OPREP
Financiado
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...
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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Duración del proyecto: 72 meses
Fecha Inicio: 2016-12-07
Fecha Fin: 2022-12-31
Fecha Fin: 2022-12-31
Línea de financiación: concedida
El organismo H2020 notifico la concesión del proyecto el día 2022-12-31
Línea de financiación objetivo
El proyecto se financió a través de la siguiente ayuda:
ERC-2016-STG:
ERC Starting Grant
Cerrada
hace 9 años
Presupuesto
El presupuesto total del proyecto asciende a
2M€
Líder del proyecto
TECHNION ISRAEL INSTITUTE OF TECHNOLOGY
No se ha especificado una descripción o un objeto social para esta compañía.
Perfil tecnológico
TRL
4-5
Perfil tecnológico
TRL
4-5
303.92K€ |
Participante