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Geometric deep learning: going beyond Euclidean data

Related publications (73)

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Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson, Iva Bogdanova Vandergheynst

We propose here some basic approaches to direct processing of the

360^o

-images as we take into consideration the geometry of each one. Obviously, the geometry of each of these images is a consequence of the geometry of the sensor's mirror used. This tech ...

2005

Point-based computer graphics

Mark Pauly

This course introduces points as a powerful and versatile graphics primitive. Speakers present their latest concepts for the acquisition, representation, modeling, processing, and rendering of point sampled geometry along with applications and research dir ...

Association for Computing Machinery2004

Implicit Meshes for Surface Reconstruction

Pascal Fua, Slobodan Ilic

Deformable 3--D models are used extensively in Computer Graphics and Computer Vision for Visualization, Animation and Modeling. They can be represented either as traditional explicit surfaces, such as triangulated meshes, or as implicit surfaces. Explicit ...

2004

Interactive 3D painting on point-sampled objects

Mark Pauly

We present a novel painting system for 3D objects. In order to overcome parameterization problems of existing applications, we propose a unified sample-based approach to represent geometry and appearance of the 3D object as well as the brush surface. The g ...

Eurographics Association2004

Rate-distortion optimal mesh simplification for communications

Laurent Balmelli

The thesis studies the optimization of a specific type of computer graphic representation: polygon-based, textured models. More precisely, we focus on meshes having 4-8 connectivity. We study a progressive and adaptive representation for textured 4-8 meshe ...

EPFL2002

Mesh Optimization Using Global Error with Application to Geometry Simplification

Martin Vetterli, Thomas Liebling, Laurent Balmelli

Meshes with (recursive) subdivision connectivity, such as subdivision surfaces, are increasingly popular in computer graphics. They present several advantages over their Delaunay-type based counterparts, e.g., Triangulated Irregular Networks (TINs), such a ...

Elsevier2002

Splines and wavelets for image warping and projection

Stefan Horbelt

This thesis investigates advanced signal processing concepts and their application to geometric processing and transformations of images and volumes. In the first part, we discuss the class of transformations that project volume data onto a plane using par ...

EPFL2001

3D surface cellular automata and their applications

Stéphane Gobron

This paper describes the generation and rendering of three-dimensional (3D) surface cellular automata (CA). Our model’s main advantage is that it gives direct texturing simulation based on the actual shape of anytriangulated input object. We first introduc ...

1999

Microstereolithography: a new process to build complex 3D objects

Philippe Renaud, Arnaud Bertsch

In this paper, a new microstereolithography apparatus is described. It is an integral process in which a complete layer can be made in one exposure only, in contrast to vector-by-vector processes which are based on the vectorial tracing of each layer. As f ...

1999

New results about 3D digital lines

The current definition of 3D digital lines, which uses the 2D digital lines of closest integer points (Bresenham's lines) of two projections, has several drawbacks: the discrete topology of this 3D digital line notion is not clear; its third projection is, ...

SPIE-Int. Soc. Opt. Eng1996

Laplacian Operator, Diffusion Flow and Active Contour on non-Euclidean Images

Jean-Philippe Thiran, Pierre Vandergheynst, Xavier Bresson, Iva Bogdanova Vandergheynst

We propose here some basic approaches to direct processing of the

360^o

-images as we take into consideration the geometry of each one. Obviously, the geometry of each of these images is a consequence of the geometry of the sensor's mirror used. This tech ...

2005