this, comprehensive work, especially for a proper shape description for pre-attentive vision, is necessary in the future.

Linear filters banks are being used extensively in image and video applications. New research results in wavelet applications for compression and de-noising are constantly appearing in the technical literature. On the other hand, non-linear filter banks are also being used regularly in image pyramid algorithms. There are some inherent advantages in using non-linear filters instead of linear filters when non-Gaussian processes are present in images. However, a consistent way of comparing performance criteria between these two schemes has not been fully developed yet. In this paper a recently discovered tool, sample selection probabilities, is used to compare the behavior of linear and non-linear filters. In the conversion from weights of order statistics (OS) filters to coefficients of the impulse response is obtained through these probabilities. However, the reverse problem: the conversion from coefficients of the impulse response to the weights of OS filters is not yet fully understood. One of the reasons for this difficulty is the highly non-linear nature of the partitions and generating function used. In the present paper the problem is posed as an optimization of integer linear programming subject to constraints directly obtained from the coefficients of the impulse response. Although the technique to be presented in not completely refined, it certainly appears to be promising. Some results will be shown.

We propose two new approaches which consider the specific sonar image segmentation problem in a statistical regularization framework, based on hierarchical Markov Random Field (MRF) modeling. Within this framework , data- driven parameters estimation is performed using a mixture distributions and the contextual parameters are estimated by using the 'qualitative box' method. Then we develop two unsupervised segmentations algorithms. The first one, based on a multigrid approach, required pyramidal structure of the label field, associated to a single observation level: the MRF energy function is re-written at each scale as a coarser MRF model. The second algorithm we proposed is based on a multiresolution approach: an observation pyramid is obtained by image projection on biorthogonal wavelets. The signal to noise ratio is thus increased and allows to given a good initialization for the regularization algorithm at each level. We also compare the robustness of these unsupervised multigrid and multiresolution approaches. Some convincing results are presented and validate these new approaches for synthetic and real sonar picture segmentation.

This paper presents the introduction and using of the generalized or parametric B-splines, namely the cubic generalized B-splines, in various signal processing applications. The theory of generalized B-splines is briefly reviewed and also some important properties of generalized B-splines are investigated. In this paper it is shown the use of generalized B-splines as a tool to solve the quasioptimal algorithm problem for nonlinear filtering. Finally, the experimental results are presented for oscillatory and other signals and images.

A chaotic signal process is generated by use of a continuous but nowhere differentiable Weierstrass function as a force function in Duffing's second-order nonlinear differential equation. In the particular cases where Duffing's equation represents the mechanical behavior of a simple pendulum where only the mass of the 'bob' changes in time, an analytical solution is obtained by the use of Hammerstein integrals. In the more-complicated case where the mass of the 'bob' and the length of the pendulum rod are both changing in time, the resulting solution is obtained numerically. In any detailed analysis of a chaotic signal process, nonlinear filters are used to determine the existence and nature of an attractor or repeller as discussed. By a simple change of parametric values in the Weierstrass function, other chaotic signal processes are easily generated.

In this paper, we address the problem of lossless multispectral compression of remote-sensing data acquired using SPOT satellites. Compression algorithms have classically two stages: a transformation of the available data and coding. In the first stage, the aim is to express the spectral data as uncorrelated data in an optimal way. In the second stage, the coding is performed via the use of either a Rice or an arithmetic coding. In the first part of this paper, we discuss two well-known schemes, namely predictive technique and S + P transform, for the spatial decorrelation of multispectral SPOT images. Obviously, using only spatial properties is not optimal. However, few works have been carried out to address simultaneously the three intrinsic dimensions of multispectral images. In order to overcome this limitation, we have developed a predictive model based on three 3D-predictors. Compression ratios obtained are presented and discussed. In particular, there is a significant improvement in the compression ratios with respect to lossless compression methods based on spatial decorrelation method.

Morphological texture classification employs moments of the granulometric pattern spectrum. Classification depends on the statistical distributions of the grain size and shape. Recent work has shown the power of using asymptotic expressions for the granulometric moments which leads to successful classification in terms of an underlying random image process. These methods depend, however, on the validity of the statistical model: robustness concerns the measure of how the results are affected by various departures from the assumed model. The model may specify a normal size distribution when in fact the grain sizes are Gamma distributed; it may specify the correct type of distribution but the wrong values of its parameters; it may specify that grains are non-overlapping when in fact some are overlapping. Investigations of the robustness of the pattern spectrum mean are presented under the indicated departures from the ideal model.

As introduced by Matheron, granulometries depend on a single sizing parameter for each structuring element. The concept of granulometry has recently been extended in such a way that each structuring element has its own sizing parameter resulting in a filter (Psi) _t depending on the vector parameter t equals (t₁..., t_n). The present paper generalizes the concept of a parameterized reconstructive (tau) -opening to the multivariate setting, where the reconstructive filter (Lambda) _t fully passes any connected component not fully eliminated by (Psi) _t. The problem of minimizing the MAE between the filtered and ideal image processes becomes one of vector optimization in an n- dimensional search space. Unlike the univariate case, the MAE achieved by the optimum filter (Lambda) _t is global in the sense that it is independent of the relative sizes of structuring elements in the filter basis. As a consequence, multivariate granulometries provide a natural environment to study optimality of the choice of structuring elements. If the shapes of the structuring elements are themselves parameterized, the expected error is a deterministic function of the shape and size parameters and its minimization yields the optimal MAE filter.

There is a lack of general models in image processing, particularly for image segmentation. Actually, each treatment must combine several classical features, such as grey level values, neighborhood and spatial distribution. In fact, an image can be studied both as an aspect of geometry and as an aspect of combinatorics. Here, to each digital image we associate a neighborhood hypergraph. This general model is in fact clearly adapted to include grey level and neighborhood informations, and particularly for image segmentation. Moreover, the pyramid constitutes an efficient tool in image analysis, simulating the human vision in its attention focusing, through an individual and a contextual analysis of each region. This multiresolution scheme allows simultaneously relevant regions detection and detailed delineation. Then, combining the two approaches, a hypergraph segmentation is associated at each level of the pyramid. Finally, we use the evolution of this pyramid of hypergraphs for image segmentation and more generally modelization.

JPEG is perhaps the most commonly used still-image standard due to its good compression rate, flexibility in choosing image quality and fast algorithm for implementation. In JPEG, the DCT is used for 8 by 8 block transforms. However the notorious block artifacts caused by the DCT are of great concern. In this article, we focus on the DCT and try different filters to smooth the annoying block boundaries which are very visible under a high compression rate. A new nonlinear filter is proposed which outperforms which are very visible under a high compression rate. A new nonlinear filter is proposed which outperforms existing techniques. The results are demonstrated for images with a comparison of mean-square-errors. For a general application, the new filter is used to cancel gaussian noise added to an image and the performance is compared with that of other commonly used filters.

In this paper, we describe a wavelet-based approach to multiresolution stochastic image modeling. The basic idea here is that a complex random field, e.g., one with long range and nonlinear spatial correlations, can be decomposed into several less complex random fields. This is done by defining a random field in each resolution level of a wavelet expansion. Texture synthesis experiments, performed by using wavelet autoregressive and radial basis function (RBF) models, have produced promising results. Both models are relatively simple in each resolution and are better than single resolution models in capturing long range correlations. In texture synthesis experiments, the RBF models, especially the non-causal model, provide good visual resemblance to the original for relatively complex textures.

Function imaging has been playing an important role in modern biomedical research and clinical diagnosis, which provides human internal biochemical information previously not available. However, for a routine dynamic study with a typical medical function imaging system, such as positron emission tomography (PET), it is easily to acquire nearly 1000 images for just one patient in one study. Such a large number of images has given a considerable burden for computer image storage space, data processing and transmission time. In this paper, we present the theory and principles for the minimization of image frames in dynamic biomedical function imaging. We show that the minimum number of image frames required is just equal to the model identifiable parameters and that the quality of the physiological parameter estimation, based on these minimum number of image frames, can be controlled at a comparable level. As a result of our study, the image storage space required can be reduced by more than 80 percent.

In this paper we suggest two new algorithms for improving approximate Karhunen-Loeve (KL) bases for image processing problems. One of them is an algorithm for finding the best 2D approximate KL basis, the second is a nonlinear 2D algorithm with previous image preparation. By 2D bases is meant the basis for which 2D-basis functions are obtained as a product of 1D-functions. We show that in such sense the best 2D basis for a given ensemble really exists, and we offer the procedure for its construction. The procedure is not fast, but in spite of this it permits to demonstrate that energy accumulation for such best basis in majority of cases is much worse than for true KL basis. Consequently, all fast 2D algorithms, such as wavelet-based algorithm of approximate KL transform, can not give sufficient energy accumulation. FOr the purpose to improve this situation we offer fast nonlinear procedure which reversibly transform image spatial properties in such a way that the processed ensemble has improved energy accumulation in KL bases obtained by above-mentioned fast algorithms of approximate KL transform.

Texture segmentation or modeling plays an important role in image segmentation. In this paper, we investigate multiscale autoregressive representation for texture modeling and segmentation. The proposed algorithm also uses a multiresolution decomposition of an image, and fits an AR model to each image of the multiresolution pyramid. The set of AR coefficient vectors, one at each level, defines a model for a texture and this model is used as a predictor for the segmentation process. AR coefficient vectors are used to generate a prediction of the image pyramid, from which the prediction of the image to model is built. The resulting prediction error is used to discriminate textures in a segmentation algorithm. In the proposed structure, feedback can be included between pyramid levels by adding the prediction error at he previous level to the current level before an AR model fitting. M-AR can therefore be used as a predictor like an AR model. This is different from previous multiscale approaches for which data is used at each scale for the segmentation. Since we do not need to link data from different scales, this simplifies model processing for segmentation. The estimation error of the proposed multiscale AR approach has lower variance than that of an AR model, and is less correlated. Segmentation results also show M-AR to be an improvement to AR modeling.

One important problem in computer vision and image processing is image resizing. Current techniques are generally based on different interpolation methods. These methods are convenient but the downsampled or upsampled image will include new gray values which are not present in the original image. Soft morphological interpolation is a new technique for resampling discrete data. The soft morphological operations are an alternative to the standard morphological operation. The generic description of hierarchical soft morphological transformations was done previously. The further development of soft morphological operations by a hierarchical structural system uses the relaxation of the requirement that the result of the operation must be the r-th largest or smallest value of the corresponding multiset, where r is an order index of the internal hard center. We will assume that any reasonable integer value is acceptable. The purpose of this paper is to derive the sot morphological convolution and compare the result of this convolution with the cubic convolution and Gaussian pyramid.

A new adaptive-neighborhood restoration filter to restore images degraded by multiplicative noise is proposed. The filter uses statistics computed over adaptive-neighborhoods which are grown to include statistically stationary regions. Results of application to synthetic and natural images degraded by multiplicative noise show that the proposed method provides better noise removal than a related 3 by 3 neighborhood method without blurring edges.