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Operator Based Representations for Geometry Processing

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... ver más

31/12/2022

TECHNION ISRAEL I...

2M€

Presupuesto del proyecto: 2M€

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TECHNION ISRAEL INSTITUTE OF TECHNOLOGY No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

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Financiación concedida El organismo H2020 notifico la concesión del proyecto el día 2022-12-31

ERC-2016-STG: ERC Starting Grant Scope:Objectives

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2 Participantes

TECHNION ISRAEL INSTITUTE O...

1.50M€ | Lider

BELLOTA HERRAMIENTAS

303.92K€ | Participante

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Duración del proyecto: 72 meses Fecha Inicio: 2016-12-07
Fecha Fin: 2022-12-31

Líder del proyecto

TECHNION ISRAEL INSTITUTE OF TECHNOLOGY No se ha especificado una descripción o un objeto social para esta compañía.

TRL 4-5

Presupuesto del proyecto 2M€

Fecha límite de participación Sin fecha límite de participación.

Descripción del proyecto 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.

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