Publications

Google_Scholar

Publication summary (Google Scholar)

List of papers ordered by popularity Papers and Citation info

Iterative Methods for Computing Eigenvectors of Nonlinear Operators

Guy Gilboa, arXiv preprint  A chapter to appear in Handbook of Mathematical Models and Algorithms in Computer Vision and Imaging.   In this chapter we are examining several iterative methods for solving nonlinear eigenvalue problems. These arise in variational image-processing, graph partition and classification, nonlinear physics and more. The canonical eigenproblem we solve is $T(u)=\lambda […]

NeurIPS 2020: Deeply Learned Spectral Total Variation Decomposition

Tamara G. Grossmann, Yury Korolev, Guy Gilboa, Carola-Bibiane Schönlieb, arXiv 2020 Accepted for NeurIPS 2020. Non-linear spectral decompositions of images based on one-homogeneous functionals such as total variation have gained considerable attention in the last few years. Due to their ability to extract spectral components corresponding to objects of different size and contrast, such decompositions […]

Adaptive LiDAR Sampling and Depth Completion using Ensemble Variance

Eyal Gofer, Shachar Praisler, Guy Gilboa,  arXiv July, 2020 Project details Abstract This work considers the problem of depth completion, with or without image data, where an algorithm may measure the depth of a prescribed limited number of pixels. The algorithmic challenge is to choose pixel positions strategically and dynamically to maximally reduce overall depth […]

Mode Decomposition for Homogeneous Symmetric Operators

Ido Cohen, Omri Azencot, Pavel Lifshitz, Guy Gilboa, arXiv, July 2020   Finding latent structures in data is drawing increasing attention in broad and diverse fields such as fluid dynamics, signal processing, and machine learning. In this work, we formulate Dynamic Mode Decomposition (DMD) for two types of dynamical system. The first, a system which is […]

Nonlinear Power Method for Computing Eigenvectors of Proximal Operators and Neural Networks

Leon Bungert,  Ester Hait-Fraenkel , Nicolas Papadakis and Guy Gilboa, arXiv Neural networks have revolutionized the field of data science, yielding remarkable solutions in a data-driven manner.  For instance, in the field of mathematical imaging, they have surpassed traditional methods based on convex regularization. However, a fundamental theory supporting the practical applications is still in […]

Super-Pixel Sampler – a Data-driven Approach for Depth Sampling and Reconstruction

Adam Wolff, Shachar Praisler, Ilya Tcenov and Guy Gilboa, “Super-Pixel Sampler – a Data-driven Approach for Depth Sampling and Reconstruction”, accepted to ICRA (Int. Conf. on Robotics and Automation) 2020. Paper See the video of our mechanical prototype Abstract Depth acquisition, based on active illumination, is essential for autonomous and robotic navigation. LiDARs (Light Detection […]

Self-Supervised Unconstrained Illumination Invariant Representation

Damian Kaliroff, Guy Gilboa, arXiv We propose a new and completely data-driven approach for generating an unconstrained illumination invariant representation of images. Our method trains a neural network with a specialized triplet loss designed to emphasize actual scene changes while downplaying changes in illumination. For this purpose we use the BigTime image dataset, which contains […]

Numeric Solutions of Eigenvalue Problems for Generic Nonlinear Operators

Ester Hait-Fraenkel, Guy Gilboa, arXiv Numerical methods for solving linear eigenvalue problem are widely studied and used in science and engineering. In this paper, we propose a generalized numerical method for solving eigenproblems for generic, nonlinear opera- tors. This has potentially wide implications, since most image processing algorithms (e.g. denoising) can be viewed as nonlinear […]

schematic

Energy Dissipating Flows for Solving Nonlinear Eigenpair Problems

Ido Cohen, Guy Gilboa, “Energy dissipating flows for solving nonlinear eigenpair problems”, Journal of Computational Physics 375 (2018), 1138-1158. This work is concerned with computing nonlinear eigenpairs, which model solitary waves and various other physical phenomena. We aim at solving nonlinear eigenvalue problems of the general form $T(u)=\lambda Q(u)$. In our setting $T$ is a […]

schematic diagram

Spectral Total-Variation Local Scale Signatures for Image Manipulation and Fusion

  Ester Hait, Guy Gilboa, “Spectral Total-Variation Local Scale Signatures for Image Manipulation and Fusion”, preprint, HAL 01722459, 2018. We propose a unified framework for isolating, comparing and differentiating objects within an image. We rely on the recently proposed total-variation transform, yielding a continuous, multi-scale, fully edge-preserving, local descriptor, referred to as spectral total-variation local […]

picture

Theoretical Analysis of Flows Estimating Eigenfunctions of One-homogeneous Functionals

  Jean-Francois Aujol, Guy Gilboa, Nicolas Papadakis, “Theoretical Analysis of Flows Estimating Eigenfunctions of One-homogeneous Functionals”, accepted to SIAM J. on Imaging Sciences. Nonlinear eigenfunctions, induced by subgradients of one-homogeneous functionals (such as the 1-Laplacian), have shown to be instrumental in segmentation, clustering and image decomposition. We present a class of ows for nding such eigenfunctions, […]

diagram

A Discrete Theory and Efficient Algorithms for Forward-and-Backward Diffusion Filtering

Martin Welk, Joachim Weickert, Guy Gilboa, “A Discrete Theory and Efficient Algorithms for Forward-and-Backward Diffusion Filtering”, preprint. Image enhancement with forward-and-backward (FAB) diffusion lacks a sound theory and is numerically very challenging due to its diffusivities that are negative within a certain gradient range. In our paper we address both problems. First we establish a comprehensive theory for space-discrete […]

diagram

Flows Generating Nonlinear Eigenfunctions

Raz Nossek, Guy Gilboa, “Flows Generating Nonlinear Eigenfunctions”, J. of Scientific Computing , Volume 75, Issue 2, pp 859–888, 2018. Image above: Eigenfunction of TGV found by the proposed flow. Abstract: Nonlinear variational methods have become very powerful tools for many image processing tasks. Recently a new line of research has emerged, dealing with nonlinear […]

picture

Blind Facial Image Quality Enhancement using Non-Rigid Semantic Patches

Ester Hait, Guy Gilboa, “Blind Facial Image Quality Enhancement using Non-Rigid Semantic Patches”, accepted to IEEE Trans. Image Processing, 2017. Abstract: We propose to combine semantic data and registration algorithms to solve various image processing problems such as denoising, super-resolution and color-correction. It is shown how such new techniques can achieve significant quality enhancement, both […]

Semi-Inner-Products for Convex Functionals and Their Use in Image Decomposition

Guy Gilboa, Journal of Mathematical Imaging and Vision (JMIV), Vol. 57, No. 1, pp. 26-42, 2017. Abstract: Semi-inner-products in the sense of Lumer are extended to convex functionals. This yields a Hilbert-space like structure to convex functionals in Banach spaces. In particular, a general expression for semi-inner-products with respect to one homogeneous functionals is given. Thus one […]

face photograph

Nonlinear Spectral Image Fusion

M Benning, M. Moeller, R. Nossek, M. Burger, D. Cremers, G. Gilboa, C. Schoenlieb, “Nonlinear Spectral Image Fusion”, Proc. Scale-Space and Variational Methods (SSVM), 2017. Abstract: In this paper we demonstrate that the framework of nonlinear spectral decompositions based on total variation (TV) regularization is very well suited for image fusion as well as more […]

diagram

In Situ Target-Less Calibration of Turbid Media

1. O. Spier, T. Treibitz, G. Gilboa, “In situ target-less calibration of turbid media”, Int. Conf. on Computational Photography (ICCP), Stanford Univ., 2017. Abstract: The color of an object imaged in a turbid medium varies with distance and medium properties, deeming color an unstable source of information. Assuming 3D scene structure has become relatively easy to estimate, the […]

photograph

Robust Recovery of Heavily Degraded Depth Measurements

G. Drozdov, Y. Shapiro, G. Gilboa, “Robust recovery of heavily degraded depth measurements”, Int. Conf. On 3D Vision (3DV), Stanford University, 2016. Abstract: The revolution of RGB-D sensors is advancing towards mobile platforms for robotics, autonomous vehicles and consumer hand-held devices. Strong pressures on power consumption and system price require new powerful algorithms that can robustly handle very low […]

picture

A Depth Restoration Occlusionless Temporal Dataset

D. Rotman, G. Gilboa, “A depth restoration occlusionless temporal dataset”, Int. Conf. On 3D Vision (3DV), Stanford University, 2016. Abstract: Depth restoration, the task of correcting depth noise and artifacts, has recently risen in popularity due to the increase in commodity depth cameras. When assessing the quality of existing methods, most researchers resort to the popular Middlebury dataset; however, […]

photograph

Spectral Decompositions using One-Homogeneous Functionals

Martin Burger, Guy Gilboa, Michael Moeller, Lina Eckardt, Daniel Cremers “Spectral Decompositions using One-Homogeneous Functionals”, SIAM Journal on Imaging Sciences, Vol. 9, No. 3, pp. 1374-1408, 2016. Abstract: This paper discusses the use of absolutely one-homogeneous regularization functionals in a variational, scale space, and inverse scale space setting to define a nonlinear spectral decomposition of […]

image

Separation Surfaces in the Spectral TV Domain for Texture Decomposition

Dikla Horesh and Guy Gilboa, “Separation Surfaces in the Spectral TV Domain for Texture Decomposition”, IEEE Trans. Image Processing, Vol. 25, No. 9, pp. 4260 – 4270, 2016. Abstract: In this paper we introduce a novel notion of separation surfaces for image decomposition. A surface is embedded in the spectral total-variation (TV) three dimensional domain and […]

function

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 […]

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 […]

photography

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. […]

photograph

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 […]

diagram

A spectral framework for one-homogeneous functionals

M. Burger, L. Eckardt, G. Gilboa, M. Moeller, “A spectral framework for one-homogeneous functionals”, Proc. Scale Space and Variational Methods in Computer Vision (SSVM), 2015. Abstract: This paper discusses a generalization of spectral representations related to convex one-homogeneous regularization functionals, e.g. total variation or $\ell^1$-norms. Those functionals serve as a substitute for a Hilbert space […]

image

Multiscale Texture Orientation Analysis using Spectral Total-Variation Decomposition

D. Horesh, G. Gilboa, “Multiscale orientation detection using the total variation transform”, Proc. Scale Space and Variational Methods in Computer Vision (SSVM), 2015. Abstract: Multi-level texture separation can considerably improve texture analysis, a significant component in many computer vision tasks. This paper aims at obtaining precise local texture orientations of images in a multiscale manner, […]

photograph

Fundamentals of Non-local Total Variation Spectral Theory

J.-F. Aujol, G. Gilboa, N. Papadakis, “Non local total variation spectral framework”, Proc. Scale Space and Variational Methods in Computer Vision (SSVM), 2015. Abstract: Eigenvalue analysis based on linear operators has been extensively used in signal and image processing to solve a variety of problems such as segmentation, dimensionality reduction and more. Recently, nonlinear spectral […]

photograph

A Total Variation Spectral Framework for Scale and Texture Analysis

G. Gilboa, “A Total Variation Spectral Framework for Scale and Texture Analysis”, SIAM Journal on Imaging Sciences, Vol. 7, No. 4, pp. 1937–1961, 2014. Abstract: A new total variation (TV) spectral framework is presented. A TV transform is proposed which can be interpreted as a spectral domain, where elementary TV features, like disks, approach impulses. A […]

image

Nonlinear Band-Pass Filtering Using the TV Transform

G. Gilboa, “Nonlinear Band-Pass Filtering Using the TV Transform”, Proc. European Signal Processing Conference (EUSIPCO-2014), Lisbon, pp. 1696 – 1700, 2014. Abstract: A distinct family of nonlinear filters is presented. It is based on a new formalism, defining a nonlinear transform based on the TV-functional. Scales in this sense are related to the size of the object and […]

photograph&diagram

Report on the Total Variation Spectral Framework

G. Gilboa, “A Total Variation Spectral Framework for Scale and Texture Analysis”, CCIT Report 833, 2013. Abstract: A new total variation (TV) spectral framework is presented. A TV transform is proposed which can be interpreted as a spectral domain, where elementary TV features, like disks, approach impulses. A reconstruction formula from the pectral to the spatial […]

imeg

A Spectral Approach to Total Variation

G. Gilboa, “A spectral approach to total variation”, Scale-Space and Variational Methods, SSVM 2013, LNCS 7893, p. 36-47, 2013. Abstract: The total variation (TV) functional is explored from a spectral perspective. We formulate a TV transform based on the second time derivative of the total variation flow, scaled by time. In the transformation domain disks yield impulse […]

imeg

Expert regularizers for task specific processing

G. Gilboa, “Expert regularizers for task specific processing”, Scale-Space and Variational Methods, SSVM 2013, LNCS 7893, p. 24-35, 2013 Abstract: This study is concerned with constructing expert regularizers for specific tasks. We discuss the general problem of what is desired from a regularizer, when one knows the type of images to be processed. The aim is to improve […]

imeg

Nonlocal linear image regularization and supervised segmentation

G. Gilboa, S. Osher, “Nonlocal linear image regularization and supervised segmentation”, SIAM Multiscale Mod. Simul. (MMS), Vol. 6, No. 2, pp. 595-630, 2007. Abstract A nonlocal quadratic functional of weighted differences is examined. The weights are based on image features and represent the affinity between different pixels in the image. By prescribing different formulas for the weights, one […]

imeg

Nonlinear Scale Space with Spatially Varying Stopping Time

G. Gilboa, “Nonlinear Scale Space with Spatially Varying Stopping Time”, PAMI, Vol. 30, No. 12, pp. 2175-2187, 2008. Abstract: A general scale space algorithm is presented for denoising signals and images with spatially varying dominant scales. The process is formulated as a partial differential equation with spatially varying time. The proposed adaptivity is semi-local and is in conjunction with the […]

diagram

Estimation of optimal PDE-based denoising in the SNR sense

G. Gilboa, N. Sochen, Y.Y. Zeevi, “Estimation of optimal PDE-based denoising in the SNR sense”, IEEE Trans. on Image Processing Vol. 15, No. 8, pp. 2269-2280, 2006. Abstract: This paper is concerned with finding the best PDE-based denoising process, out of a set of possible ones. We focus either on finding the proper weight of the fidelity term […]

photograph

Nonlocal Convex Functionals for Image Regularization

G. Gilboa, J. Darbon, S. Osher and T. Chan, Nonlocal Convex Functionals for Image Regularization. UCLA CAM Report 06-57 Abstract: We examine weighted nonlocal convex functionals. The weights determine the affinities between different regions in the image and are computed according to image features. The L1 energy of this type can be viewed as a nonlocal extension of […]

MORE TO COME SOON

Older papers will be uploaded within a few weeks