Achi Brandt

Weizmann Institute of Science, Israel

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Publications (41)89.03 Total impact

  • Or Cohen, Leeor Kronik, Achi Brandt
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    ABSTRACT: We present a fully numerical multigrid approach for solving the all-electron Kohn–Sham equation in molecules. The equation is represented on a hierarchy of Cartesian grids, from coarse ones that span the entire molecule to very fine ones that describe only a small volume around each atom. This approach is adaptable to any type of geometry. We demonstrate it for a variety of small molecules and obtain high accuracy agreement with results obtained previously for diatomic molecules using a prolate-spheroidal grid. We provide a detailed presentation of the numerical methodology and discuss possible extensions of this approach.
    Journal of Chemical Theory and Computation 10/2013; 9(11):4744–4760. · 5.39 Impact Factor
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    ABSTRACT: We present a bottom-up aggregation approach to image segmentation. Beginning with an image, we execute a sequence of steps in which pixels are gradually merged to produce larger and larger regions. In each step, we consider pairs of adjacent regions and provide a probability measure to assess whether or not they should be included in the same segment. Our probabilistic formulation takes into account intensity and texture distributions in a local area around each region. It further incorporates priors based on the geometry of the regions. Finally, posteriors based on intensity and texture cues are combined using “a mixture of experts” formulation. This probabilistic approach is integrated into a graph coarsening scheme, providing a complete hierarchical segmentation of the image. The algorithm complexity is linear in the number of the image pixels and it requires almost no user-tuned parameters. In addition, we provide a novel evaluation scheme for image segmentation algorithms, attempting to avoid human semantic considerations that are out of scope for segmentation algorithms. Using this novel evaluation scheme, we test our method and provide a comparison to several existing segmentation algorithms.
    IEEE Transactions on Software Engineering 06/2011; 34(2):315-26. · 2.59 Impact Factor
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    Dan Kushnir, Meirav Galun, Achi Brandt
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    ABSTRACT: Multigrid solvers proved very efficient for solving massive systems of equations in various fields. These solvers are based on iterative relaxation schemes together with the approximation of the "smooth" error function on a coarser level (grid). We present two efficient multilevel eigensolvers for solving massive eigenvalue problems that emerge in data analysis tasks. The first solver, a version of classical algebraic multigrid (AMG), is applied to eigenproblems arising in clustering, image segmentation, and dimensionality reduction, demonstrating an order of magnitude speedup compared to the popular Lanczos algorithm. The second solver is based on a new, much more accurate interpolation scheme. It enables calculating a large number of eigenvectors very inexpensively.
    IEEE Transactions on Software Engineering 08/2010; 32(8):1377-91. · 2.59 Impact Factor
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    Dorit Ron, Ilya Safro, Achi Brandt
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    ABSTRACT: In this paper we generalize and improve the multiscale organization of graphs by introducing a new measure that quantifies the "closeness" between two nodes. The calculation of the measure is linear in the number of edges in the graph and involves just a small number of relaxation sweeps. A similar notion of distance is then calculated and used at each coarser level. We demonstrate the use of this measure in multiscale methods for several important combinatorial optimization problems and discuss the multiscale graph organization.
    04/2010;
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    ABSTRACT: We introduce a multiscale approach that combines segmentation with classification to detect abnormal brain structures in medical imagery, and demonstrate its utility in automatically detecting multiple sclerosis (MS) lesions in 3-D multichannel magnetic resonance (MR) images. Our method uses segmentation to obtain a hierarchical decomposition of a multichannel, anisotropic MR scans. It then produces a rich set of features describing the segments in terms of intensity, shape, location, neighborhood relations, and anatomical context. These features are then fed into a decision forest classifier, trained with data labeled by experts, enabling the detection of lesions at all scales. Unlike common approaches that use voxel-by-voxel analysis, our system can utilize regional properties that are often important for characterizing abnormal brain structures. We provide experiments on two types of real MR images: a multichannel proton-density-, T2-, and T1-weighted dataset of 25 MS patients and a single-channel fluid attenuated inversion recovery (FLAIR) dataset of 16 MS patients. Comparing our results with lesion delineation by a human expert and with previously extensively validated results shows the promise of the approach.
    IEEE transactions on bio-medical engineering 10/2009; 56(10):2461-9. · 2.15 Impact Factor
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    Dorit Ron, Ilya Safro, Achi Brandt
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    ABSTRACT: The two-dimensional layout optimization problem reinforced by the efficient space utilization demand has a wide spectrum of practical applications. Formulating the problem as a nonlinear minimization problem under planar equality and/or inequality density constraints, we present a linear time multigrid algorithm for solving correction to this problem. The method is demonstrated on various graph drawing (visualization) instances.
    03/2009;
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    Ilya Safro, Dorit Ron, Achi Brandt
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    ABSTRACT: Linear ordering problems are combinatorial optimization problems which deal with the minimization of dierent functionals in which the graph vertices are mapped onto (1,2,...,n). These problems are widely used and studied in many practical and theoretical applications. In this paper we present a variety of linear-time algorithms for these problems inspired by the Algebraic Multi- grid approach which is based on weighted edge contraction. The experimental result for four such problems turned out to be better than every known result in almost all cases, while the short running time of the algorithms enables testing very large graphs.
    ACM Journal of Experimental Algorithmics. 01/2008; 13.
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    S. Alpert, M. Galun, R. Basri, A. Brandt
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    ABSTRACT: We present a parameter free approach that utilizes multiple cues for image segmentation. Beginning with an image, we execute a sequence of bottom-up aggregation steps in which pixels are gradually merged to produce larger and larger regions. In each step we consider pairs of adjacent regions and provide a probability measure to assess whether or not they should be included in the same segment. Our probabilistic formulation takes into account intensity and texture distributions in a local area around each region. It further incorporates priors based on the geometry of the regions. Finally, posteriors based on intensity and texture cues are combined using a mixture of experts formulation. This probabilistic approach is integrated into a graph coarsening scheme providing a complete hierarchical segmentation of the image. The algorithm complexity is linear in the number of the image pixels and it requires almost no user-tuned parameters. We test our method on a variety of gray scale images and compare our results to several existing segmentation algorithms.
    Computer Vision and Pattern Recognition, 2007. CVPR '07. IEEE Conference on; 07/2007
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    ABSTRACT: We present a novel automatic multiscale algorithm applied to segmentation of anatomical structures in brain MRI. The algorithm which is derived from algebraic multigrid, uses a graph representation of the image and performs a coarsening process that produces a full hierarchy of segments. Our main contribution is the incorporation of prior knowledge information into the multiscale framework through a Bayesian formulation. The probabilistic information is based on an atlas prior and on a likelihood function estimated from a manually labeled training set. The significance of our new approach is that the constructed pyramid, reflects the prior knowledge formulated. This leads to an accurate and efficient methodology for detection of various anatomical structures simultaneously. Quantitative validation results on gold standard MRI show the benefit of our approach.
    Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. 02/2007; 10(Pt 2):118-26.
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    Ilya Safro, Dorit Ron, Achi Brandt
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    ABSTRACT: Linear ordering problems are combinatorial optimization problems which deal with the minimization of different functionals in which the graph vertices are mapped onto (1, 2, ..., n). These problems are widely used and studied in many practical and theoret-ical applications. In this review we summarize a variety of linear-time algorithms for these problems inspired by the Algebraic Multigrid approach which is based on weighted edge contraction. The experimental results for four such problems turned out to be better than ev-ery known results in almost all cases, while the short running time of the algorithms enables applications on very large graphs.
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    ABSTRACT: We present a novel approach that allows us to reliably compute many useful properties of a silhouette. Our approach assigns, for every internal point of the silhouette, a value reflecting the mean time required for a random walk beginning at the point to hit the boundaries. This function can be computed by solving Poisson's equation, with the silhouette contours providing boundary conditions. We show how this function can be used to reliably extract various shape properties including part structure and rough skeleton, local orientation and aspect ratio of different parts, and convex and concave sections of the boundaries. In addition to this, we discuss properties of the solution and show how to efficiently compute this solution using multigrid algorithms. We demonstrate the utility of the extracted properties by using them for shape classification and retrieval.
    IEEE Transactions on Pattern Analysis and Machine Intelligence 01/2007; 28(12):1991-2005. · 4.80 Impact Factor
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    Meirav Galun, Ronen Basri, Achi Brandt
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    ABSTRACT: We present an algorithm for edge detection suitable for both natural as well as noisy images. Our method is based on efficient multiscale utilization of elongated filters measuring the difference of oriented means of various lengths and orientations, along with a theoretical estimation of the effect of noise on the response of such filters. We use a scale adaptive threshold along with a recursive decision process to reveal the significant edges of all lengths and orientations and to localize them accurately even in low-contrast and very noisy images. We further use this algorithm for fiber detection and enhancement by utilizing stochastic completion-like process from both sides of a fiber. Our algorithm relies on an efficient multiscale algorithm for computing all "significantly different" oriented means in an image in O(N log rho), where N is the number of pixels, and p is the length of the longest structure of interest. Experimental results on both natural and noisy images are presented.
    IEEE 11th International Conference on Computer Vision, ICCV 2007, Rio de Janeiro, Brazil, October 14-20, 2007; 01/2007
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    12/2006: pages 235-239;
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    Achi Brandt, Dorit Ron, Daniel J. Amit
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    ABSTRACT: Fast multi-level techniques are developed for large-scale problems whose variables may assume only discrete values (such as spins with only “up” and “down” states), and/or where the relations between variables is probabilistic. Motivation and examples are taken from statistical mechanics and field theory. Detailed procedures are developed for the fast global minimization of discretestate functionals, or other functionals with many local minima, using new principles of multilevel interactions. Tests with Ising spin models are reported. Of special interest to physicists are the Ising model in a random field and spin glasses, which are known to lead to difficulties in conventional Monte-Carlo algorithms.
    11/2006: pages 65-98;
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    ABSTRACT: The maxima of the scalar dissipation rate in turbulence appear in the form of sheets and correspond to the potentially most intensive scalar mixing events. Their cross section extension determines a locally varying diffusion scale of the mixing process and extends the classical Batchelor picture of one mean diffusion scale. The distribution of the local diffusion scales is analyzed for different Reynolds and Schmidt numbers with a fast multiscale technique applied to very high-resolution simulation data. The scales always take values across the whole Batchelor range and beyond. Furthermore, their distribution is traced back to the distribution of the contractive short-time Lyapunov exponent of the flow.
    Physical Review Letters 10/2006; 97(12):124502. · 7.73 Impact Factor
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    ABSTRACT: Finding salient, coherent regions in images is the basis for many visual tasks, and is especially important for object recognition. Human observers perform this task with ease, relying on a system in which hierarchical processing seems to have a critical role. Despite many attempts, computerized algorithms have so far not demonstrated robust segmentation capabilities under general viewing conditions. Here we describe a new, highly efficient approach that determines all salient regions of an image and builds them into a hierarchical structure. Our algorithm, segmentation by weighted aggregation, is derived from algebraic multigrid solvers for physical systems, and consists of fine-to-coarse pixel aggregation. Aggregates of various sizes, which may or may not overlap, are revealed as salient, without predetermining their number or scale. Results using this algorithm are markedly more accurate and significantly faster (linear in data size) than previous approaches.
    Nature 09/2006; 442(7104):810-3. · 38.60 Impact Factor
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    ABSTRACT: We present a novel multiscale approach that combines segmentation with classification to detect abnormal brain structures in medical imagery, and demonstrate its utility in detecting multiple sclerosis lesions in 3D MRI data. Our method uses segmentation to obtain a hierarchical decomposition of a multi-channel, anisotropic MRI scan. It then produces a rich set of features describing the segments in terms of intensity, shape, location, and neighborhood relations. These features are then fed into a decision tree-based classifier, trained with data labeled by experts, enabling the detection of lesions in all scales. Unlike common approaches that use voxel-by-voxel analysis, our system can utilize regional properties that are often important for characterizing abnormal brain structures. We provide experiments showing successful detections of lesions in both simulated and real MR images.
    Computer Vision and Pattern Recognition, 2006 IEEE Computer Society Conference on; 07/2006
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    [Show abstract] [Hide abstract]
    ABSTRACT: We present a novel multiscale approach that combines segmentation with classification to detect abnormal brain structures in medical imagery, and demonstrate its utility in detecting multiple sclerosis lesions in 3D MRI data. Our method uses segmentation to obtain a hierarchical decomposition of a multi-channel, anisotropic MRI scan. It then produces a rich set of features describing the segments in terms of intensity, shape, location, and neighborhood relations. These features are then fed into a decision tree-based classifier, trained with data labeled by experts, enabling the detection of lesions in all scales. Unlike common approaches that use voxel-by-voxel analysis, our system can utilize regional properties that are often important for characterizing abnormal brain structures. We provide experiments showing successful detections of lesions in both simulated and real MR images.
    Proceedings / CVPR, IEEE Computer Society Conference on Computer Vision and Pattern Recognition. IEEE Computer Society Conference on Computer Vision and Pattern Recognition 06/2006; 1:1122-1129.
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    ABSTRACT: This study presents a novel automatic approach for the identification of anatomical brain structures in magnetic resonance images (MRI). The method combines a fast multiscale multi-channel three dimensional (3D) segmentation algorithm providing a rich feature vocabulary together with a support vector machine (SVM) based classifier. The segmentation produces a full hierarchy of segments, expressed by an irregular pyramid with only linear time complexity. The pyramid provides a rich, adaptive representation of the image, enabling detection of various anatomical structures at different scales. A key aspect of the approach is the thorough set of multiscale measures employed throughout the segmentation process which are also provided at its end for clinical analysis. These features include in particular the prior probability knowledge of anatomic structures due to the use of an MRI probabilistic atlas. An SVM classifier is trained based on this set of features to identify the brain structures. We validated the approach using a gold standard real brain MRI data set. Comparison of the results with existing algorithms displays the promise of our approach.
    Medical image computing and computer-assisted intervention : MICCAI ... International Conference on Medical Image Computing and Computer-Assisted Intervention. 02/2006; 9(Pt 2):209-16.
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    Ilya Safro, Dorit Ron, Achi Brandt
    J. Algorithms. 01/2006; 60:24-41.

Publication Stats

996 Citations
89.03 Total Impact Points

Institutions

  • 2000–2011
    • Weizmann Institute of Science
      • • Faculty of Mathematics and Computer Science
      • • Department of Computer Science and Applied Mathematics
      Israel
  • 2010
    • Yale University
      • Department of Mathematics
      New Haven, CT, United States
  • 2009
    • Harvard Medical School
      Boston, Massachusetts, United States
  • 2007
    • Hadassah Medical Center
      Yerushalayim, Jerusalem District, Israel