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.
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The paper "Radiative Backpropagation with Non-Static Geometry" has been accepted to EGSR 2025. It extends the theory of radiative backpropagation, which is a technique for efficient physically-based differentiable rendering, to account for the derivatives with respect to geometry movement. This is, for example, required in the context of 3D reconstruction.
Two papers were submitted to SIGGRAPH Asia 2023 by CG group members and both have been accepted, published in ACM Transactions on Graphics (Vol. 42, Issue 6). The contributions are an interactive method for modeling spline surfaces based on curvature handles ("K-surfaces: Bézier-Splines Interpolating at Gaussian Curvature Extrema") and techniques for robust inverse rendering with parametric spline surfaces ("Differentiable Rendering of Parametric Geometry").
Next week on Tuesday 21.11 at 15:00 there will be a talk on "Higher-Order Meshing with Hard Guarantees" by Prof. Campen in MAR 6.051. He is part of the Computer Graphics Group at the University of Osnabrück.
Feel free to attend if you are interested in current research in CG or looking for your own project/seminar ideas.
We launched a new beta version of our new website. If you find any error, inconvenience or have general feedback feel free to write Ugo an e-mail. The old website is still available under www.cg.tu-berlin.de
We present tools for generating planar embeddings of triangulated topological spheres using a representation based on Schnyder labelings. These linear algorithms use only integers, enabling exact computations. The fast conversion between representations enables efficient fixing of flipped triangles in planar triangulations and is significantly faster than existing robust approaches.
More info at the project page.
The As-Rigid-As-Possible Surface Modeling paper of Olga Sokine-Hornung and Marc Alexa won the test of time award of this years Symposium on Geometry Processing. Unfortunatly Olga was not able to attend the event, so Marc presented how the paper was born, at least from his perspective.
Over a decade after the original ARAP Paper was published, we found a derivation of the continous energy presented by Chao et. al. using a discontinous transformation function. This perspective helped us to understand the flaws of the original energy. We where able to fix the problem of divergence and the problem of asymetries in the results of Chao et. al.
In the footsteps of the original paper, this work will also be presented at the SGP (within the International Graphics Summit 2023).
More info at the project page.
We show how shadow mapping, a method for approximating visibility in real-time graphics, can be made differentiable. Our central observation is that pre-filtered shadow mapping, in combination with differentiable rasterizers, permits the efficient generation of shadow derivatives. In gradient-based optimizations, differentiable rasterizers with shadow mapping can be an efficient alternative to differentiable ray tracing. The paper has been accepted to CVPR 2023. Additional information, including a presentation video and the source code, can be found on the project page.
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.
CG group members submitted two papers to CVPR 2022 and both were accepted. Markus Worchel’s work Multi-View Mesh Reconstruction with Deferred Shading is on recovering geometry from calibrated input images based on neural shading. Marc Alexa’s Super-Fibonacci Spirals provide a simple method for quickly generating orientation samples with low discrepancy.
We developed a normal driven stylization tool. The set of preferred normals can be chosen arbitrarily from the Gauss sphere, including semi-discrete sets to model preference for cylinder- or cone-like shapes. The resulting paper has been accepted for presentation at this year’s Symposium on Geometry Processing. We created a project web site. where you can find more information like the presentation video and code.
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).
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.
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.
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.
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 has been selected as Editor in Chief of ACM Transactions on Graphics (TOG), the leading technical journal in the field of computer graphics.
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.
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.
We present HeatSpace, a system that records and empirically analyzes user behavior in a space and automatically suggests positions and sizes for new displays. The system uses depth cameras to capture 3D geometry and users’ perspectives over time. To derive possible display placements, it calculates volumetric heatmaps describing geometric persistence and planarity of structures inside the space. It evaluates visibility of display poses by calculating a volumetric heatmap describing occlusions, position within users’ field of view, and viewing angle. Optimal display size is calculated through a heatmap of average viewing distance. Based on the heatmaps and user constraints we sample the space of valid display placements and jointly optimize their positions. This can be useful when installing displays in multi-display environments such as meeting rooms, offices, and train stations.
Please see the paper for details.
Mass market digital manufacturing devices are severely limited in accuracy and material, resulting in a significant gap between the appearance of the virtual and the real shape. In imaging as well as rendering of shapes, it is common to enhance features so that they are more apparent. We provide an approach for feature enhancement that directly operates on the geometry of a given shape, with particular focus on improving the visual appearance for 3D printing. The technique is based on unsharp masking, modified to handle arbitrary free-form geometry in a stable, efficient way, without causing large scale deformation. On a series of manufactured shapes we show how features are lost as size of the object decreases, and how our technique can compensate for this. We evaluate this effect in a human subject experiment and find significant preference for modified geometry.
We present an approach to alter the perceived appearance of physical objects by controlling their surrounding space. Many real-world objects cannot easily be equipped with displays or actuators in order to change their shape. While common approaches such as projection mapping enable changing the appearance of objects without modifying them, certain surface properties (e. g. highly reflective or transparent surfaces) can make employing these techniques difficult. In this work, we present a conceptual design exploration on how the appearance of an object can be changed by solely altering the space around it, rather than the object itself. In a proof-of-concept implementation, we place objects onto a tabletop display and track them together with users to display perspective-corrected 3D graphics for augmentation. This enables controlling properties such as the perceived size, color, or shape of objects. We characterize the design space of our approach and demonstrate potential applications. For example, we change the contour of a wallet to notify users when their bank account is debited. We envision our approach to gain in importance with increasing ubiquity of display surfaces.
Please see our project page for more details.
We define Voronoi cells and centroids based on heat diffusion. These heat cells and heat centroids coincide with the common definitions in Euclidean spaces. On curved surfaces they compare favorably with definitions based on geodesics: they are smooth and can be computed in a stable way with a single linear solve. We analyze the numerics of this approach and can show that diffusion diagrams converge quadratically against the smooth case under mesh refinement, which is better than other common discretization of distance measures in curved spaces. By factorizing the system matrix in a preprocess, computing Voronoi diagrams or centroids amounts to just back-substitution. We show how to localize this operation so that the complexity is linear in the size of the cells and not the underlying mesh. We provide several example applications that show how to benefit from this approach.
See the project page for more details.
Slicing is the procedure necessary to prepare a shape for layered manufacturing. There are degrees of freedom in this process, such as the starting point of the slicing sequence and the thickness of each slice. The choice of these parameters influences the manufacturing process and its result: the number of slices significantly affects the time needed for manufacturing, while their thickness affects the error. Assuming a discrete setting, we measure the error as the number of voxels that are incorrectly assigned due to slicing. We provide an algorithm that generates, for a given set of available slice heights and a shape, a slicing that is provably optimal. By optimal we mean that the algorithm generates sequences with minimal error for any possible number of slices. The algorithm is fast and flexible, it can accommodate a user driven importance modulation of the error function and allows the interactive exploration of the desired quality/time tradeoff.
We can demonstrate the practical importance of our optimization on several 3D-printed results.
The technical background is described in a paper that now appeared in ACM TOG.
We present physical interfaces that change their appearance through controlled transparency. These transparency-controlled physical interfaces are well suited for applications where communication through optical appearance is sufficient, such as ambient display scenarios. They transition between perceived shapes within milliseconds, require no mechanically moving parts and consume little energy. We build 3D physical interfaces with individually controllable parts by laser cutting and folding a single sheet of transparency-controlled material. We explore the benefits of transparency-controlled physical interfaces by characterizing their design space and showcase four physical prototypes.
Please see our project page for more details.
Our work was featured on Fast Company Co.Design, Vice Motherboard and Futurism.
We investigate human viewing behavior on physical realizations of 3D objects. Using an eye tracker with scene camera and fiducial markers we are able to gather fixations on the surface of the presented stimuli. This data is used to validate assumptions regarding visual saliency so far only experimentally analyzed using flat stimuli. We provide a way to compare fixation sequences from different subjects as well as a model for generating test sequences of fixations unrelated to the stimuli. This way we can show that human observers agree in their fixations for the same object under similar viewing conditions – as expected based on similar results for flat stimuli. We also develop a simple procedure to validate computational models for visual saliency of 3D objects and use it to show that popular models of mesh salience based on the center surround patterns fail to predict fixations.
Please see our project page for more details.
Learning expressive curve styles from example is crucial for interactive or computer-based narrative illustrations. We propose a method for online synthesis of free-hand drawing styles along arbitrary base paths by means of an autoregressive Markov Model. Choice on further curve progression is made while drawing, by sampling from a series of previously learned feature distributions subject to local curvature. The algorithm requires no user adjustable parameters other than one short example style. It may be used as a custom “random brush” designer in any task that requires rapid placement of a large number of detail-rich shapes that are tedious to create manually.
See the project page for more details.
We consider the problem of manufacturing free-form geometry with classical manufacturing techniques, such as mold casting or 3-axis milling. We determine a set of constraints that are necessary for manufacturability and then decompose and, if necessary, deform the shape to satisfy the constraints per segment. We show that many objects can be generated from a small number of (mold-)pieces if some deformation is acceptable. We provide examples of actual molds and the resulting manufactured objects.
See the project page for more details.
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Panono’s panoramic camera, originally developed as a thesis work by CG alumnus Jonas Pfeil is now in it’s second revision and has been selected one of the 36 coolest gadgets in 2014 by CNN.
Prof. Alexa receives the Outstanding Technical Contributions Award of Eurographics. The award is “given each year to an individual in computer graphics to highlight some outstanding technical achievement.”
The award has been presented at the yearly main conference of Eurographics, which took place in Strasbourg, France this year.
Prominently featured in an episode of The Simpson was CG alumnus Andy Nealen’s game, Osmos: Milhouse had his iPad stolen on “The Simpsons.” When he finds it in Bart’s possession and begins to confront him, he is entranced by “the music of this bubble game.”
Prof. Alexa has been elected to the executive board of the Hybrid Plattform. He had been active in trans-disciplinary projects for years, strongly believing that this keeps science and research well-grounded.
Prof. Alexa had been elected to chair the technical program of SIGGRAPH 2013. SIGGRAPH regularly gathers thousands of scientists and professionals in the visual effects industry, and its technical program is the most prestigious and selective in the field. On the left, he opens the fast forward, a 30 second presentation for each of the accepted papers.
Most additive manufacturing technologies work by layering, i.e. slicing the shape and then generating each slice independently. This introduces an anisotropy into the process, often as different accuracies in the tangential and normal directions, but also in terms of other parameters such as build speed or tensile strength and strain. We model this as an anisotropic cubic element. Our approach then finds a compromise between modeling each part of the shape individually in the best possible direction and using one direction for the whole shape part. In particular, we compute an orthogonal basis and consider only the three basis vectors as slice normals (i.e. fabrication directions). Then we optimize a decomposition of the shape along this basis so that each part can be consistently sliced along one of the basis vectors.
In simulation, we show that this approach is superior to slicing the whole shape in one direction, only. It also has clear benefits if the shape is larger than the build volume of the available equipment.
The Dagstuhl seminar on ‘Computational Aspects of Fabrication’ organized by Alexa, Bickel, Matusik, McMains, Rushmeier has been accepted. More information here.
A radio feature about our recent research on sketch-based based modeling and sketch recognition on Deutschlandradio Kultur (German only): DRadio Kultur - Strichzeichnungen
We develop a system for 3D object retrieval based on sketched feature lines as input. For objective evaluation, we collect a large number of query sketches from human users that are related to an existing data base of objects. The sketches turn out to be generally quite abstract with large local and global deviations from the original shape. Based on this observation, we decide to use a bag-of-features approach over computer generated line drawings of the objects. We develop a targeted feature transform based on Gabor filters for this system. We can show objectively that this transform is better suited than other approaches from the literature developed for similar tasks. Moreover, we demonstrate how to optimize the parameters of our, as well as other approaches, based on the gathered sketches. In the resulting comparison, our approach is significantly better than any other system described so far.
Please see our project page for more details.
Humans have used sketching to depict our visual world since prehistoric times. Even today, sketching is possibly the only rendering technique readily available to all humans. This paper is the first large scale exploration of human sketches. We analyze the distribution of non-expert sketches of everyday objects such as ‘teapot’ or ‘car’. We ask humans to sketch objects of a given category and gather 20,000 unique sketches evenly distributed over 250 object categories. With this dataset we perform a perceptual study and find that humans can correctly identify the object category of a sketch 73% of the time. We compare human performance against computational recognition methods. We develop a bag-of-features sketch representation and use multi-class support vector machines, trained on our sketch dataset, to classify sketches. The resulting recognition method is able to identify unknown sketches with 56% accuracy (chance is 0.4%). Based on the computational model, we demonstrate an interactive sketch recognition system. We release the complete crowd-sourced dataset of sketches to the community.
Please see our project page for more details.
We introduce an algorithm and representation for fabricating 3D shape abstractions using mutually intersecting planar cut-outs. The planes have prefabricated slits at their intersections and are assembled by sliding them together. Based on an analysis of construction rules, we propose an extended binary space partitioning tree as an efficient representation of such cardboard models which allows us to quickly evaluate the feasibility of newly added planar elements. The complexity of insertion order quickly increases with the number of planar elements and manual analysis becomes intractable. We provide tools for generating cardboard sculptures with guaranteed constructibility.
