Computer Graphics

Computer Graphics is about digital models for threedimensional geometric objects as well as images. These shapes and images may represent approximations of the real world or could be synthetic, i.e., exist only in the computer. Goals of computer graphics research are the generation of plausible and informative images, and computation with reasonable resources, i.e. in a short amount of time with little storage requirements. The models and algorithms for this task combine knowledge from different areas of mathematics and computer science..

ERC Advanced Grant: EMERGE

Prof. Alexa has been awarded an ERC Advanced Grant for his research project “EMERGE” (“Geometry Processing as Inference”). The European Research Council will finance the project with 2.5 million euros over the next five years. They exclusively fund groundbreaking, innovative and pioneering basic research. The applicants’ scientific excellence and the projects are the sole selection criterion. 

EMERGE aims to use the methods of geometry processing also for the processing of higher-dimensional structures. The hope and central thesis of the project is that the refinement of methods in geometry processing over the last decades will still be successful when extended to higher dimensions and exploit potentials that are complementary to developments in machine intelligence and classical digital signal processing.

Properties of Laplace Operators for Tetrahedral Meshes – Best Paper Award at SGP

In joint work with ETH Zurich we have investigated the properties of different Laplace operators for tetrahedral meshes. The resulting paper has been accepted for presentation at this year’s Symposium on Geometry Processing and received the best paper award. More information on the work, including presentation slides and code, can be found at the project web site (hosted at ETH Zurich).

ABC: A Big CAD Model Dataset For Geometric Deep Learning (CVPR 2019)

We introduce ABC-Dataset, a collection of one million Computer-Aided Design (CAD) models for research of geometric deep learning methods and applications. Each model is a collection of explicitly parametrized curves and surfaces, providing ground truth for differential quantities, patch segmentation, geometric feature detection, and shape reconstruction. Sampling the parametric descriptions of surfaces and curves allows generating data in different formats and resolutions, enabling fair comparisons for a wide range of geometric learning algorithms. As a use case for our dataset, we perform a large-scale benchmark for estimation of surface normals, comparing existing data driven methods and evaluating their performance against both the ground truth and traditional normal estimation methods.

See our project page for more details.

CHI’19: I Can See What You Think: The Mental Image Revealed by Gaze Tracking

Humans involuntarily move their eyes when retrieving an image from memory. This motion is often similar to actually observing the image. We suggest to exploit this behavior as a new modality in human computer interaction, using the motion of the eyes as a descriptor of the image. Interaction requires the user’s eyes to be tracked but no voluntary physical activity. We perform a controlled experiment and develop matching techniques using machine learning to investigate if images can be discriminated based on the gaze patterns recorded while users merely think about image. Our results indicate that image retrieval is possible with an accuracy significantly above chance. We also show that this result generalizes to images not used during training of the classifier and extends to uncontrolled settings in a realistic scenario.

Check out our project page for more details.

Siggraph Asia 2018: Tracking the Gaze on Objects in 3D: How do People Really Look at the Bunny?


We provide the first large dataset of human fixations on physical 3D objects presented in varying viewing conditions and made of different materials. Our experimental setup is carefully designed to allow for accurate calibration and measurement. We estimate a mapping from the pair of pupil positions to 3D coordinates in space and register the presented shape with the eye tracking setup. By modeling the fixated positions on 3D shapes as a probability distribution, we analysis the similarities among different conditions. The resulting data indicates that salient features depend on the viewing direction. Stable features across different viewing directions seem to be connected to semantically meaningful parts. We also show that it is possible to estimate the gaze density maps from view dependent data. The dataset provides the necessary ground truth data for computational models of human perception in 3D.

Check out our project page for more details.

Siggraph Asia 2018: Factor Once: Reusing Cholesky Factorizations on Sub-Meshes

A common operation in geometry processing is solving symmetric and positive semi-definite systems on a subset of a mesh with conditions for the vertices at the boundary of the region. This is commonly done by setting up the linear system for the sub-mesh, factorizing the system (potentially applying preordering to improve sparseness of the factors), and then solving by back-substitution. This approach suffers from a comparably high setup cost for each local operation. We propose to reuse factorizations defined on the full mesh to solve linear problems on sub-meshes. We show how an update on sparse matrices can be performed in a particularly efficient way to obtain the factorization of the operator on a sun-mesh significantly outperforming general factor updates and complete refactorization. We analyze the resulting speedup for a variety of situations and demonstrate that our method outperforms factorization of a new matrix by a factor of up to 10 while never being slower in our experiments.

See our project page for more details.

Prof. Alexa selected as Editor-in-Chief of ACM Transactions on Graphics

Prof. Alexa has been selected as Editor in Chief of ACM Transactions on Graphics (TOG), the leading technical journal in the field of computer graphics.

Prof. Alexa elected as Fellow of Eurographics

Each year, the European Association for Computer Graphics elects up to three members for their longstanding contributions to be Fellows of the Association. Prof. Alexa has been elected as one of two new Fellows in 2018. Citation and more information.

Siggraph Asia 2017: Localized solutions of sparse linear systems for geometry processing

Computing solutions to linear systems is a fundamental building block of many geometry processing algorithms. In many cases the Cholesky factorization of the system matrix is computed to subsequently solve the system, possibly for many right-hand sides, using forward and back substitution. We demonstrate how to exploit sparsity in both the right-hand side and the set of desired solution values to obtain significant speedups. The method is easy to implement and potentially useful in any scenarios where linear problems have to be solved locally. We show that this technique is useful for geometry processing operations, in particular we consider the solution of diffusion problems. All problems profit significantly from sparse computations in terms of runtime, which we demonstrate by providing timings for a set of numerical experiments.

See the project page for more details.