http://ieeexplore.ieee.org TOC Alert for Publication# 83 2009 November 19 18 12 C1 C4 129 18 12 C2 C2 39 18 12 2617 2617 25 The octahedral group is one of the finite subgroups of the rotation group in 3-D Euclidean space and a symmetry group of the cubic grid. Compression and filtering of 3-D volumes are given as application examples of its representation theory. We give an overview over the finite subgroups of the 3-D rotation group and their classification. We summarize properties of the octahedral group and basic results from its representation theory. Wide-sense stationary processes are processes with group theoretical symmetries whose principal components are closely related to the representation theory of their symmetry group. Linear filter systems are defined as projection operators and symmetry-based filter systems are generalizations of the Fourier transforms. The algorithms are implemented in Maple/Matlab functions and worksheets. In the experimental part, we use two publicly available MRI volumes. It is shown that the assumption of wide-sense stationarity is realistic and the true principal components of the correlation matrix are very well approximated by the group theoretically predicted structure. We illustrate the nature of the different types of filter systems, their invariance and transformation properties. Finally, we show how thresholding in the transform domain can be used in 3-D signal processing. ]]> 18 12 2618 2628 2609 Shannon entropy is a powerful tool in image analysis, but its reliable computation from image data faces an inherent dimensionality problem that calls for a low-dimensional and closed form model for the pixel value distributions. The most promising such models are Markovian, however, the conventional Markov random field is hampered by noncausality and its causal versions are also not free of difficulties. For example, the Markov mesh random field has its own limitations due to the strong diagonal dependency in its local neighboring system. A new model, named quadrilateral Markov random field (QMRF) is introduced in this paper in order to overcome these limitations. A property of QMRF with neighboring size of 2 is then used to decompose an image prior into a product of 2-D joint pdfs in which they are estimated using a joint histogram under the homogeneity assumption. In addition, the paper includes an extension of the introduced method to the computation of image spatial mutual information. Comparisons on synthesized images as well as two applications with real images are presented to motivate the developments in this paper and demonstrate the advantages in the performance of the introduced method over the existing ones. ]]> 18 12 2629 2639 1236 Image restoration and simplification methods that respect important features such as edges play a fundamental role in digital image processing. However, known edge-preserving methods like common nonlinear diffusion methods tend to round vertices for large diffusion times. In this paper, we adapt the diffusion tensor for anisotropic diffusion to avoid this effects in images containing rotated and sheared rectangles, respectively. In this context, we propose a new method for estimating rotation angles and shear parameters based on the so-called structure tensor. Further, we show how the knowledge of appropriate diffusion tensors can be used in variational models. Numerical examples including orientation estimation, denoising and segmentation demonstrate the good performance of our methods. ]]> 18 12 2640 2648 1585 We present an in-depth analysis of a variation of the nonlocal means (NLM) image denoising algorithm that uses principal component analysis (PCA) to achieve a higher accuracy while reducing computational load. Image neighborhood vectors are first projected onto a lower dimensional subspace using PCA. The dimensionality of this subspace is chosen automatically using parallel analysis. Consequently, neighborhood similarity weights for denoising are computed using distances in this subspace rather than the full space. The resulting algorithm is referred to as principal neighborhood dictionary (PND) nonlocal means. We investigate PND's accuracy as a function of the dimensionality of the projection subspace and demonstrate that denoising accuracy peaks at a relatively low number of dimensions. The accuracy of NLM and PND are also examined with respect to the choice of image neighborhood and search window sizes. Finally, we present a quantitative and qualitative comparison of PND versus NLM and another image neighborhood PCA-based state-of-the-art image denoising algorithm. ]]> 18 12 2649 2660 3441 Image denoising is an important problem in image processing since noise may interfere with visual or automatic interpretation. This paper presents a new approach for image denoising in the case of a known uncorrelated noise model. The proposed filter is an extension of the nonlocal means (NL means) algorithm introduced by Buades , which performs a weighted average of the values of similar pixels. Pixel similarity is defined in NL means as the Euclidean distance between patches (rectangular windows centered on each two pixels). In this paper, a more general and statistically grounded similarity criterion is proposed which depends on the noise distribution model. The denoising process is expressed as a weighted maximum likelihood estimation problem where the weights are derived in a data-driven way. These weights can be iteratively refined based on both the similarity between noisy patches and the similarity of patches extracted from the previous estimate. We show that this iterative process noticeably improves the denoising performance, especially in the case of low signal-to-noise ratio images such as synthetic aperture radar (SAR) images. Numerical experiments illustrate that the technique can be successfully applied to the classical case of additive Gaussian noise but also to cases such as multiplicative speckle noise. The proposed denoising technique seems to improve on the state of the art performance in that latter case. ]]> 18 12 2661 2672 6152 In this paper, a new type of deconvolution algorithm is proposed that is based on estimating the image from a shearlet decomposition. Shearlets provide a multidirectional and multiscale decomposition that has been mathematically shown to represent distributed discontinuities such as edges better than traditional wavelets. Constructions such as curvelets and contourlets share similar properties, yet their implementations are significantly different from that of shearlets. Taking advantage of unique properties of a new M-channel implementation of the shearlet transform, we develop an algorithm that allows for the approximation inversion operator to be controlled on a multiscale and multidirectional basis. A key improvement over closely related approaches such as ForWaRD is the automatic determination of the threshold values for the noise shrinkage for each scale and direction without explicit knowledge of the noise variance using a generalized cross validation (GCV). Various tests show that this method can perform significantly better than many competitive deconvolution algorithms. ]]> 18 12 2673 2685 5636 In this paper, we propose a new encoding algorithm for matching pursuit image coding. We show that coding performance is improved when correlations between atom positions and atom coefficients are both used in encoding. We find the optimum tradeoff between efficient atom position coding and efficient atom coefficient coding and optimize the encoder parameters. Our proposed algorithm outperforms the existing coding algorithms designed for matching pursuit image coding. Additionally, we show that our algorithm results in better rate distortion performance than JPEG 2000 at low bit rates. ]]> 18 12 2686 2694 1010 We propose a novel solution to the problem of robust, low-latency video transmission over lossy channels. Predictive video codecs, such as MPEG and H.26x, are very susceptible to prediction mismatch between encoder and decoder or “drift” when there are packet losses. These mismatches lead to a significant degradation in the decoded quality. To address this problem, we propose an auxiliary codec system that sends additional information alongside an MPEG or H.26x compressed video stream to correct for errors in decoded frames and mitigate drift. The proposed system is based on the principles of distributed source coding and uses the (possibly erroneous) MPEG/H.26x decoder reconstruction as side information at the auxiliary decoder. The distributed source coding framework depends upon knowing the statistical dependency (or correlation) between the source and the side information. We propose a recursive algorithm to analytically track the correlation between the original source frame and the erroneous MPEG/H.26x decoded frame. Finally, we propose a rate-distortion optimization scheme to allocate the rate used by the auxiliary encoder among the encoding blocks within a video frame. We implement the proposed system and present extensive simulation results that demonstrate significant gains in performance both visually and objectively (on the order of 2 dB in PSNR over forward error correction based solutions and 1.5 dB in PSNR over intrarefresh based solutions for typical scenarios) under tight latency constraints. ]]> 18 12 2695 2705 649 Almost all existing color demosaicking algorithms for digital cameras are designed on the assumption of high correlation between red, green, blue (or some other primary color) bands. They exploit spectral correlations between the primary color bands to interpolate the missing color samples, but in areas of no or weak spectral correlations, these algorithms are prone to large interpolation errors. Such demosaicking errors are visually objectionable because they tend to correlate with object boundaries and edges. This paper proposes a remedy to the above problem that has long been overlooked in the literature. The main contribution of this work is a hybrid demosaicking approach that supplements an existing color demosaicking algorithm by combining its results with those of adaptive intraband interpolation. This is formulated as an optimal data fusion problem, and two solutions are proposed: one is based on linear minimum mean-square estimation and the other based on support vector regression. Experimental results demonstrate that the new hybrid approach is more robust and eliminates the worst type of color artifacts of existing color demosaicking methods. ]]> 18 12 2706 2717 1927 A generalization of periodic clustered-dot halftones is proposed, wherein the phase of the halftone spots is modulated using a secondary signal. The process is accomplished by using an analytic halftone threshold function that allows halftones to be generated with controlled phase variation in different regions of the printed page. The method can also be used to modulate the screen frequency, albeit with additional constraints. Visible artifacts are minimized/eliminated by ensuring the continuity of the modulation in phase. Limitations and capabilities of the method are analyzed through a quantitative model. The technique can be exploited for two applications that are presented in this paper: a) embedding watermarks in the halftone image by encoding information in phase or in frequency and b) modulating the screen frequency according to the frequency content of the continuous tone image in order to improve spatial and tonal rendering. Experimental performance is demonstrated for both applications. ]]> 18 12 2718 2734 3296 Many automatic algorithms have been proposed for analyzing magnetic resonance imaging (MRI) data sets. With the increasingly large data sets being used in brain mapping, there has been a significant rise in the need for accelerating these algorithms. Partial volume estimation (PVE), a brain tissue classification algorithm for MRI, was implemented on a field-programmable gate array (FPGA)-based high performance reconfigurable computer using the Mitrion-C high-level language (HLL). This work develops on prior work in which we conducted initial studies on accelerating the prior information estimation algorithm. In this paper, we extend the work to include probability density estimation and present new results and additional analysis. We used several simulated and real human brain MR images to evaluate the accuracy and performance improvement of the proposed algorithm. The FPGA-based probability density estimation and prior information estimation implementation achieved an average speedup over an Itanium 2 CPU of 2.5$times$ and 9.4$times$ , respectively. The overall performance improvement of the FPGA-based PVE algorithm was 5.1$times$ with four FPGAs. ]]> 18 12 2735 2746 1724 This paper presents a novel fast model for active contours to detect objects in an image, based on techniques of curve evolution. The proposed model can detect objects whose boundaries are not necessarily defined by gradient, based on the minimization of a fuzzy energy, which can be seen as a particular case of a minimal partition problem. This fuzzy energy is used as the model motivation power evolving the active contour, which will stop on the desired object boundary. However, the stopping term does not depend on the gradient of the image, as most of the classical active contours, but instead is related to the image color and spatial segments. The fuzziness of the energy provides a balanced technique with a strong ability to reject “weak” local minima. Moreover, this approach converges to the desired object boundary very fast, since it does not solve the Euler–Lagrange equations of the underlying problem, but, instead, calculates the fuzzy energy alterations directly. The theoretical properties and various experiments presented demonstrate that the proposed fuzzy energy-based active contour is better and more robust than classical snake methods based on the gradient or other kind of energies. ]]> 18 12 2747 2755 1045 A robust, theoretically founded approach for the extraction of temporal templates corresponding to areas of motion in video, is presented. Higher order statistics (kurtosis) are employed to extract activity areas, i.e., binary masks indicating which pixels in a video are active. The application of the kurtosis on illumination changes modeled as Gaussians and mixture of Gaussians is shown to be sensitive to outliers for both models, thus correctly localizing active pixels. Activity areas are compared to existing, difference-based temporal templates, known as motion energy images, and the robustness of both categories of temporal templates to additive noise is analyzed theoretically. Experiments with numerous real videos with additive noise, both indoors and outdoors, are conducted to compare the robustness of the activity areas and motion energy images, and their temporal extensions, the activity history areas, and motion history images. As expected from the theoretical analysis, the kurtosis-based activity areas prove to be more robust than the difference-based templates. Challenging videos containing occlusions, varying backgrounds, and shadows are also examined, and it is shown that the proposed approach outperforms the difference-based method for these cases, as well, consistently providing reliable localization of activity under a wide range of difficult circumstances. The proposed approach provides good results at a very low computational cost, and without requiring prior knowledge about the scene, nor training of any kind. ]]> 18 12 2756 2768 1283 This study presents a rapid image completion system comprising a training (or analysis) process and an image completion (or synthesis) process. The proposed system adopts a multiresolution approach, which not only improves the convergence rate of the synthesis process, but also provides the ability to deal with large replaced regions. In the training process, a down-sampling approach is applied to create a patch-based texture eigenspace based on multiresolution background region information. In the image completion process, an up-sampling approach is applied to synthesize the replaced foreground regions. To ensure the continuity of the geometric texture structure between the original background scene regions and the replaced foreground regions, directional and nondirectional image completion approaches are developed to reconstruct the global geometric structure and to enhance the local detailed features of the replaced foreground regions in the lower and higher resolution level images, respectively. Moreover, the synthesis priority order of the individual patches and the appropriate choice of completion scheme (i.e., directional or nondirectional) are both determined in accordance with a Hessian matrix decision value (HMDV) parameter. Finally, a texture refinement process is performed to optimize the resolution of the synthesized result. ]]> 18 12 2769 2779 1453 Motivated by the need to efficiently leverage user relevance feedback in content-based retrieval from image databases, we propose a fast, clustering-based indexing technique for exact nearest-neighbor search that adapts to the Mahalanobis distance with a varying weight matrix. We derive a basic property of point-to-hyperplane Mahalanobis distance, which enables efficient recalculation of such distances as the Mahalanobis weight matrix is varied. This property is exploited to recalculate bounds on query-cluster distances via projection on known separating hyperplanes (available from the underlying clustering procedure), to effectively eliminate noncompetitive clusters from the search and to retrieve clusters in increasing order of (the appropriate) distance from the query. We compare performance with an existing variant of VA-File indexing designed for relevance feedback, and observe considerable gains. ]]> 18 12 2780 2789 811 Two-dimensional fast Gabor transform algorithms are useful for real-time applications due to the high computational complexity of the traditional 2-D complex-valued discrete Gabor transform (CDGT). This paper presents two block time-recursive algorithms for 2-D DHT-based real-valued discrete Gabor transform (RDGT) and its inverse transform and develops a fast parallel approach for the implementation of the two algorithms. The computational complexity of the proposed parallel approach is analyzed and compared with that of the existing 2-D CDGT algorithms. The results indicate that the proposed parallel approach is attractive for real time image processing. ]]> 18 12 2790 2796 281 In this paper, we construct a Lattice Boltzmann scheme to simulate the well known total variation based restoration model, that is, ROF model. The advantages of the Lattice Boltzmann method include the fast computational speed and the easily implemented fully parallel algorithm. A conservative property of the LB method is discussed. The macroscopic PDE associated with the LB algorithm is derived which is just the ROF model. Moreover, the linearized stability of the method is analyzed. The numerical computations demonstrate that the LB algorithm is efficient and robust. Even though the quality of the restored images is slightly lower than those by using the ROF model, the restored images of the LB method are satisfactory. Furthermore, computational speed of the LB method is much faster than ROF model. In general, CPU time of the LB method for restored images is about one tenth of ROF model. ]]> 18 12 2797 2802 1701 18 12 2803 2808 39 18 12 2809 2809 21 18 12 2810 2811 46 18 12 2812 2812 146 18 12 2813 2813 600 18 12 2814 2840 287 18 12 C3 C3 32