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Operator Based Representations for Geometry Processing

Total Cost €


EC-Contrib. €






Project "OPREP" data sheet

The following table provides information about the project.


Organization address
city: HAIFA
postcode: 32000

contact info
title: n.a.
name: n.a.
surname: n.a.
function: n.a.
email: n.a.
telephone: n.a.
fax: n.a.

 Coordinator Country Israel [IL]
 Project website
 Total cost 1˙500˙000 €
 EC max contribution 1˙500˙000 € (100%)
 Programme 1. H2020-EU.1.1. (EXCELLENT SCIENCE - European Research Council (ERC))
 Code Call ERC-2016-STG
 Funding Scheme ERC-STG
 Starting year 2017
 Duration (year-month-day) from 2017-01-01   to  2021-12-31


Take a look of project's partnership.

# participants  country  role  EC contrib. [€] 


 Project objective

Geometric data is prevalent in many areas of science and technology. From the surface of the brain to the intricate shapes of free-form architecture, complex geometric structures arise in many fields, and problems such as analysis, processing and synthesis of geometric data are of great importance. One major challenge in tackling such problems is choosing an adequate discrete representation of the geometric data. Traditionally, surface geometric data is treated as an irregularly sampled signal in three-dimensional space, yielding a representation as either a point cloud, or a polygonal mesh. Further analysis and manipulation are done directly on this discrete representation, resulting in algorithms which are often combinatorial, leading to difficult numerical optimization problems. The goal of this research is to explore a fundamentally different approach of representing geometric data through the space of scalar functions defined on it, and representing geometric operations as algebraic manipulations of linear operators acting on such functions. We will investigate the basic theory behind such a representation, addressing questions such as: what are the best function spaces to work with? Which operators can be consistently discretized, leading to discrete theorems analogous to continuous ones? How should multi-scale processing of geometric data be treated in this novel representation? To validate our approach, we will explore how this representation can be leveraged for devising efficient solutions to difficult real-world geometry processing problems, such as numerical simulation of intricate phenomena on curved surfaces, surface correspondence and quadrangular remeshing. By shifting the focus from geometry-centric representations and considering instead shapes through the lens of functional operators, we could potentially lay the ground for a fundamental change in the way that geometric data is treated and understood.


year authors and title journal last update
List of publications.
2019 Orestis Vantzos, Saar Raz, Mirela Ben-Chen
Real-time viscous thin films
published pages: 1-10, ISSN: 0730-0301, DOI: 10.1145/3272127.3275086
ACM Transactions on Graphics 37/6 2019-09-04
2019 David Cohen, Mirela Ben-Chen
Generalized volumetric foliation from inverted viscous flow
published pages: 152-162, ISSN: 0097-8493, DOI: 10.1016/j.cag.2019.05.015
Computers & Graphics 82 2019-09-04
2019 Yu Wang, Mirela Ben-Chen, Iosif Polterovich, Justin Solomon
Steklov Spectral Geometry for Extrinsic Shape Analysis
published pages: 1-21, ISSN: 0730-0301, DOI: 10.1145/3152156
ACM Transactions on Graphics 38/1 2019-09-04
2019 Or Yair, Mirela Ben-Chen, Ronen Talmon
Parallel Transport on the Cone Manifold of SPD Matrices for Domain Adaptation
published pages: 1797-1811, ISSN: 1053-587X, DOI: 10.1109/tsp.2019.2894801
IEEE Transactions on Signal Processing 67/7 2019-09-04
2019 Danielle Ezuz, Justin Solomon, Mirela Ben-Chen
Reversible Harmonic Maps between Discrete Surfaces
published pages: 1-12, ISSN: 0730-0301, DOI: 10.1145/3202660
ACM Transactions on Graphics 38/2 2019-09-04
2018 Nahum Farchi, Mirela Ben-Chen
Integer-only cross field computation
published pages: 1-13, ISSN: 0730-0301, DOI: 10.1145/3197517.3201375
ACM Transactions on Graphics 37/4 2019-09-04
2018 Omri Azencot, Orestis Vantzos, Mirela Ben‐Chen
An explicit structure‐preserving numerical scheme for EPDiff
published pages: 107-119, ISSN: 1467-8659, DOI: 10.1111/cgf.13495
Computer Graphics Forum 37/5 2019-09-04
2017 Danielle Ezuz, Mirela Ben-Chen
Deblurring and Denoising of Maps between Shapes
published pages: 165-174, ISSN: 0167-7055, DOI: 10.1111/cgf.13254
Computer Graphics Forum 36/5 2019-06-13
2017 Omri Azencot, Etienne Corman, Mirela Ben-Chen, Maks Ovsjanikov
Consistent functional cross field design for mesh quadrangulation
published pages: 1-13, ISSN: 0730-0301, DOI: 10.1145/3072959.3073696
ACM Transactions on Graphics 36/4 2019-06-13

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