Statistical design of window-based nonlinear filters for signal and image processing is closely related to pattern recognition. The theory of pattern recognition is concerned with estimating the errors of optimal classifiers and with designing classifiers from sample data whose errors are close to minimal. Of special importance is the Vapnik- Chervonenkis theory, which relates the design cost to the VC dimension of a classification rule. This paper discusses both constraint and design costs for the design of nonlinear filters, and discusses the relation to the theory of pattern recognition. As to the question posed in the title, the paper argues that nonlinear filtering possesses its own integrity because classification rules and constraints depend on signal and image properties, both in theory and the manner in which expert knowledge is applied in design.

Geometric moments have been widely used in many shape recognition and object classification tasks. These monomials are usually computed from binary or gray-level images for the object shape recognition invariant to rotation, translation, and scaling. In this paper, we attempt to calculate the shape related moments from color images, and study their noise immunity and color invariance property for the application areas of face recognition and content based image retrieval. To this end, we describe a computationally efficient method of converting a vector-valued color image into a gray scale for robust moment computation. Geometric moments are calculated from the resultant scalar representation of a color image data, and proven to be robust shape descriptors for the face and flower images. The generated shape invariants appear to have better noise immunity than the Hu moments and exhibit characteristics invariant to hue changes in the object colors. As compared to the Zernike polynomials, the proposed feature set has higher discriminatory power although the Zernike polynomials present superior noise rejection capability. Robust performance, computational efficiency, high noise immunity, and hue invariance property of the new approach are particularly useful for fast image retrieval tasks requiring high query accuracy.

This paper presents a simulation toolbox for counting illuminated 3D bodies. The current model is limited to illuminated balls but can be extended to other illuminated bodies. Upon simulation of a set of balls in space, horizontal slices are taken to provide a stack of 2D gray- scale images. Based on these images, a morphological algorithm estimates the number of balls. Construction of the toolbox has been motivated by the need to count spots in FISH images to test for elevated gene copy numbers. The toolbox facilitates analysis of various algorithm parameters based on the distribution of the 3D bodies. These include the number of slices and various settings for the morphological filters composing the algorithm.

The objective of this work is to identify geological circular forms, impact and volcano craters, using satellite images. The recognition of objects (circular forms) in the scene is the last step in a processing chain, which can be described in four phases: image preprocessing, pattern detection, pattern recognition, and identification of the targets (models). The paper presents the detection of circular forms on images including the south region of the Minas Gerais State in Brazil.

In this work, we introduced an unsupervised segmentation and classification method based on combining two approaches: the wavelet analysis and a neural network indexation technique. The wavelet approach exploits multispectral and multiresolution analysis, providing texture description, which is a very interesting attribute. The resulting extracted features are used to perform the classification of a database of pollen grain images. This classification is performed by a neural network together with a clustering algorithm.

Phonocardiograms (PCGs) have many advantages over traditional auscultation (listening to the heart) because they may be replayed, may be analyzed for spectral and frequency content, and frequencies inaudible to the human ear may be recorded. However, various sources of noise may pollute a PCG including lung sounds, environmental noise and noise generated from contact between the recording device and the skin. Because PCG signals are known to be nonlinear and it is often not possible to determine their noise content, traditional de-noising methods may not be effectively applied. However, other methods including wavelet de-noising, wavelet packet de-noising and averaging can be employed to de-noise the PCG. This study examines and compares these de-noising methods. This study answers such questions as to which de-noising method gives a better SNR, the magnitude of signal information that is lost as a result of the de-noising process, the appropriate uses of the different methods down to such specifics as to which wavelets and decomposition levels give best results in wavelet and wavelet packet de-noising. In general, the wavelet and wavelet packet de-noising performed roughly equally with optimal de-noising occurring at 3-5 levels of decomposition. Averaging also proved a highly useful de- noising technique; however, in some cases averaging is not appropriate. The Hilbert Transform is used to illustrate the results of the de-noising process and to extract instantaneous features including instantaneous amplitude, frequency, and phase.

This work reports and illustrates the application of enhancement techniques to animal nervous system images from a Laser Scanning Confocal Microscope. Images obtained from this equipment are used to help researchers on localizing several organelles and proteins. Different image components of the same tissue sample can be acquired varying the confocal microscope laser beam wavelength. Due to non-ideal acquisition, numerous images contain artifacts, poor distribution of gray levels and unsystematic contrast gradient. Several techniques have been implemented in order to enhance the images, including noise and artifacts reduction, contrast expansion and enhancements on organelles borders, such as emboss and 3D-visualization. A methodology to accurately solve the frequent contrast gradient problem has been implemented. The approach is based on blurring filter, histogram equalization and arithmetic operations. Image coloring is another issue. Each of the acquired components must be merged into one single image with its respective color. The final phase of the work consisted of gathering all implemented techniques to elaborate an application that enclosed facilities to automatically open files from confocal file format (.pic format), apply the developed methodologies to enhance the images, build the multi-component artificial color image and save the results in common formats. This application must deal with large amounts of images easily, providing facilities to batch processing and image indexing and labeling.

We present a real-time compact architecture for translation- invariant windowed nonlinear discrete filters represented in computational mathematical morphology (CMM). The architecture enables filter values to be computed in a deterministic number of operations and thus can be pipelined. Memory requirements are proportional to the size of the filter basis. A filter is implemented by three steps: 1) each component of a vector observation is used as an index into a table of bit vectors; 2) all retrieved bit vectors are ANDed together; and 3) the position of the unique nonzero bit is used as an index to a table of filter values. We motivate and describe CMM and illustrate the architecture through examples. We also formally analyze the representation upon which the architecture rests. A modification of the basic architecture provides for increasing filters.

This paper proposes an FPGA architecture for a videowall image processor. To create a videowall, a set of high resolution displays is arranged in order to present a single large image or smaller multiple images. An image processor is needed to perform the appropriate format conversion corresponding to the required output configuration, and to properly enhance the image contrast. Input signals either in the interlaced or in the progressive format must be managed. The image processor we propose is integrated into two different blocks: the first one implements the deinterlacing task for a YCbCr input video signal, then it converts the progressive YCbCr to the RGB data format and performs the optional contrast enhancement; the other one performs the format conversion of the RGB data format. Motion-adaptive vertico-temporal deinterlacing is used for the luminance signal Y; the color difference signals Cb and Cr instead are processed by means of line average deinterlacing. Image contrast enhancement is achieved via a modified Unsharp Masking technique and involves only the luminance Y. The format conversion algorithm is the bilinear interpolation technique employing the Warped Distance approach and is performed on the RGB data. Two different subblocks have been considered in the system architecture since the interpolation is performed column-wise and successively row- wise.

In the field of video technology for surveillance applications it is often necessary to cope with the phenomenon of illumination variations. In fact, if not compensated, such variations can falsely trigger the change detection module that detects intrusions in video surveillance systems, thus affecting their reliability. Many studies have been made to solve the change detection problem under varying illumination conditions. Most of the published methods, however, rely only on the luminance information. The algorithm proposed in this paper exploits independently the information of each band of the RGB color space of the video sequences, thus producing a change detection algorithm that is more robust to illumination variations. These illumination variations are globally modeled by the so- called Von Kries model (also known as diagonal scaling model). This model is generally used to solve the color constancy problems, where conformance to a reference image illumination has to be guaranteed, like in color image retrieval applications. The use of this model is motivated by its low computational cost and by the interest of studying the relationship between color constancy and change detection. Based on practical experiments which confirm the interest in this method, new and more robust change detection algorithms are expected to be designed. In addition, the paper proposes the use of an iterative scheme whose aim is to improve the results obtained in the change detection module, and which is independent of this module, i.e., it can be used with other change detection schemes. It will be shown that the iteration can improve the quality of the final change mask, thus permitting to obtain a more effective change detection scheme.

A novel scheme for edge/detail-preserving image interpolation is introduced, which is based on fuzzy inference. The proposed method reconstructs sharp edges and peaks accurately. Simulation results show the superior performance of the proposed approach, with respect to other linear interpolation techniques.

The peculiarities of radar images and the problems of their filtering are considered. A two-stage procedure of radar image despeckling based on successive application of the local statistic Lee and sigma filters is proposed. The recommendations concerning filter parameter selection are presented. The performance characteristics of the proposed procedure are evaluated for a set of test artificial images. It is shown that the two-stage despeckling can be successfully applied to both images formed by side look aperture radar (SLAR) or synthetic aperture radar (SAR). An available trade-off of filter basic properties is provided. The examples for real data demonstrating the proposed procedure efficiency and benefits are also given.

This paper addresses the issue of motion-based description of video contents within the framework of the future MPEG-7 standard. Motion is a highly relevant feature related to the spatio-temporal structure of a video and therefore should play a central role within any attempt of content-based video description. We show that parametric motion models provide a powerful tool for characterizing motion of arbitrary (foreground or background) video objects within a unified mathematical framework. The parametric object motion descriptor (POMD) principle consists of describing the motion of objects in video sequences as a 2D geometric transform. The motion models considered in this paper are those currently adopted in the future MPEG-7 standard: constant, simplified scale/rotation, affine, planar perspective and parabolic. The descriptor is defined as the vector of parameters associated with the geometric transform providing thus a very compact representation of the video object motion. Several similarity measures between motion models are considered, including simple L₁ or L₂ distances in the parameter space, and more elaborate similarity measures based upon distance functions directly related to the velocity fields. The experimental results, carried out upon the data sets created by the authors for evaluating the motion descriptors within the MPEG-7 development process, are presented and discussed.

Because of the continuous development of multimedia technologies, virtual worlds and augmented reality, 3D contents become a common feature of the today information systems. Hence, standardizing tools for content-based indexing of visual data is a key issue for computer vision related applications. Within the framework of the future MPEG-7 standard, tools for intelligent content-based access to 3D information, targeting applications such as search and retrieval and browsing of 3D model databases, have been recently considered and evaluated. In this paper, we present the 3D Shape Spectrum Descriptor (3D SSD), recently adopted within the current MPEG-7 Committee Draft (CD). The proposed descriptor aims at providing an intrinsic shape description of a 3D mesh and is defined as the distribution of the shape index over the entire mesh. The shape index is a local geometric attribute of a 3D surface, expressed as the angular coordinate of a polar representation of the principal curvature vector. Experimental results have been carried out upon the MPEG-7 3D model database consisting of about 1300 meshes in VRML 2.0 format. Objective retrieval results, based upon the definition of a ground truth subset, are reported in terms of Bull Eye Percentage (BEP) score.

Two families of transform domain signal restoration (denoising and deblurring) and enhancement methods well suited to processing non-stationary signals are reviewed and comprehensively compared in their different modifications in terms of their signal restoration capability and computational complexity: sliding window transform domain (SWTD) filters and wavelet (WL) based algorithms. SWTD filters work in sliding window in the domain of an orthogonal transform and, in each position of the window, nonlinearly transform window transform coefficients to generate an estimate of the central pixel of the window. As a transform, DCT has been found to be one of the most efficient in most applications. WL methods act globally and apply element-wise nonlinear transformation similar to those used in SWTD methods to the wavelet transform coefficients to generate an estimate of the output signal. The paper provides results of extensive experimental comparisons of image restoration capabilities of the methods and demonstrates that they can naturally be interpreted in a unified way as different implementations of signal sub-band decomposition with uniform (in SWTD filters) or logarithmic (for WL-methods) arrangement of signal sub-bands and element-wise processing decomposed components. As a bridge, a hybrid wavelet/sliding window processing that combines advantages of both methods is described.

We consider the problems of speckle removal in radar images. The proposed filtering techniques make use of local DCT denoising based on adaptive thresholding or homomorphic transformation. Two-stage DT denoising procedure in combination with local statistic filtering are also introduced and analyzed. The effectiveness of the proposed speckle removal algorithms is demonstrated by means of numerical simulations.

This paper describes a new technique for removing blocking artifacts in heavily compressed JPEG images. This technique employs fuzzy wavelets, a form of nonlinear subband decomposition, to produce an estimate of the input JPEG image at a finer spatial resolution. The interpolated image is then subsampled to obtain an output image at the original image spatial resolution with smoothed boundaries between adjacent 8 x 8 pixel JPEG blocks.

In this paper, a new progressive switching type filter is proposed in order to restore images corrupted by salt-pepper impulse noise. The algorithm consists of two main processes: 1) noise detection - an impulse detection algorithm is used before filtering, a noise position image is obtained and 2) noise filtering - disturbed pixels are only filtered by using the noise position image. In this paper, we study the second process (i.e., noise filtering). In the past, the median filter is used for the second process. In this paper, we introduce a weighted average (WA) filter into second process. Using the directional property of input images derives the weights of the WA filter. Therefore, better restoration results are expected. Simulation results demonstrate that the proposed method is superior to the conventional filters which used the median filter in the second process.

Optimal translation-invariant binary windowed filters are determined by probabilities of the form P(Y equals 1|x), where x is a vector (template) of observed values in the observation window and Y is the value in the image to be estimated by the filter. The optimal window filter is defined by y(x) equals 1 if P(Y equals 1|x) (greater than) 0.5 and y(x) equals 0 if P(Y equals 1|x) (less than or equal to) 0.5, which is the binary conditional expectation. The fundamental problem of filter design is to estimate P(Y equals 1|x) from data (image realizations), where x ranges over all possible observation vectors in the window. A Bayesian approach to the problem can be employed by assuming, for each x, a prior distribution for P(Y equals 1|x). These prior distributions result from considering a range of model states by which the observed images are obtained from the ideal. Instead of estimating P(Y equals 1|x) directly from observations by its sample mean relative to an image sample, P(Y equals 1|x) is estimated in the Bayesian fashion, its Bayes estimator being the conditional expectation of P(Y equals 1|x) given the data. Recently the authors have shown that, with accurate prior information, the Bayesian multiresolution filter has significant benefits from multiresolution filter design. Further, since the Bayesian filter is trained over a wider range of degradation levels, it inherits the added benefit of filtering a degraded image at different degradation levels in addition permitting iterative filtering. We discuss the necessary conditions that make a binary filter a good iterative filter and show that the Bayesian multiresolution filter is a natural candidate.

A filter aimed at denoising should strongly smooth uniform regions, while preserving edges. On textured areas, the filter should attain a compromise to achieve some enhancement without destroying useful information. Filtering performances, however, locally depend on the statistical characteristics of the imaged signal, which can be embodied by the concept of local heterogeneity. It is shown that statistically homogeneous regions originate clusters in the scatterplot of standard deviation to mean. Textured regions yield scatterpoints spread apart to a larger extent. Edges produce outliers. Thus, the homogeneity may be locally measured from the joint PDF of estimated local standard deviation to estimated local mean. For each pixel having a measured local mean and a measured standard deviation, a point is detected in the PDF plane: the corresponding density is taken as a measure of homogeneity of that pixel. In this work a hybrid filter, i.e., a set of filters is considered, the denoising capability of each of which depends on the degree of local homogeneity. Images are individually processed by each filter, and the filtered image is obtained by switching among such channels at each pixel position, based on thresholding a heterogeneity feature in order to identify a number of classes, for each of which the noise-free image signal is best estimated by one of the filters. Visual judgments on simulated noisy images agree with this tendency.

A new approach to nonlinear filtering is considered in the paper. The key point of this approach is a combination of spatial and frequency domain filtering. The following filtering technique is proposed for noise reduction. On the first stage a noisy image has to be processed using some powerful nonlinear spatial-domain filter. Since the image will be smoothed after this operation, then its spectra has to be corrected. Taking into account that a major part of a noise is concentrated in the spectra amplitude, also as image smoothing involves a significant spectra amplitude distortion, a method for its correction is proposed. The same technique is also used for solving of the frequency correction (extraction of image details) problem.

A novel filtering technique based on local information and Fuzzy Logic is proposed. The performance of the proposed method is evaluated through different criteria. Preliminary experimental results show that proposed method is effective for different filtering tasks.

The Haar transform is generalized to the case of an arbitrary time and scale splitting. To any binary tree we associate an orthogonal system of Haar-type functions - tree-structured Haar (TSH) functions. Unified fast algorithm for computation of the introduced tree-structured Haar transforms is presented. It requires 2(N - 1) additions and 3N - 2 multiplications, where N is transform order or, equivalently, the number of leaves of the binary tree.

This paper studies pyramidal multiresolution design of aperture and W-operators for grayscale images. The multiresolution approach has been used previously to design binary filters with good results, which motivated us to extend the theory for grayscale. The initial results, theoretical and practical are also motivating.

This paper introduces the family of Finite Lattice Dynamical Systems (FLDS), that includes, for example, the family of finite chain dynamical systems. It also gives a constructive algebraic representation for these systems, based on classical lattice operator morphological representations, and formalizes the problem of FLDS identification from stochastic initial condition, input and ideal output. Under acceptable practical conditions, the identification problem reduces to a set of problems of lattice operator design from observed input-output data, that has been extensively studied in the context of designing morphological image operators. Finally, an application of this technique for the identification of Boolean Networks (i.e., Boolean lattice dynamical systems) from simulated data is presented and analyzed.

This paper considers the problem of image deconvolution, or more precisely, sharpening blurred and noisy images. Using common sharpening methods, which include for example convolution with Laplacian, produces amplified noise. To reduce noise, a median filter is used, resulting in a sequence of sharpening-median cascade filtering, to be applied to an image sequentially. Now, using different sharpening-median filtering sequences produces different kinds of sharpening results. Examples of these differences are given by simulations in one-dimensional cases with noisy edges. Examples of sharpening real photographs are given and comparison with existing techniques is reported.

In addition to suppressing noise, smoothers also cause an unwanted deformation of the image. In this paper we show how such deformation can be compensated. We consider the spectral behavior of noise removal by standard median filters. Observing the power spectrum, we notice that the deformation caused by median filter obeys the general form of the corresponding moving average filter, at least for i.i.d. input. We show that it is possible to cancel this deformation by using an approximation of the linear inverse filter, which can be easily implemented for images as well as 1D data.

We consider a median pyramidal transform for denoising applications. Traditional techniques of pyramidal denoising are similar to those in wavelet-based methods. In order to remove noise, they use the thresholding of transform coefficients. We propose to model the structure of the transform coefficients as a Markov random field. The goal of modeling transform coefficients is to retain significant coefficients on each scale and to discard the rest. Estimation of the transform coefficient structure is obtained via a Markov chain sampler. The advantage of our method is that we are able to utilize the interactions between transform coefficients, both within each scale and among the scales, which leads to denoising improvement as demonstrated by numerical simulations.

A new algorithm for the interpolation of temporal intermediate images using polyphase weighted median filters is proposed in this paper. To achieve a good interpolation quality not only in still but also in moving areas of the image, vector based interpolation techniques have to be used. However, motion estimation on natural image scenes always suffers from errors in the estimated motion vector field. Therefore it is of great importance that the interpolation algorithm possesses a sufficient robustness against vector errors. Depending on the input and output frame repetition rate, different cyclically repeated interpolation phases can be distinguished. The new interpolation algorithm uses dedicated weighted median filters for each interpolation phase (polyphase weighted median filters) which are (due to their shift property) able to achieve a correct positioning of moving edges in the interpolated image, even if the estimated vector differs from the true motion vector up to a certain degree. A new design method for these dedicated error tolerant weighted median filters is presented in the paper. Other aspects like e.g. the preservation of fine image details can also be regarded in the design process. The results of the new algorithm are compared to other existing interpolation algorithms.

This paper discusses an improved nonlinear filtering approach based on anisotropic diffusion technique. This modified anisotropic diffusion method smooths along curve directions, i.e. the directions of level sets. The upwind scheme for level set is used to solve the diffusion equation. Compared with the conventional anisotropic diffusion, which depends only on the local gradient of intensities of the processed image, this modified scheme overcomes the defect of indefinite edge enhancement associated with Perona-Malik model while depressing noises in a better performance. Moreover, a multi-scale diffusion technique is applied to limit blurring by the presence of edges as measured at the scale of interest, so that accurate information about boundaries of objects could be preserved and small details that fall below the scale of interest be removed. Then an extension into vector-valued diffusion is also presented in this paper, which is capable of smoothing small objects while maintaining boundaries information in vector-valued images. Experiments on gray-scale and color images demonstrate the efficacy of this method in image smoothing as well as image enhancement.

In this paper we study the number of Euclidean distance transform values. We show that there is (from the number- theoretic point of view) a high redundancy in the number of different Euclidean distance values. Our number-theoretic approach allows us to give an approximation of the number of algebraic independent transform values. This can be used to optimize the future hardware implementation.