Showing papers in "IEEE Transactions on Image Processing in 1995"

Texture classification and segmentation using wavelet frames

Abstract: This paper describes a new approach to the characterization of texture properties at multiple scales using the wavelet transform. The analysis uses an overcomplete wavelet decomposition, which yields a description that is translation invariant. It is shown that this representation constitutes a tight frame of l/sub 2/ and that it has a fast iterative algorithm. A texture is characterized by a set of channel variances estimated at the output of the corresponding filter bank. Classification experiments with l/sub 2/ Brodatz textures indicate that the discrete wavelet frame (DWF) approach is superior to a standard (critically sampled) wavelet transform feature extraction. These results also suggest that this approach should perform better than most traditional single resolution techniques (co-occurrences, local linear transform, and the like). A detailed comparison of the classification performance of various orthogonal and biorthogonal wavelet transforms is also provided. Finally, the DWF feature extraction technique is incorporated into a simple multicomponent texture segmentation algorithm, and some illustrative examples are presented. >

Adaptive median filters: new algorithms and results

Abstract: Based on two types of image models corrupted by impulse noise, we propose two new algorithms for adaptive median filters. They have variable window size for removal of impulses while preserving sharpness. The first one, called the ranked-order based adaptive median filter (RAMF), is based on a test for the presence of impulses in the center pixel itself followed by a test for the presence of residual impulses in the median filter output. The second one, called the impulse size based adaptive median filter (SAMF), is based on the detection of the size of the impulse noise. It is shown that the RAMF is superior to the nonlinear mean L/sub p/ filter in removing positive and negative impulses while simultaneously preserving sharpness; the SAMF is superior to Lin's (1988) adaptive scheme because it is simpler with better performance in removing the high density impulsive noise as well as nonimpulsive noise and in preserving the fine details. Simulations on standard images confirm that these algorithms are superior to standard median filters. >

Nonlinear image recovery with half-quadratic regularization

Abstract: One popular method for the recovery of an ideal intensity image from corrupted or indirect measurements is regularization: minimize an objective function that enforces a roughness penalty in addition to coherence with the data. Linear estimates are relatively easy to compute but generally introduce systematic errors; for example, they are incapable of recovering discontinuities and other important image attributes. In contrast, nonlinear estimates are more accurate but are often far less accessible. This is particularly true when the objective function is nonconvex, and the distribution of each data component depends on many image components through a linear operator with broad support. Our approach is based on an auxiliary array and an extended objective function in which the original variables appear quadratically and the auxiliary variables are decoupled. Minimizing over the auxiliary array alone yields the original function so that the original image estimate can be obtained by joint minimization. This can be done efficiently by Monte Carlo methods, for example by FFT-based annealing using a Markov chain that alternates between (global) transitions from one array to the other. Experiments are reported in optical astronomy, with space telescope data, and computed tomography. >

A new criterion for automatic multilevel thresholding

Abstract: A new criterion for multilevel thresholding is proposed. The criterion is based on the consideration of two factors. The first one is the discrepancy between the thresholded and original images and the second one is the number of bits required to represent the thresholded image. Based on a new maximum correlation criterion for bilevel thresholding, the discrepancy is defined and then a cost function that takes both factors into account is proposed for multilevel thresholding. By minimizing the cost function, the classification number that the gray-levels should be classified and the threshold values can be determined automatically. In addition, the cost function is proven to possess a unique minimum under very mild conditions. Computational analyses indicate that the number of required mathematical operations in the implementation of our algorithm is much less than that of maximum entropy criterion. Finally, simulation results are included to demonstrate their effectiveness. >

Wavelet filter evaluation for image compression

Abstract: Choice of filter bank in wavelet compression is a critical issue that affects image quality as well as system design. Although regularity is sometimes used in filter evaluation, its success at predicting compression performance is only partial. A more reliable evaluation can be obtained by considering an L-level synthesis/analysis system as a single-input, single-output, linear shift-variant system with a response that varies according to the input location module (2/sup L/,2/sup L/). By characterizing a filter bank according to its impulse response and step response in addition to regularity, we obtain reliable and relevant (for image coding) filter evaluation metrics. Using this approach, we have evaluated all possible reasonably short (less than 36 taps in the synthesis/analysis pair) minimum-order biorthogonal wavelet filter banks. Of this group of over 4300 candidate filter banks, we have selected and present here the filters best suited to image compression. While some of these filters have been published previously, others are new and have properties that make them attractive in system design. >

Successive elimination algorithm for motion estimation

Abstract: The correspondence presents a fast exhaustive search algorithm for motion estimation. The basic idea is to obtain the best estimate of the motion vectors by successively eliminating the search positions in the search window and thus decreasing the number of matching evaluations that require very intensive computations. Simulation results demonstrate that although the performance of the proposed algorithm is the same as that using the exhaustive search, the computation time has been reduced significantly. >

Flat zones filtering, connected operators, and filters by reconstruction

Abstract: This correspondence deals with the notion of connected operators. Starting from the definition for operator acting on sets, it is shown how to extend it to operators acting on function. Typically, a connected operator acting on a function is a transformation that enlarges the partition of the space created by the flat zones of the functions. It is shown that from any connected operator acting on sets, one can construct a connected operator for functions (however, it is not the unique way of generating connected operators for functions). Moreover, the concept of pyramid is introduced in a formal way. It is shown that, if a pyramid is based on connected operators, the flat zones of the functions increase with the level of the pyramid. In other words, the flat zones are nested. Filters by reconstruction are defined and their main properties are presented. Finally, some examples of application of connected operators and use of flat zones are described. >

A contour-based approach to multisensor image registration

Abstract: Image registration is concerned with the establishment of correspondence between images of the same scene. One challenging problem in this area is the registration of multispectral/multisensor images. In general, such images have different gray level characteristics, and simple techniques such as those based on area correlations cannot be applied directly. On the other hand, contours representing region boundaries are preserved in most cases. The authors present two contour-based methods which use region boundaries and other strong edges as matching primitives. The first contour matching algorithm is based on the chain-code correlation and other shape similarity criteria such as invariant moments. Closed contours and the salient segments along the open contours are matched separately. This method works well for image pairs in which the contour information is well preserved, such as the optical images from Landsat and Spot satellites. For the registration of the optical images with synthetic aperture radar (SAR) images, the authors propose an elastic contour matching scheme based on the active contour model. Using the contours from the optical image as the initial condition, accurate contour locations in the SAR image are obtained by applying the active contour model. Both contour matching methods are automatic and computationally quite efficient. Experimental results with various kinds of image data have verified the robustness of the algorithms, which have outperformed manual registration in terms of root mean square error at the control points. >

Subpixel edge localization and the interpolation of still images

Abstract: In this paper, we present a nonlinear interpolation scheme for still image resolution enhancement. The algorithm is based on a source model emphasizing the visual integrity of detected edges and incorporates a novel edge fitting operator that has been developed for this application. A small neighborhood about each pixel in the low-resolution image is first mapped to a best-fit continuous space step edge. The bilevel approximation serves as a local template on which the higher resolution sampling grid can then be superimposed (where disputed values in regions of local window overlap are averaged to smooth errors). The result is an image of increased resolution with noticeably sharper edges and, in all tried cases, lower mean-squared reconstruction error than that produced by linear techniques. >

Optimal Gabor filters for texture segmentation

Abstract: Texture segmentation involves subdividing an image into differently textured regions. Many texture segmentation schemes are based on a filter-bank model, where the filters, called Gabor filters, are derived from Gabor elementary functions. The goal is to transform texture differences into detectable filter-output discontinuities at texture boundaries. By locating these discontinuities, one can segment the image into differently textured regions. Distinct discontinuities occur, however, only if the Gabor filter parameters are suitably chosen. Some previous analysis has shown how to design filters for discriminating simple textures. Designing filters for more general natural textures, though, has largely been done ad hoc. We have devised a more rigorously based method for designing Gabor filters. It assumes that an image contains two different textures and that prototype samples of the textures are given a priori. We argue that Gabor filter outputs can be modeled as Rician random variables (often approximated well as Gaussian rv's) and develop a decision-theoretic algorithm for selecting optimal filter parameters. To improve segmentations for difficult texture pairs, we also propose a multiple-filter segmentation scheme, motivated by the Rician model. Experimental results indicate that our method is superior to previous methods in providing useful Gabor filters for a wide range of texture pairs. >

Concealment of damaged block transform coded images using projections onto convex sets

Abstract: An algorithm for lost signal restoration in block-based still image and video sequence coding is presented. Problems arising from imperfect transmission of block-coded images result in lost blocks. The resulting image is flawed by the absence of square pixel regions that are notably perceived by human vision, even in real-time video sequences. Error concealment is aimed at masking the effect of missing blocks by use of temporal or spatial interpolation to create a subjectively acceptable approximation to the true error-free image. This paper presents a spatial interpolation algorithm that addresses concealment of lost image blocks using only intra-frame information. It attempts to utilize spatially correlated edge information from a large local neighborhood of surrounding pixels to restore missing blocks. The algorithm is a Gerchberg (1974) type spatial domain/spectral domain constraint-satisfying iterative process, and may be viewed as an alternating projections onto convex sets method. >

Projection-based spatially adaptive reconstruction of block-transform compressed images

Abstract: At the present time, block-transform coding is probably the most popular approach for image compression. For this approach, the compressed images are decoded using only the transmitted transform data. We formulate image decoding as an image recovery problem. According to this approach, the decoded image is reconstructed using not only the transmitted data but, in addition, the prior knowledge that images before compression do not display between-block discontinuities. A spatially adaptive image recovery algorithm is proposed based on the theory of projections onto convex sets. Apart from the data constraint set, this algorithm uses another new constraint set that enforces between-block smoothness. The novelty of this set is that it captures both the local statistical properties of the image and the human perceptual characteristics. A simplified spatially adaptive recovery algorithm is also proposed, and the analysis of its computational complexity is presented. Numerical experiments are shown that demonstrate that the proposed algorithms work better than both the JPEG deblocking recommendation and our previous projection-based image decoding approach. >

Globally convergent algorithms for maximum a posteriori transmission tomography

Abstract: This paper reviews and compares three maximum likelihood algorithms for transmission tomography. One of these algorithms is the EM algorithm, one is based on a convexity argument devised by De Pierro (see IEEE Trans. Med. Imaging, vol.12, p.328-333, 1993) in the context of emission tomography, and one is an ad hoc gradient algorithm. The algorithms enjoy desirable local and global convergence properties and combine gracefully with Bayesian smoothing priors. Preliminary numerical testing of the algorithms on simulated data suggest that the convex algorithm and the ad hoc gradient algorithm are computationally superior to the EM algorithm. This superiority stems from the larger number of exponentiations required by the EM algorithm. The convex and gradient algorithms are well adapted to parallel computing. >

A distortion measure for blocking artifacts in images based on human visual sensitivity

Abstract: A visual model that gives a distortion measure for blocking artifacts in images is presented. Given the original and reproduced image as inputs, the model output is a numerical value that quantifies the visibility of blocking error in the reproduced image. The model is derived based on the human visual sensitivity to horizontal and vertical edge artifacts that result from blocking. Psychovisual experiments have been carried out to measure the visual sensitivity to these artifacts. In the experiments, typical edge artifacts are shown to subjects and the sensitivity to them is measured with the variation of background luminance, background activity, edge length, and edge amplitude. Synthetic test patterns are used as background images in the experiments. The sensitivity measures thus obtained are used to estimate the model parameters. The final model is tested on real images, and the results show that the error visibility predicted by the model correlates well with the subjective ranking. >

Penalized maximum-likelihood image reconstruction using space-alternating generalized EM algorithms

Abstract: Most expectation-maximization (EM) type algorithms for penalized maximum-likelihood image reconstruction converge slowly, particularly when one incorporates additive background effects such as scatter, random coincidences, dark current, or cosmic radiation. In addition, regularizing smoothness penalties (or priors) introduce parameter coupling, rendering intractable the M-steps of most EM-type algorithms. This paper presents space-alternating generalized EM (SAGE) algorithms for image reconstruction, which update the parameters sequentially using a sequence of small "hidden" data spaces, rather than simultaneously using one large complete-data space. The sequential update decouples the M-step, so the maximization can typically be performed analytically. We introduce new hidden-data spaces that are less informative than the conventional complete-data space for Poisson data and that yield significant improvements in convergence rate. This acceleration is due to statistical considerations, not numerical overrelaxation methods, so monotonic increases in the objective function are guaranteed. We provide a general global convergence proof for SAGE methods with nonnegativity constraints. >

Three-dimensional subband coding of video

Abstract: We describe and show the results of video coding based on a three-dimensional (3-D) spatio-temporal subband decomposition. The results include a 1-Mbps coder based on a new adaptive differential pulse code modulation scheme (ADPCM) and adaptive bit allocation. This rate is useful for video storage on CD-ROM. Coding results are also shown for a 384-kbps rate that are based on ADPCM for the lowest frequency band and a new form of vector quantization (geometric vector quantization (GVQ)) for the data in the higher frequency bands. GVQ takes advantage of the inherent structure and sparseness of the data in the higher bands. Results are also shown for a 128-kbps coder that is based on an unbalanced tree-structured vector quantizer (UTSVQ) for the lowest frequency band and GVQ for the higher frequency bands. The results are competitive with traditional video coding techniques and provide the motivation for investigating the 3-D subband framework for different coding schemes and various applications. >

Interpolation of missing data in image sequences

Abstract: This paper presents a number of model based interpolation schemes tailored to the problem of interpolating missing regions in image sequences. These missing regions may be of arbitrary size and of random, but known, location. This problem occurs regularly with archived film material. The film is abraded or obscured in patches, giving rise to bright and dark flashes, known as "dirt and sparkle" in the motion picture industry. Both 3-D autoregressive models and 3-D Markov random fields are considered in the formulation of the different reconstruction processes. The models act along motion directions estimated using a multiresolution block matching scheme. It is possible to address this sort of impulsive noise suppression problem with median filters, and comparisons with earlier work using multilevel median filters are performed. These comparisons demonstrate the higher reconstruction fidelity of the new interpolators. >

Convolution-based interpolation for fast, high-quality rotation of images

Abstract: This paper focuses on the design of fast algorithms for rotating images and preserving high quality. The basis for the approach is a decomposition of a rotation into a sequence of one-dimensional translations. As the accuracy of these operations is critical, we introduce a general theoretical framework that addresses their design and performance. We also investigate the issue of optimality and present an improved least-square formulation of the problem. This approach leads to a separable three-pass implementation of a rotation using one-dimensional convolutions only. We provide explicit filter formulas for several continuous signal models including spline and bandlimited representations. Finally, we present rotation experiments and compare the currently standard techniques with the various versions of our algorithm. Our results indicate that the present algorithm in its higher-order versions outperforms all standard high-accuracy methods of which we are aware, both in terms of speed and quality. Its computational complexity increases linearly with the order of accuracy. The best-quality results are obtained with the sine-based algorithm, which can be implemented using simple one-dimensional FFTs. >

General choice of the regularization functional in regularized image restoration

Abstract: The determination of the regularization parameter is an important issue in regularized image restoration, since it controls the trade-off between fidelity to the data and smoothness of the solution. A number of approaches have been developed in determining this parameter. In this paper, a new paradigm is adopted, according to which the required prior information is extracted from the available data at the previous iteration step, i.e., the partially restored image at each step. We propose the use of a regularization functional instead of a constant regularization parameter. The properties such a regularization functional should satisfy are investigated, and two specific forms of it are proposed. An iterative algorithm is proposed for obtaining a restored image. The regularization functional is defined in terms of the restored image at each iteration step, therefore allowing for the simultaneous determination of its value and the restoration of the degraded image. Both proposed iteration adaptive regularization functionals are shown to result in a smoothing functional with a global minimum, so that its iterative optimization does not depend on the initial conditions. The convergence of the algorithm is established and experimental results are shown. >

Enlargement or reduction of digital images with minimum loss of information

Abstract: The purpose of this paper is to derive optimal spline algorithms for the enlargement or reduction of digital images by arbitrary (noninteger) scaling factors. In our formulation, the original and rescaled signals are each represented by an interpolating polynomial spline of degree n with step size one and /spl Delta/, respectively. The change of scale is achieved by determining the spline with step size /spl Delta/ that provides the closest approximation of the original signal in the L/sub 2/-norm. We show that this approximation can be computed in three steps: (i) a digital prefilter that provides the B-spline coefficients of the input signal, (ii) a resampling using an expansion formula with a modified sampling kernel that depends explicitly on /spl Delta/, and (iii) a digital postfilter that maps the result back into the signal domain. We provide explicit formulas for n=0, 1, and 3 and propose solutions for the efficient implementation of these algorithms. We consider image processing examples and show that the present method compares favorably with standard interpolation techniques. Finally, we discuss some properties of this approach and its connection with the classical technique of bandlimiting a signal, which provides the asymptotic limit of our algorithm as the order of the spline tends to infinity. >

A new algorithm for image noise reduction using mathematical morphology

Abstract: Morphological openings and closings are useful for the smoothing of gray-scale images. However, their use for image noise reduction is limited by their tendency to remove important, thin features from an image along with the noise. The paper presents a description and analysis of a new morphological image cleaning algorithm (MIC) that preserves thin features while removing noise. MIC is useful for gray-scale images corrupted by dense, low-amplitude, random, or patterned noise. Such noise is typical of scanned or still-video images. MIC differs from previous morphological noise filters in that it manipulates residual images-the differences between the original image and morphologically smoothed versions. It calculates residuals on a number of different scales via a morphological size distribution. It discards regions in the various residuals that it judges to contain noise. MIC creates a cleaned image by recombining the processed residual images with a smoothed version. The paper describes the MIC algorithm in detail, discusses the effects of parametric variations, presents the results of a noise analysis and shows a number of examples of its use, including the removal of scanner noise. It also demonstrates that MIC significantly improves the JPEG compression of a gray-scale image. >

Unsupervised texture segmentation of images using tuned matched Gabor filters

Abstract: Recent studies have confirmed that the multichannel Gabor decomposition represents an excellent tool for image segmentation and boundary detection. Unfortunately, this approach when used for unsupervised image analysis tasks imposes excessive storage requirements due to the nonorthogonality of the basis functions and is computationally highly demanding. In this correspondence, we propose a novel method for efficient image analysis that uses tuned matched Gabor filters. The algorithmic determination of the parameters of the Gabor filters is based on the analysis of spectral feature contrasts obtained from iterative computation of pyramidal Gabor transforms with progressive dyadic decrease of elementary cell sizes. The method requires no a priori knowledge of the analyzed image so that the analysis is unsupervised. Computer simulations applied to different classes of textures illustrate the matching property of the tuned Gabor filters derived using our determination algorithm. Also, their capability to extract significant image information and thus enable an easy and efficient low-level image analysis will be demonstrated. >

Detection of missing data in image sequences

Abstract: Bright and dark flashes are typical artifacts in degraded motion picture material. The distortion is referred to as "dirt and sparkle" in the motion picture industry. This is caused either by dirt becoming attached to the frames of the film, or by the film material being abraded. The visual result is random patches of the frames having grey level values totally unrelated to the initial information at those sites. To restore the film without causing distortion to areas of the frames that are not affected, the locations of the blotches must be identified. Heuristic and model-based methods for the detection of these missing data regions are presented in this paper, and their action on simulated and real sequences is compared. >

On the modeling of DCT and subband image data for compression

Abstract: Image subband and discrete cosine transform coefficients are modeled for efficient quantization and noiseless coding. Quantizers and codes are selected based on Laplacian, fixed generalized Gaussian, and adaptive generalized Gaussian models. The quantizers and codes based on the adaptive generalized Gaussian models are always superior in mean-squared error distortion performance but, generally, by no more than 0.08 bit/pixel, compared with the much simpler Laplacian model-based quantizers and noiseless codes. This provides strong motivation for the selection of pyramid codes for transform and subband image coding. >

Phase unwrapping of MR phase images using Poisson equation

Abstract: The authors have developed a technique based on a solution of the Poisson equation to unwrap the phase in magnetic resonance (MR) phase images. The method is based on the assumption that the magnitude of the inter-pixel phase change is less than /spl pi/ per pixel. Therefore, the authors obtain an estimate of the phase gradient by "wrapping" the gradient of the original phase image. The problem is then to obtain the absolute phase given the estimate of the phase gradient. The least-squares (LS) solution to this problem is shown to be a solution of the Poisson equation allowing the use of fast Poisson solvers. The absolute phase is then obtained by mapping the LS phase to the nearest multiple of 2 K from the measured phase. The proposed technique is evaluated using MR phase images and is proven to be robust in the presence of noise. An application of the proposed method to the 3-point Dixon technique for water and fat separation is demonstrated. >

Invariant matching and identification of curves using B-splines curve representation

Abstract: There have been many techniques for curve shape representation and analysis, ranging from Fourier descriptors, to moments, to implicit polynomials, to differential geometry features, to time series models, to B-splines, etc. The B-splines stand as one of the most efficient curve (surface) representations and possess very attractive properties such as spatial uniqueness, boundedness and continuity, local shape controllability, and invariance to affine transformations. These properties made them very attractive for curve representation, and consequently, they have been extensively used in computer-aided design and computer graphics. Very little work, however, has been devoted to them for recognition purposes. One possible reason might be due to the fact that the B-spline curve is not uniquely described by a single set of parameters (control points), which made the curve matching (recognition) process difficult when comparing the respective parameters of the curves to be matched. This paper is an attempt to find matching solutions despite this limitation, and as such, it deals the problem of using B-splines for shape recognition and identification from curves, with an emphasis on the following applications: affine invariant matching and classification of 2-D curves with applications in identification of aircraft types based on image silhouettes and writer-identification based on handwritten text

Transform coded image reconstruction exploiting interblock correlation

Abstract: Transmission of still images and video over lossy packet networks presents a reconstruction problem at the decoder. Specifically, in the case of block-based transform coded images, loss of one or more packets due to network congestion or transmission errors can result in errant or entirely lost blocks in the decoded image. This article proposes a computationally efficient technique for reconstruction of lost transform coefficients at the decoder that takes advantage of the correlation between transformed blocks of the image. Lost coefficients are linearly interpolated from the same coefficients in adjacent blocks subject to a squared edge error criterion, and the resulting reconstructed coefficients minimize blocking artifacts in the image while providing visually pleasing reconstructions. The required computational expense at the decoder per reconstructed block is less than 1.2 times a non-recursive DCT, and as such this technique is useful for low power, low complexity applications that require good visual performance. >

A perceptually motivated three-component image model-Part I: description of the model

Abstract: Some psychovisual properties of the human visual system are discussed and interpreted in a mathematical framework. The formation of perception is described by appropriate minimization problems and the edge information is found to be of primary importance in visual perception. Having introduced the concept of edge strength, it is demonstrated that strong edges are of higher perceptual importance than weaker edges (textures). We have also found that smooth areas of an image influence our perception together with the edge information, and that this influence can be mathematically described via a minimization problem. Based on this study, we have proposed to decompose the image into three components: (i) primary, (ii) smooth, and (iii) texture, which contain, respectively, the strong edges, the background, and the textures. An algorithm is developed to generate the three-component image model, and an example is provided in which the resulting three components demonstrate the specific properties as expected. Finally, it is shown that the primary component provides a superior representation of the strong edge information as compared with the popular Laplacian-Gaussian operator edge extraction scheme. >

Focused image recovery from two defocused images recorded with different camera settings

Abstract: Two new methods are presented for recovering the focused image of an object from only two blurred images recorded with different camera parameter settings. The camera parameters include lens position, focal length, and aperture diameter. First a blur parameter 0 is estimated using one of our two recently proposed depth-from-defocus methods. Then one of the two blurred images is deconvolved to recover the focused image. The first method is based on a recently proposed spatial domain convolutioddeconvolution transform. This method requires only the knowledge of ~7 of the camera’s point spread function (PSF). It does not require information about the actual form of the camera’s PSF. The second method, in contrast to the first, requires full knowledge of the form of the PSF. As part of the second method, we present a calibration procedure for estimating the camera’s PSF for different values of the blur parameter 0. In the second method, the focused image is obtained through deconvolution in the Fourier domain using the Wiener filter. For both methods, results of experiments on actual defocused images recorded by a CCD camera are given. The first method requires much less computation than the second method. The first method gives satisfactory results for up to medium levels of blur and the second method gives good results for up to relatively high levels of blur.

Information loss recovery for block-based image coding techniques-a fuzzy logic approach

Abstract: A new technique to recover the information loss in a block-based image coding system is developed in this paper. The proposed scheme is based on fuzzy logic reasoning and can be divided into three main steps: (1) hierarchical compass interpolation/extrapolation (HCIE) in the spatial domain for initial recovery of lost blocks that mainly contain low-frequency information such as smooth background (2) coarse spectra interpretation by fuzzy logic reasoning for recovery of lost blocks that contain high-frequency information such as complex textures and fine features (3) sliding window iteration (SWI), which is performed in both spatial and spectral domains to efficiently integrate the results obtained in steps (1) and (2) such that the optimal result can be achieved in terms of surface continuity on block boundaries and a set of fuzzy inference rules. The proposed method, which is suitable for recovering both isolated and contiguous block losses, provides a new approach for error concealment of block-based image coding systems such as the JPEG coding standard and vector quantization-based coding algorithms. The principle of the proposed scheme can also be applied to block-based video compression schemes such as the H.261, MPEG, and HDTV standards. Simulation results are presented to illustrate the effectiveness of the proposed method. >