Author

# Anat Levin

Other affiliations: Stanford University, Hebrew University of Jerusalem, Tel Aviv Sourasky Medical Center ...read more

Bio: Anat Levin is an academic researcher from Technion – Israel Institute of Technology. The author has contributed to research in topic(s): Image restoration & Speckle pattern. The author has an hindex of 42, co-authored 91 publication(s) receiving 12993 citation(s). Previous affiliations of Anat Levin include Stanford University & Hebrew University of Jerusalem.

Topics: Image restoration, Speckle pattern, Rendering (computer graphics), Image segmentation, Deconvolution

##### Papers

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TL;DR: A closed-form solution to natural image matting that allows us to find the globally optimal alpha matte by solving a sparse linear system of equations and predicts the properties of the solution by analyzing the eigenvectors of a sparse matrix, closely related to matrices used in spectral image segmentation algorithms.

Abstract: Interactive digital matting, the process of extracting a foreground object from an image based on limited user input, is an important task in image and video editing. From a computer vision perspective, this task is extremely challenging because it is massively ill-posed - at each pixel we must estimate the foreground and the background colors, as well as the foreground opacity ("alpha matte") from a single color measurement. Current approaches either restrict the estimation to a small part of the image, estimating foreground and background colors based on nearby pixels where they are known, or perform iterative nonlinear estimation by alternating foreground and background color estimation with alpha estimation. In this paper, we present a closed-form solution to natural image matting. We derive a cost function from local smoothness assumptions on foreground and background colors and show that in the resulting expression, it is possible to analytically eliminate the foreground and background colors to obtain a quadratic cost function in alpha. This allows us to find the globally optimal alpha matte by solving a sparse linear system of equations. Furthermore, the closed-form formula allows us to predict the properties of the solution by analyzing the eigenvectors of a sparse matrix, closely related to matrices used in spectral image segmentation algorithms. We show that high-quality mattes for natural images may be obtained from a small amount of user input.

1,660 citations

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29 Jul 2007TL;DR: A simple modification to a conventional camera is proposed to insert a patterned occluder within the aperture of the camera lens, creating a coded aperture, and introduces a criterion for depth discriminability which is used to design the preferred aperture pattern.

Abstract: A conventional camera captures blurred versions of scene information away from the plane of focus. Camera systems have been proposed that allow for recording all-focus images, or for extracting depth, but to record both simultaneously has required more extensive hardware and reduced spatial resolution. We propose a simple modification to a conventional camera that allows for the simultaneous recovery of both (a) high resolution image information and (b) depth information adequate for semi-automatic extraction of a layered depth representation of the image. Our modification is to insert a patterned occluder within the aperture of the camera lens, creating a coded aperture. We introduce a criterion for depth discriminability which we use to design the preferred aperture pattern. Using a statistical model of images, we can recover both depth information and an all-focus image from single photographs taken with the modified camera. A layered depth map is then extracted, requiring user-drawn strokes to clarify layer assignments in some cases. The resulting sharp image and layered depth map can be combined for various photographic applications, including automatic scene segmentation, post-exposure refocusing, or re-rendering of the scene from an alternate viewpoint.

1,424 citations

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01 Aug 2004

TL;DR: This paper presents a simple colorization method that requires neither precise image segmentation, nor accurate region tracking, and demonstrates that high quality colorizations of stills and movie clips may be obtained from a relatively modest amount of user input.

Abstract: Colorization is a computer-assisted process of adding color to a monochrome image or movie The process typically involves segmenting images into regions and tracking these regions across image sequences Neither of these tasks can be performed reliably in practice; consequently, colorization requires considerable user intervention and remains a tedious, time-consuming, and expensive taskIn this paper we present a simple colorization method that requires neither precise image segmentation, nor accurate region tracking Our method is based on a simple premise; neighboring pixels in space-time that have similar intensities should have similar colors We formalize this premise using a quadratic cost function and obtain an optimization problem that can be solved efficiently using standard techniques In our approach an artist only needs to annotate the image with a few color scribbles, and the indicated colors are automatically propagated in both space and time to produce a fully colorized image or sequence We demonstrate that high quality colorizations of stills and movie clips may be obtained from a relatively modest amount of user input

1,311 citations

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20 Jun 2009

TL;DR: The previously reported failure of the naive MAP approach is explained by demonstrating that it mostly favors no-blur explanations and it is shown that since the kernel size is often smaller than the image size a MAP estimation of the kernel alone can be well constrained and accurately recover the true blur.

Abstract: Blind deconvolution is the recovery of a sharp version of a blurred image when the blur kernel is unknown. Recent algorithms have afforded dramatic progress, yet many aspects of the problem remain challenging and hard to understand. The goal of this paper is to analyze and evaluate recent blind deconvolution algorithms both theoretically and experimentally. We explain the previously reported failure of the naive MAP approach by demonstrating that it mostly favors no-blur explanations. On the other hand we show that since the kernel size is often smaller than the image size a MAP estimation of the kernel alone can be well constrained and accurately recover the true blur. The plethora of recent deconvolution techniques makes an experimental evaluation on ground-truth data important. We have collected blur data with ground truth and compared recent algorithms under equal settings. Additionally, our data demonstrates that the shift-invariant blur assumption made by most algorithms is often violated.

1,014 citations

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17 Jun 2006

TL;DR: A closed-form solution to natural image matting that allows us to find the globally optimal alpha matte by solving a sparse linear system of equations and predicts the properties of the solution by analyzing the eigenvectors of a sparse matrix, closely related to matrices used in spectral image segmentation algorithms.

Abstract: Interactive digital matting, the process of extracting a foreground object from an image based on limited user input, is an important task in image and video editing. From a computer vision perspective, this task is extremely challenging because it is massively ill-posed - at each pixel we must estimate the foreground and the background colors, as well as the foreground opacity ("alpha matte") from a single color measurement. Current approaches either restrict the estimation to a small part of the image, estimating foreground and background colors based on nearby pixels where they are known, or perform iterative nonlinear estimation by alternating foreground and background color estimation with alpha estimation. In this paper we present a closed form solution to natural image matting. We derive a cost function from local smoothness assumptions on foreground and background colors, and show that in the resulting expression it is possible to analytically eliminate the foreground and background colors to obtain a quadratic cost function in alpha. This allows us to find the globally optimal alpha matte by solving a sparse linear system of equations. Furthermore, the closed form formula allows us to predict the properties of the solution by analyzing the eigenvectors of a sparse matrix, closely related to matrices used in spectral image segmentation algorithms. We show that high quality mattes can be obtained on natural images from a surprisingly small amount of user input.

870 citations

##### Cited by

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07 Jun 2015

Abstract: We propose a deep convolutional neural network architecture codenamed Inception that achieves the new state of the art for classification and detection in the ImageNet Large-Scale Visual Recognition Challenge 2014 (ILSVRC14). The main hallmark of this architecture is the improved utilization of the computing resources inside the network. By a carefully crafted design, we increased the depth and width of the network while keeping the computational budget constant. To optimize quality, the architectural decisions were based on the Hebbian principle and the intuition of multi-scale processing. One particular incarnation used in our submission for ILSVRC14 is called GoogLeNet, a 22 layers deep network, the quality of which is assessed in the context of classification and detection.

29,453 citations

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28,684 citations

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TL;DR: This survey provides an overview of higher-order tensor decompositions, their applications, and available software.

Abstract: This survey provides an overview of higher-order tensor decompositions, their applications, and available software. A tensor is a multidimensional or $N$-way array. Decompositions of higher-order tensors (i.e., $N$-way arrays with $N \geq 3$) have applications in psycho-metrics, chemometrics, signal processing, numerical linear algebra, computer vision, numerical analysis, data mining, neuroscience, graph analysis, and elsewhere. Two particular tensor decompositions can be considered to be higher-order extensions of the matrix singular value decomposition: CANDECOMP/PARAFAC (CP) decomposes a tensor as a sum of rank-one tensors, and the Tucker decomposition is a higher-order form of principal component analysis. There are many other tensor decompositions, including INDSCAL, PARAFAC2, CANDELINC, DEDICOM, and PARATUCK2 as well as nonnegative variants of all of the above. The N-way Toolbox, Tensor Toolbox, and Multilinear Engine are examples of software packages for working with tensors.

7,526 citations

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09 Dec 2003

TL;DR: These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold.

Abstract: Many problems in information processing involve some form of dimensionality reduction. In this paper, we introduce Locality Preserving Projections (LPP). These are linear projective maps that arise by solving a variational problem that optimally preserves the neighborhood structure of the data set. LPP should be seen as an alternative to Principal Component Analysis (PCA) – a classical linear technique that projects the data along the directions of maximal variance. When the high dimensional data lies on a low dimensional manifold embedded in the ambient space, the Locality Preserving Projections are obtained by finding the optimal linear approximations to the eigenfunctions of the Laplace Beltrami operator on the manifold. As a result, LPP shares many of the data representation properties of nonlinear techniques such as Laplacian Eigenmaps or Locally Linear Embedding. Yet LPP is linear and more crucially is defined everywhere in ambient space rather than just on the training data points. This is borne out by illustrative examples on some high dimensional data sets.

4,091 citations