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Image Processing, IEEE Transactions on

Issue 10 • Date Oct 2000

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Displaying Results 1 - 16 of 16
  • Parallelizable Bayesian tomography algorithms with rapid, guaranteed convergence

    Page(s): 1745 - 1759
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    Bayesian tomographic reconstruction algorithms generally require the efficient optimization of a functional of many variables. In this setting, as well as in many other optimization tasks, functional substitution (FS) has been widely applied to simplify each step of the iterative process. The function to be minimized is replaced locally by an approximation having a more easily manipulated form, e.g., quadratic, but which maintains sufficient similarity to descend the true functional while computing only the substitute. We provide two new applications of FS methods in iterative coordinate descent for Bayesian tomography. The first is a modification of our coordinate descent algorithm with one-dimensional (1-D) Newton-Raphson approximations to an alternative quadratic which allows convergence to be proven easily. In simulations, we find essentially no difference in convergence speed between the two techniques. We also present a new algorithm which exploits the FS method to allow parallel updates of arbitrary sets of pixels using computations similar to iterative coordinate descent. The theoretical potential speed up of parallel implementations is nearly linear with the number of processors if communication costs are neglected View full abstract»

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  • O(N2log2N) filtered backprojection reconstruction algorithm for tomography

    Page(s): 1760 - 1773
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    We present a new fast reconstruction algorithm for parallel beam tomography. The new algorithm is an accelerated version of the standard filtered backprojection (FBP) reconstruction, and uses a hierarchical decomposition of the backprojection operation to reduce the computational cost from O(N3) to O(N2log2 N). We discuss the choice of the various parameters that affect the behavior of the algorithm, and present numerical studies that demonstrate the cost versus distortion tradeoff. Comparisons with Fourier reconstruction algorithms and a multilevel inversion algorithm by Brandt et al., both of which also have O(N2log2N) cost, suggest that the proposed hierarchical scheme has a superior cost versus distortion performance. It offers RMS reconstruction errors comparable to the FBP with considerable speedup. For an example with a 512×512-pixel image and 1024 views, the speedup achieved with a particular implementation is over 40 fold, with reconstructions visually indistinguishable from the FBP View full abstract»

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  • Bayesian winner-take-all reconstruction of intermediate views from stereoscopic images

    Page(s): 1710 - 1722
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    This paper presents a new algorithm for the reconstruction of intermediate views from a pair of still stereoscopic images. The algorithm is designed to address the issue of blur caused by linear filtering often employed in such reconstruction. The proposed algorithm is block-based and to reconstruct the intermediate views employs nonlinear disparity-compensated filtering by means of a winner-take-all strategy. The reconstructed image is modeled as a tiling by fixed-size blocks coming from various positions (disparity compensation) of either the left or right images, while the tiling map itself is modeled by a binary decision field. In addition to that, an observation model relating the left and right images via a disparity field, and a disparity field model are used. All models are probabilistic and are combined into a maximum a posteriori probability criterion. The intermediate intensities, disparities and the binary decision field are estimated jointly using the expectation-maximization algorithm. The new approach is compared experimentally on complex natural images with a reference block-based algorithm employing linear filtering. Although the improvements are localized and often subtle, they demonstrate that a high-quality intermediate view reconstruction for complex scenes is feasible View full abstract»

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  • Modeling and efficient optimization for object-based scalability and some related problems

    Page(s): 1677 - 1692
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (312 KB)  

    MPEG-4 is the first visual coding standard that allows coding of scenes as a collection of individual audio-visual objects. We present mathematical formulations for modeling object-based scalability and some functionalities that it brings with it. Our goal is to study algorithms that aid in semi-automating the authoring and subsequent selective addition/dropping of objects from a scene to provide content scalability. We start with a simplistic model for object-based scalability using the “knapsack problem”-a problem for which the optimal object set can be found using known schemes such as dynamic programming, the branch and bound method and approximation algorithms. The above formulation is then generalized to model authoring or multiplexing of scalable objects (e.g., objects encoded at various target bit-rates) using the “multiple choice knapsack problem.” We relate this model to several problems that arise in video coding, the most prominent of these being the bit allocation problem. Unlike previous approaches to solve the operational bit allocation problem using Lagrangean relaxation, we discuss an algorithm that solves linear programming (LP) relaxation of this problem. We show that for this problem the duality gap for Lagrange and LP relaxations is exactly the same. The LP relaxation is solved using strong duality with dual descent-a procedure that can be completed in “linear” time. We show that there can be at most two fractional variables in the optimal primal solution and therefore this relaxation can be justified for many practical applications. This work reduces problem complexity, guarantees similar performance, is slightly more generic, and provides an alternate LP-duality based proof for earlier work by Shoham and Gersho (1988). In addition, we show how additional constraints may be added to impose inter-dependencies among objects in a presentation and discuss how object aggregation can be exploited in reducing problem complexity. The marginal analysis approach of Fox (1966) is suggested as a method of re-allocation with incremental inputs. It helps in efficiently re-optimizing the allocation when a system has user interactivity, appearing or disappearing objects, time driven events, etc. Finally, we suggest that approximation algorithms for the multiple choice knapsack problem, which can be used to quantify complexity vs. quality tradeoff at the encoder in a tunable and universal way View full abstract»

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  • A mathematical analysis of the DCT coefficient distributions for images

    Page(s): 1661 - 1666
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    Over the past two decades, there have been various studies on the distributions of the DCT coefficients for images. However, they have concentrated only on fitting the empirical data from some standard pictures with a variety of well-known statistical distributions, and then comparing their goodness of fit. The Laplacian distribution is the dominant choice balancing simplicity of the model and fidelity to the empirical data. Yet, to the best of our knowledge, there has been no mathematical justification as to what gives rise to this distribution. We offer a rigorous mathematical analysis using a doubly stochastic model of the images, which not only provides the theoretical explanations necessary, but also leads to insights about various other observations from the literature. This model also allows us to investigate how certain changes in the image statistics could affect the DCT coefficient distributions View full abstract»

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  • The EM/MPM algorithm for segmentation of textured images: analysis and further experimental results

    Page(s): 1731 - 1744
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    In this paper we present new results relative to the “expectation-maximization/maximization of the posterior marginals” (EM/MPM) algorithm for simultaneous parameter estimation and segmentation of textured images. The EM/MPM algorithm uses a Markov random field model for the pixel class labels and alternately approximates the MPM estimate of the pixel class labels and estimates parameters of the observed image model. The goal of the EM/MPM algorithm is to minimize the expected value of the number of misclassified pixels. We present new theoretical results in this paper which show that the algorithm can be expected to achieve this goal, to the extent that the EM estimates of the model parameters are close to the true values of the model parameters. We also present new experimental results demonstrating the performance of the EM/MPM algorithm View full abstract»

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  • Hierarchical Bayesian image restoration from partially known blurs

    Page(s): 1784 - 1797
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (476 KB)  

    We examine the restoration problem when the point-spread function (PSF) of the degradation system is partially known. For this problem, the PSF is assumed to be the sum of a known deterministic and an unknown random component. This problem has been examined before; however, in most previous works the problem of estimating the parameters that define the restoration filters was not addressed. In this paper, two iterative algorithms that simultaneously restore the image and estimate the parameters of the restoration filter are proposed using evidence analysis (EA) within the hierarchical Bayesian framework. We show that the restoration step of the first of these algorithms is in effect almost identical to the regularized constrained total least-squares (RCTLS) filter, while the restoration step of the second is identical to the linear minimum mean square-error (LMMSE) filter for this problem. Therefore, in this paper we provide a solution to the parameter estimation problem of the RCTLS filter. We further provide an alternative approach to the expectation-maximization (EM) framework to derive a parameter estimation algorithm for the LMMSE filter. These iterative algorithms are derived in the discrete Fourier transform (DFT) domain; therefore, they are computationally efficient even for large images. Numerical experiments are presented that test and compare the proposed algorithms View full abstract»

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  • Generalized interframe vertex-based shape encoding scheme for video sequences

    Page(s): 1667 - 1676
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (348 KB)  

    The efficiency of shape coding is an important problem concerning content-based image manipulations and object-based coding of the video sequences. In order to encode the shape information of an object, the boundary is approximated by a polygon which can be encoded with the smallest number of bits for maximum allowable distortion. The conventional boundary coding schemes, however, does not successfully remove the temporal redundancy of the video sequences. This paper proposes a new boundary encoding scheme by which the temporal redundancy between two successive frames is efficiently removed, resulting in lower bit-rate than the conventional algorithms. The interframe vertex selection problem is solved by finding the path with the minimum cost in the directed acyclic graph (DAG) and its fast version using a simplified graph is introduced to reduce the computational load. The vertices were selected from both the current frame to be encoded and the previous frame already encoded, and thus, the temporal redundancy was effectively removed View full abstract»

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  • Adaptive polyphase subband decomposition structures for image compression

    Page(s): 1649 - 1660
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (744 KB)  

    Subband decomposition techniques have been extensively used for data coding and analysis. In most filter banks, the goal is to obtain subsampled signals corresponding to different spectral regions of the original data. However, this approach leads to various artifacts in images having spatially varying characteristics, such as images containing text, subtitles, or sharp edges. In this paper, adaptive filter banks with perfect reconstruction property are presented for such images. The filters of the decomposition structure which can be either linear or nonlinear vary according to the nature of the signal. This leads to improved image compression ratios. Simulation examples are presented View full abstract»

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  • Fourth-order partial differential equations for noise removal

    Page(s): 1723 - 1730
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    A class of fourth-order partial differential equations (PDEs) are proposed to optimize the trade-off between noise removal and edge preservation. The time evolution of these PDEs seeks to minimize a cost functional which is an increasing function of the absolute value of the Laplacian of the image intensity function. Since the Laplacian of an image at a pixel is zero if the image is planar in its neighborhood, these PDEs attempt to remove noise and preserve edges by approximating an observed image with a piecewise planar image. Piecewise planar images look more natural than step images which anisotropic diffusion (second order PDEs) uses to approximate an observed image. So the proposed PDEs are able to avoid the blocky effects widely seen in images processed by anisotropic diffusion, while achieving the degree of noise removal and edge preservation comparable to anisotropic diffusion. Although both approaches seem to be comparable in removing speckles in the observed images, speckles are more visible in images processed by the proposed PDEs, because piecewise planar images are less likely to mask speckles than step images and anisotropic diffusion tends to generate multiple false edges. Speckles can be easily removed by simple algorithms such as the one presented in this paper View full abstract»

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  • A quasi-Euclidean norm to speed up vector median filtering

    Page(s): 1704 - 1709
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    For reducing impulsive noise without degrading image contours, median filtering is a powerful tool. In multiband images, as for example color images or vector fields obtained by optic flow computation, a vector median filter can be used. Vector median filters are defined on the basis of a suitable distance, the best performing distance being the Euclidean. Euclidean distance is evaluated by using the Euclidean norm which is quite demanding from the point of view of computation given that a square root is required. In this paper an optimal piece-wise linear approximation of the Euclidean norm is presented which is applied to vector median filtering View full abstract»

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  • Improving gamut mapping color constancy

    Page(s): 1774 - 1783
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (236 KB)  

    The color constancy problem, that is, estimating the color of the scene illuminant from a set of image data recorded under an unknown light, is an important problem in computer vision and digital photography. The gamut mapping approach to color constancy is, to date, one of the most successful solutions to this problem. In this algorithm the set of mappings taking the image colors recorded under an unknown illuminant to the gamut of all colors observed under a standard illuminant is characterized. Then, at a second stage, a single mapping is selected from this feasible set. In the first version of this algorithm Forsyth (1990) mapped sensor values recorded under one illuminant to those recorded under a second, using a three-dimensional (3-D) diagonal matrix. However because the intensity of the scene illuminant cannot be recovered Finlayson (see IEEE Trans. Pattern Anal. Machine Intell. vol.18, no.10, p.1034-38, 1996) modified Forsyth's algorithm to work in a two-dimensional (2-D) chromaticity space and set out to recover only 2-D chromaticity mappings. While the chromaticity mapping overcomes the intensity problem it is not clear that something has not been lost in the process. The first result of this paper is to show that only intensity information is lost. Formally, we prove that the feasible set calculated by Forsyth's original algorithm, projected into 2-D, is the same as the feasible set calculated by the 2-D algorithm. Thus, there is no advantage in using the 3-D algorithm and we can use the simpler, 2-D version of the algorithm to characterize the set of feasible illuminants. Another problem with the chromaticity mapping is that it is perspective in nature and so chromaticities and chromaticity maps are perspectively distorted. Previous work demonstrated that the effects of perspective distortion were serious for the 2-D algorithm. Indeed, in order to select a sensible single mapping from the feasible set this set must first be mapped back up to 3-D. We extend this work to the case where a constraint on the possible color of the illuminant is factored into the gamut mapping algorithm. We show here that the illumination constraint can be enforced during selection without explicitly intersecting the two constraint sets. In the final part of this paper we reappraise the selection task. Gamut mapping returns the set of feasible illuminant maps. Our new algorithm is tested using real and synthetic images. The results of these tests show that the algorithm presented delivers excellent color constancy View full abstract»

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  • Filtering requirements for gradient-based optical flow measurement

    Page(s): 1817 - 1820
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    The accuracy of gradient-based optical flow algorithms depends on the ability to measure intensity gradients accurately. We show how the temporal gradient can be compromised by temporal aliasing arising from motion and how appropriate post-sampling spatial filtering improves the situation. We also demonstrate a benefit of using higher-order gradient estimators View full abstract»

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  • Texture classification using logical operators

    Page(s): 1693 - 1703
    Save to Project icon | Request Permissions | Click to expandQuick Abstract | PDF file iconPDF (828 KB)  

    In this paper, a new algorithm for texture classification based on logical operators is presented. Operators constructed from logical building blocks are convolved with texture images. An optimal set of six operators are selected based on their texture discrimination ability. The responses are then converted to standard deviation matrices computed over a sliding window. Zonal sampling features are computed from these matrices. A feature selection process is applied and the new set of features are used for texture classification. Classification of several natural and synthetic texture images are presented demonstrating the excellent performance of the logical operator method. The computational superiority and classification accuracy of the algorithm is demonstrated by comparison with other popular methods. Experiments with different classifiers and feature normalization are also presented. The Euclidean distance classifier is found to perform best with this algorithm. The algorithm involves only convolutions and simple arithmetic in the various stages which allows faster implementations. The algorithm is applicable to different types of classification problems which is demonstrated by segmentation of remote sensing images, compressed and reconstructed images and industrial images View full abstract»

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  • Lossless coding of multichannel signals using optimal vector hierarchical decomposition

    Page(s): 1811 - 1816
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    A methodology is presented for the optimal construction of multichannel reduced pyramids by selecting the interpolation synthesis postfilters so as to minimize the error variance at each level of the pyramid. The general optimization methodology is applied for the optimization of pyramids for the compression of electrocardiographic signals and RGB colored images View full abstract»

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  • A generalized fuzzy mathematical morphology and its application in robust 2-D and 3-D object representation

    Page(s): 1798 - 1810
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    In this paper, the generalized fuzzy mathematical morphology (GFMM) is proposed, based on a novel definition of the fuzzy inclusion indicator (FII). FII is a fuzzy set used as a measure of the inclusion of a fuzzy set into another, that is proposed to be a fuzzy set. It is proven that the FII obeys a set of axioms, which are proposed to be extensions of the known axioms that any inclusion indicator should obey, and which correspond to the desirable properties of any mathematical morphology operation. The GFMM provides a very powerful and flexible tool for morphological operations. The binary and grayscale mathematical morphologies can be considered as special cases of the proposed GFMM. An application for robust skeletonization and shape decomposition of two-dimensional (2-D) and three-dimensional (3-D) objects is presented. Simulation examples show that the object reconstruction from their skeletal subsets that can be achieved by using the GFMM is better than by using the binary mathematical morphology in most cases. Furthermore, the use of the GFMM for skeletonization and shape decomposition preserves the shape and the location of the skeletal subsets and spines View full abstract»

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Aims & Scope

IEEE Transactions on Image Processing focuses on signal-processing aspects of image processing, imaging systems, and image scanning, display, and printing.

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Meet Our Editors

Editor-in-Chief
Scott Acton
University of Virginia
Charlottesville, VA, USA
E-mail: acton@virginia.edu 
Phone: +1 434-982-2003