Author: eeeditor

imeg

Nonlocal Operators in Image Processing

Processing image in a nonlocal manner using a variational approach. Nonlocal operators such as gradient and divergence are defined and used to form nonlocal functionals, such as nonlocal total variation (NLTV). Also evolution processes can be used (e.g. for denoising), for instance nonlocal diffusion. Segmentation, NL-TV-L1 and NL-TV-G minimizations are examined, as well as extensions of Chambolle’s projection algorithm to solve numerically the minimization problems.

Related papers (see PDF’s in publicaton part)

  1. J.-F. Aujol, G. Gilboa, N. Papadakis, “Non local total variation spectral framework”, Scale Space and Variational Methods in Computer  Vision, SSVM 2015, LNCS 9087, p. 66-77, 2015.
  2. G. Gilboa, E. Appleboim, E. Saucan, Y.Y. Zeevi, “On the Role of Non-local Menger Curvature in Image Processing”, Proc. IEEE Int. Conf. Image Processing (ICIP), pp. 4337-4341, 2015. Recognized as part of the Top 10% papers in ICIP 2015.
  3. G. Gilboa, S. Osher, “Nonlocal Operators with Applications to Image Processing”, SIAM Multiscale Mod. Simul. (MMS), Vol. 7, No. 3, pp. 1005-1028, 2008.
  4. G. Gilboa, S. Osher, “Nonlocal linear image regularization and supervised segmentation”, SIAM Multiscale Mod. Simul. (MMS), Vol. 6, No. 2, pp. 595-630, 2007.
  5. G. Gilboa, S. Osher,  “Nonlocal evolutions for image regularization”, Proc. SPIE Electronic Imaging, SPIE Vol. 6498, 64980U, 2007.
  6. G. Gilboa, J. Darbon, S. Osher and T. Chan, “Nonlocal Convex Functionals for Image Regularization“, UCLA CAM Report 06-57.
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Postdoc position

Requirements

  1. Strong mathemetical and theoretical background. Knowledge in PDE’s, variational methods and convex analysis.
  2. PhD from departments of Applied Math/EE/CS.
  3. Solid publication record.
  4. Creativity.
  5. Knowledge in image processing – an advantage (not a must).
  6. Knowledge in Matlab – an advantage (not a must).
  7. English – high writing and speaking skills.

Description of Position

  1. Performing research in a new exciting field of nonlinear spectral representations, based on convex analysis.
  2. Research focus has a main theoretical aspect but can involve also design of new applications.
  3. No need to teach.
  4. Not attached to any industrial project.
  5. Will be conducted at the Electrical Engineering Department, Technion – Israel Institute of Technology, Haifa, Israel.

To Apply

Send mail to Guy Gilboa with your CV.

imeg

Depth Cameras

Previous related publications (mostly patents):

  1. G. Drozdov, Y. Shapiro, G. Gilboa, “Robust recovery of heavily degraded depth measurements”, Int. Conf. On 3D Vision (3DV), Stanford Univ., 2016.
  2. D. Rotman, G. Gilboa, “A depth restoration occlusionless temporal dataset”, Int. Conf. On 3D Vision (3DV), Stanford Univ., 2016.
  3. D.N. Rotman, O. Cohen, G. Gilboa, “Frame Rate Reduction of Depth Cameras by RGB-Based Depth Prediction”, CCIT Report 867, 2014.
  4. G. Gilboa, D. Cohen, G. Yahav, “Ambient light alert for an image sensor”, US 2013/0208091, 2013.
  5. G. Gilboa, “Learning from high quality depth measurements”, US 2012/0249738, 2012.
  6.  G. Gilboa, A. Adler, S. Katz, “Depth camera compatibility” – part I, US 2011/0187820, 2011.
  7.  S. Katz, A. Adler, G. Gilboa, “Depth camera compatibility” – part II, US 2011/0187819, 2011.
  8.  A. Adler, S. Katz, G. Gilboa, J. Tardif, “De-aliasing depth images”, US 2011/0234756, 2011.
  9.  G. Gilboa, D. Cohen, G. Yahav, E. Larry, S. Felzenshtein, “Adaptive high dynamic range camera”, US 2012/0287242, 2012.
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Nonlinear Spectral Analysis via One-homogeneous Functionals – Overview and Future Prospects

Guy Gilboa, Michael Moeller, Martin Burger, “Nonlinear Spectral Analysis via One-homogeneous Functionals – Overview and Future Prospects”, accepted to Journal of Mathematical Imaging and Vision (JMIV), 2016.

Abstract:

We present in this paper the motivation and theory of nonlinear spectral representations, based on convex regularizing functionals. Some comparisons and analogies are drawn to the fields of signal processing, harmonic analysis and sparse representations. The basic approach, main results and initial applications are shown. A discussion of open problems and future directions concludes this work.

imeg@diagrams

Learning Nonlinear Spectral Filters for Color Image Reconstruction

Michael Moeller, Julia Diebold, Guy Gilboa, Daniel Cremers, “Learning Nonlinear Spectral Filters for Color Image Reconstruction”, ICCV 2015.

Abstract:

This paper presents the idea of learning optimal filters for color image reconstruction based on a novel concept of nonlinear spectral image decompositions recently proposed by Gilboa. The general idea is to use total variation regularization along with Bregman iterations to represent the input data as the sum over image layers containing features at different scales. Filtered images can be obtained by weighted linear combinations of the different frequency layers. We show that learning the optimal weights can significantly improve the results in comparison to the standard variational approach, and can achieve state-of-the-art results. While we focus on the problem of image denoising, our general framework extends to a number of image reconstruction tasks.

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Talk at Cambridge (Oct 2015)

Talk at the Department of Applied Mathematics and Theoretical Physics, University of Cambridge, at the Applied and Computational Analysis Seminar on “Processing Textures in the Spectral Total-Variation Domain”, Oct. 2015.

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Talk at the International Applied Math Congress, ICIAM (Aug. 2015)

The International Congress on Industrial and Applied Mathematics (ICIAM) is the premier international congress in the field of applied mathematics held every four years under the auspices of the International Council for Industrial and Applied Mathematics. From August 10 to 14, 2015, mathematicians from around the world will gather in Beijing, China for the 8th ICIAM to be held at China National Convention Center inside the Beijing Olympic Green.

See more about ICIAM 2015

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A Maximal Interest-Point Strategy Applied to Image Enhancement with External Priors

O. Katzir and G. Gilboa, “A Maximal Interest-Point Strategy Applied to Image Enhancement with External Priors”, IEEE International Conference on Image Processing (ICIP-2015) , pp. 1324-1328, 2015.

Abstract:

Curvature is a fundamental component in differential geometry. It is used extensively in signal, image and shape processing, as a feature and in segmentation flows and regularization processes. In this paper we extend the notion of curvature in two ways. First, we present the Menger curvature which goes beyond classical curves and Riemannian manifolds to general metric spaces and is rigorously defined on a variety of discrete settings. We further extend the curvature to become a non-local entity using an adaptive, non-local integration measure, allowing curvature to be computed in a robust manner. Examples on natural and textural images highlight potential applications of these new concepts.

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On the Role of Non-local Menger Curvature in Image Processing

G. Gilboa, E. Appleboim, E. Saucan and Y.Y. Zeevi, “On the Role of Non-local Menger Curvature in Image Processing”, IEEE International Conference on Image Processing (ICIP-2015) , pp. 4337-4341, 2015.

Abstract:

Curvature is a fundamental component in differential geometry. It is used extensively in signal, image and shape processing, as a feature and in segmentation flows and regularization processes. In this paper we extend the notion of curvature in two ways. First, we present the Menger curvature which goes beyond classical curves and Riemannian manifolds to general metric spaces and is rigorously defined on a variety of discrete settings. We further extend the curvature to become a non-local entity using an adaptive, non-local integration measure, allowing curvature to be computed in a robust manner. Examples on natural and textural images highlight potential applications of these new concepts

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