In this paper we study robustness of stack filters by using a recently introduced method called output distributional influence function (ODIF). Unlike the traditionally used methods, such as the influence function and the change-of- variance function, the ODIF provides information about the robustness of finite length filters. So the ODIF is not only a good theoretical analysis tool but it can also be used in real filtering situations for selecting filters behaving as desired in the presence of contamination. We present the ODIFs for the independent but not identically distributed inputs which can be used, e.g., to study the robustness against outliers in linearly increasing or decreasing signals. For independent and identically distributed inputs there are three practical expressions for the output distribution of a stack filter and thus for that case we present three alternative expressions also for the ODIFs. The usefulness of the ODIF in the analysis of the robustness of different stack filters is demonstrated in several illustrative examples by using the ODIFs for the expectation and the variance giving local robustness of the value and the variance, respectively. We also present how to obtain in a straightforward manner the ODIFs for the duals of the stack filters.

The performance of a designed digital filter is measured by the sum of the errors of the optimal filter and the estimation error. Viewing an image at a high resolution results in optimal filters having smaller errors than at lower resolutions; however, higher resolutions bring increased estimation error. Hence, choosing an appropriate resolution for filter design is important. This paper discusses estimation of optimal filters in a pyramidal multiresolution framework. To take advantage of data at all resolutions, one can use a hybrid multiresolution design. In hybrid design, a sequence of filters is designed using data at increasing resolutions. With hybrid multiresolution design, the value of the designed filter at a given observation is based on the highest resolution at which conditioning by the observation is considered significant.

This paper discusses a multiresolution approach to Bayesian design of binary filters. The key problem with Bayesian design is that for any window one needs enough observations of a template across the states of nature to estimate its prior distribution, thus introducing severe constraints on single window Bayesian filter designs. By using a multiresolution approach and optimized training methods, we take advantage of prior probability information in designing large-window multiresolution filters. The key point is that we define each filter value at the largest resolution for which we have sufficient prior knowledge to form a prior distribution for the relevant conditional probability, and move to a sub-window when a non-uniform prior is not available. This is repeated until we are able to make a filtering decision at some window size with a known prior for the probability P(Y equals 1x), which is guaranteed for smaller windows. We consider edge noise for our experiments with emphasis on realistically degraded document images.

Wavelet-based methods are, at the present time, the most efficient methods for the improvement of the signal to-noise ratio of very noisy images. In this paper, we attempt to improve the quality of restored images by considering multiple realizations of noisy images instead of a unique realization, at constant acquisition time. We investigate several variants for thresholding or shrinking the wavelet coefficients, taking into account the relative standard deviation of the wavelet coefficients, over the multiple realizations, at a given scale, orientation and position. Moreover, for simulations, we try to quantify the quality of restoration by other criteria than the usual mean-square error or signal-to-noise ratio. For doing this, we try to quantify the structuration of the residues.

Nonlinear cellular neural filters (NCNF) were introduced recently. They are based on the complex non-linearity of multi-valued and universal binary neurons. NCNF include multi- valued filters and cellular neural Boolean filters. Applications of the NCNF to noise reduction, extraction of image details and precise edge detection have been considered recently. This paper develops the previous ideas and presents the new results. The following problems are considered in the paper: (1) Solution of the Super-resolution problem using iterative extrapolation of the orthogonal spectra and final correction of the resulting image using NCNF; (2) Precise edge detection using NCNF within a 5 X 5 window and precise edge detection for the color images.

The sigma and mean filters with adaptive window size are proposed. The sigma filter with adaptive window size is intended for processing radar images with multiplicative noise and the main goal in its design is to improve the noise suppression effectiveness for homogeneous regions of images. The mean filter with adaptive window size can be applied for relief recovery when one initially has the isogram map and its primary approximation by constant level regions. The performance of the proposed filters is tested for simulated images and then analyzed for real data.

The quality of ultrasound images is limited by granular speckle noise. This paper presents two nonlinear restoration methods based on multiscale signal decomposition. Initially, signal-dependent multiplicative speckle noise is transformed to additive noise by a logarithm point operation. Rectangular coordinates are obtained by a polar coordinate transform of the sector image. The lateral distortions require filter masks that are locally adapted to the ellipsoidal speckle spots. The images are decomposed into frequency bands and morphological scales by a Laplacian pyramid and self-dual morphological filtering, respectively. In both cases the subbands are filtered by special rank-order/morphological filters depending on lateral and radial resolutions of the ultrasound image. In case of Laplacian subbands, multistage filters consider elongated structures by unidirectional median filtering and subsequent rank-order operations. Morphological scales contain size-dependent speckle-shaped objects and are filtered by a novel self-dual reconstruction operator that equally treats noise resulting from amplified and attenuated reflected sound- waves. The performance of the despeckle algorithms is demonstrated for different types of B-mode sector scans. Both methods show significant noise reduction capability preserving object contours due to nonlinear filtering of the subbands.

Median filtering, both scalar and vector, has been proposed in the literature as an effective tool to refine estimated velocity fields. In this paper, the use of weighted median filtering is suggested to enhance motion estimation. Information about the confidence of pixel velocities is exploited for the design of median filtering weights, so as to enhance the estimation across boundaries, thus resulting in a better segmentation of the velocity field. A new approach to the estimation of optical flow fields is described, coupling the simplicity of a spatial filtering with the accuracy of statistical techniques based on confidence measurements. A rough vector field is first estimated by means of an LS technique. Refinement is then achieved through weighted median filtering, either vector or componentwise scalar. Experimental results show the effectiveness of the weighted median approach: performances have been evaluated both on synthetic image sequences and verified on real world video sequences. Although vector filtering is generally more accurate than scalar filtering, it is less robust to noise than componentwise filtering.

It is well known that nonlinear time-invariant filtering may be viewed as a nonlinear superposition of time-shifted versions of the input signal, that is described as a time invariant Volterra convolution. Nonlinear superposition of time- and frequency shifted versions of the input signal is called Volterra-Weyl convolution. In the present paper, we associate with each orthogonal transform (Legandre, Hermite, Laguerre, Walsh, Haar, Gabor, fractional Fourier, wavelet, etc.) a family of generalized shift operators. Using them we construct a nonlinear superposition of generalized time-shifted versions of the input signal. We call such a superposition a generalized Volterra-Weyl convolution (VWC). Particular cases of the VWC are nonlinear Gabor and Zak transformations, generalized higher-order Wigner distribution and ambiguity functions.

Integral transforms and the signal representations associated with them are important tools in applied mathematics and signal theory. The Fourier transform and the Laplace transform are certainly the best known and most commonly used integral transforms. However, the Fourier transform is just one of many ways of signal representation and there are many other transforms of interest. In the past 20 years, other analytical methods have been proposed and applied, for example, wavelet, Walsh, Legandre, Hermite, Gabor, fractional Fourier analysis, etc. Regardless of their particular merits they are not as useful as the classical Fourier representation that is closely connected to such powerful concepts of signal theory as linear and nonlinear convolutions, classical and high-order correlations, invariance with respect to shift, ambiguity and Wigner distributions, etc. To obtain the general properties and important tools of the classical Fourier transform for an arbitrary orthogonal transform we associate to it generalized shift operators and develop the theory of abstract harmonic analysis of signals and linear and nonlinear systems that are invariant with respect to these generalized shift operators.

This paper discusses the development of an iterative algorithm for fully automatic (gross or fine) segmentation of color images. The basic idea here is to automate segmentation for on-line operations. This is needed for such critical applications as internet communication, video indexing, target tracking, visual guidance, remote control, and motion detection. The method is composed of an edge-suppressed clustering (learning) and principal component thresholding (classification) step. In the learning phase, image clusters are well formed in the (R,G,B) space by considering only the non-edge points. The unknown number (N) of mutually exclusive image segments is learned in an unsupervised operation mode developed based on the cluster fidelity measure and K-means algorithm. The classification phase is a correlation-based segmentation strategy that operates in the K-L transform domain using the Otsu thresholding principal. It is demonstrated experimentally that the method is effective and efficient for color images of natural scenes with irregular textures and objects of varying sizes and dimension.

At low bit rates, the linear subband coders are susceptible to the ringing effect, which causes rippling and blurring around the edges in the images. On the other hand, the nonlinear coders are affected by the smearing effect wherein the detail regions are removed. In this paper, we introduce fuzzy subband coding system. This system uses fuzzy median filters in the analysis and synthesis stage of the coder. The motivation for this study is to determine if this novel system can reduce both ringing and smearing effect. Experimental results show that this new subband coder does out-perform linear and median filter subband coders, both in PSNR and visually.

A new processing scheme for large high-resolution displays such as Videowalls is proposed in this paper. The scheme consists in a deinterlacing, an interpolation and an optional enhancement algorithm; its hardware implementation requires a low computational cost. The deinterlacing algorithm is motion- adaptive. A simple hierarchical three-level motion detector provides indications of static, slow and fast motion to activate a temporal FIR filter, a three-tap vertico-temporal median operator and a spatial FIR filter respectively. This simple algorithm limits the hardware requirements to three field memories plus a very reduced number of algebraic operations per interpolated pixel. Usually linear techniques such as pixel repetition or the bilinear method are employed for image interpolation, which however either introduce artifacts (e.g. blocking effects) or tend to smooth edges. A higher quality rendition of the image is obtained by the concept of the Warped Distance among the pixels of an image. The computational load of the proposed approach is very small if compared to that of state-of-the-art nonlinear interpolation operators. Finally the contrast enhancement algorithm is a modified Unsharp Masking technique: a polynomial function is added to modulate the sharpening signal, which allows to discriminate between noise and signal and, at the same time, provides an appropriate amplification to low-contrast image details.

The systems such as infrared search and trackers (IRST's), forward looking infrared systems (FLIR's), sonars, and 2-D radars consist of two functional blocks; a detection unit and a tracker. The detection unit which has matched filters followed by a threshold device generates a set of multiple two-dimensional points or detects at every sampling time. For a radar or sonar, each generated detect has polar coordinates, the range and azimuth while an IRST or FLIR produces detects in cartesian coordinates. In practice, the detection unit always has a non-zero false alarm rate, and therefore, the set of detects usually contains clutter points as well as the target. In this paper, we shall present a new target tracking algorithm for clutter environment applicable to a wide range of tracking systems. More specifically, the two-dimensional tracking problem in clutter environment is solved in the discrete-time Bayes optimal (nonlinear, and non-Gaussian) estimation framework. The proposed method recursively finds the entire probability density functions of the target position and velocity. With our approach, the nonlinear estimation problem is converted into simpler linear convolution operations, which can efficiently be implemented with optical devices such as lenses, CCD's (charge coupled devices), SLM's (spatial light modulators) and films.

We have proposed fuzzy filters in order to remove additive non-impulsive noise (e.g., Gaussian noise) while preserving signal details. In this paper, we propose a novel fuzzy filter for removing mixed noise (i.e., Guassian noise and impulse noise are mixed). Furthermore, we apply the proposed method to color image processing. In order to remove mixed noise efficiently, we set fuzzy rules by using multiple difference values between arbitrary two pixels in a filter window. We show tuning result of the proposed fuzzy filter and present some simulation results.

We present novel enlarging methods of digital images based on Laplacian pyramid representation. First, 'direct method,' which is based on Laplacian pyramid representation, is proposed. The direct method is simple, however derive excellent enlargement results for only relative smooth regions of the image. Thus, we present the 'hybrid method' which is integrated the direct method and the Greenspan's method which is also based on Laplacian pyramid representation and has excellent property for enraging edge/detail regions. The effectiveness of the hybrid method is shown through a lot of experimental results.

A case of dominant multiplicative noise typical for radar images is considered. The filtering of such images corrupted by speckle, and possibly spikes, can be done both without and with the use of homomorphic transformations. The application of locally adaptive filtering is explored for both cases. It is shown that the use of homomorphic transformations is reasonable for solving some particular tasks, for example, better detection of small size objects with negative contrasts with respect to surrounding background and their preservation while processing the images. Other kinds of homomorphic filtering techniques can be useful for providing better noise suppression.

In this paper we present a method of segmentation using a multiagent system, and an application to fish otolith growth ring detection. The otoliths images are composed of alternative concentric dark and light rings, the number of which increases with the age of the fish. Up to now, the identification of growth rings, for age estimation, is routinely achieved by human readers, but this task is tedious and depends on the reader's subjectivity. The system proposed here is composed of several agents whose individual task is to detect local extremes on a grayscale image. For this aim the agents are provided with sensors on the gray levels of the image. By computing the mean gray level of two sensors placed in front of it, the agent, if it searches for light rings (respectively dark) will decide to turn in the direction of the lighter (respectively darker) sensor. The path of the agents has been tested as a roof edge detector, using the Canny criteria: good detection, good localization, and low multiple response, in order to choose the best parameters ruling the agents behavior, according to the image structures. Tests have been first achieved on synthetic images, and then on otoliths images.

Computing Devices Canada, a General Dynamics company, undertakes research in image processing focusing on the automatic recognition of sea mines. This paper presents the use of advanced gray-scale morphological filters for the detection of sea mines in side-scan sonar imagery. Sea mines in side-scan sonar imagery can be characterized by a mine-body and a mine shadow. Mine-bodies consist of bright regions, relative to the background, with a specific shape and size. Mine-shadows consist of dark regions, relative to the background, with a specific shape and size. The shapes and sizes of these regions depend on the mine type, the orientation of the mine, the physical acquisition process of the sonar imagery, and the environment in which the mine is located. Advanced gray-scale morphological filters provide very powerful and robust tools to extract bright and dark regions with low signal to noise ratio in very noisy imagery using geometric constraints such as shape, size and total surface area. For the detection of sea mines we use these morphological filters with the minimum and maximum geometric constraints for the mine-bodies and mine-shadows. The independent detection of mine-bodies and mine-shadows allows the detection of bottom, moored and drifting mines with the same detection algorithm. Consistent mine-body and mine-shadow combinations are resolved into mine like objects.

Dynamic programming (DP) algorithms are frequently used in speech processing for dynamic time warping of speech signals. In this approach, DP is applied to image processing for contrast correction. Defining one image as reference, the object image is contrast-corrected by DP based on the (cumulative) grayscale value histograms of the images. DP ensures a nonlinear histogram warping, and therefore an optimal nonlinear mapping between grayscale values of the images. If no path restrictions are used, assignments can be ambiguous; i.e., the grayscale value of the object image can be assigned to more than one grayscale value of the reference image. In this case, histogram-based analysis selects the most probable grayscale value. The algorithm works on the condition that image contents of the images to be compared are equal and differences only based on contrast. Unfortunately, medical images of follow-up studies or slices of 3D data volumes differ not only in contrast, but also in image content. The condition can then be met only approximately. For example, neighboring slices of gradient-spoiled T₁-weighted 3D- FLASH image data are contrast-corrected with this method. In experiments with simulated 3D MRI images, the DP approach performs best compared to another nonlinear method or to linear mapping.

Shape analysis of light-micrographs of cell populations is important for cytotoxicity evolution. This paper presents a morphological method for quantitative analysis of shape deformations of cells in contact to a biomaterial. After illumination normalization, a morphological multiscale segmentation yields separated cells. Shape deformation, and hence, toxicity of the substance under scrutiny, is quantified by means of compactness distribution and pattern spectrum of the population. Since the logarithmic image model is applicable to transmitted light, illumination normalization is achieved by removing the illumination component from the log- image by a tophat transform utilizing a large reconstruction filter. Subsequent thresholding and noise filtering yields connected binary cells, which are segmented by a marker-based, multiscale approach. For this, size-specific marker scales are generated removing noise and false markers. Each cell is now represented by an isolated marker. Converse integration of marker scales is performed by successive reconstruction of the original cell shapes, preventing merging of markers. Our method yields reasonable cell segmentations that go along with cell morphology even for differently sized and very distinct shapes. The obtained quantitative data is significantly correlated to the toxicity of the substance to be evaluated. Currently, the method is used for extensive biocompatibility tests.

Detection and binarization of local objects of interest (defects and abnormalities) in radiographic images is considered with application to industrial (non-destructive testing) and medical diagnostic imaging. The known standard approaches such as the histogram-based binarization or the method of dynamic thresholding yield poor segmentation results on the images containing small low-contrast objects and noisy background. The proposed method for object detection using binary segmentation has the following advantageous features. A model-based approach is applied which exploits the object multi-scale morphological representation in order to perform a time-effective image analysis. The intensity function is modeled by a polynomial regression representation with the so- called conformable two-region model. The estimation of the model parameters is made by using a robust non-linear estimation procedure. The concept of a multi-scale relevance function has been introduced for rapid location of local objects invariantly to the object shape, size, and orientation. The relevance function is a function that has the local maximum at the location center of an object of interest or its relevant part such as the corner edge. The developed segmentation method has been comparatively tested on radiographic images in non-destructive testing of weld joins and medical images from chest radiography.

In this paper we describe the concept of the total and the fine fractal dimensions, respectively. Then, an efficient low- complexity algorithm for computing the fractal dimension is described. The method is then extended to the concept of fine fractal dimensions in order to separate textural and structural information of fractal curves and surfaces. A multiresolution approach for further improvement of the measurement results is introduced. The application results for topographic images are shown.