I am a Juniorprofessor (assistant professor) at Otto-von-Guericke Universität Magdeburg where I am affiliated with the Institute for Simulation and Graphics. My research centers around the development of quantitatively effective image synthesis techniques, for examples for augmented reality and visualizations in architecture and design. I also work on other questions in computer graphics, computational science, and applied mathematics, such as the processing of geometry and the simulation of fluids.

- In the fall / winter 2020/21 term I will be teaching the following courses (please see the LSF links for details; all information subject to change until 16/10/2020!):
- GPU Programmierung (Lecture, B.Sc.)
- Scientific Computing II: Introduction to Dynamical Systems (Lecture, B.Sc. / M.Sc.)
- Scientific Computing V: Structure Preserving Simulations and Geometric Mechanics (Lecture, M.Sc.)
- Mathematics and Numerics of Deep Neural Networks for Physical Simulations (Seminar, M.Sc., with Thomas Richter)

- October 2020: My work on Psiec, a local spectral exterior calculus, has been accepted to Applied and Computational Harmonic Analysis. A reference implementation is available on the project page.
- Nils Margenberg, Dirk Hartmann, Thomas Richter and myself just uploaded our manuscript A neural network multigrid solver for the Navier-Stokes equations to the ArXiv. In the work we show how a multigrid solver and neural networks can be combined to improve the overall efficiency of simulations of the Navier-Stokes equations.
- Thomas Richter (from the Dept. of Mathematics) and myself will be offering a seminar on the use of neural networks and deep learning for physical simulations in the fall / winter term 2020/21.
- The Question and Answer session for my paper Local Fourier Slice Photography at Siggraph 2020 will be 24. August 2020 from 2:00 - 2:30 PST.
- I wrote a small note for my tensor analysis class that details why the anti-symmetry of differential forms is required for the covariance of the exterior derivative. Perhaps other people find this useful as well.
- June 2020: A trailer for my Siggraph presentation in July is now available.
- May 2020: I am part of the new Sonderforschungsbereich "BULK REACTION" funded by the DFG. The official press release can be found here.
- March 2020: Our joint work with Boyko Dodov, Henk Dijkstra, and Themis Sapsis on a local spectral exterior calculus on the sphere is now available on the arXiv. It provides a wavelet-based discretization of Cartan's exterior calculus of differential forms. We demonstrate its numerical practicality with simulations of the rotating shallow water equations.
- April 2020: My work on Local Fourier Slice Photography has been published in ACM Transactions of Graphics. I will also present it at Siggraph 2020. Resources are available on the project page.
- March 2020: This year's Turing award goes to Ed Catmull and Pat Hanrahan. Congratulations Ed and Pat!
- March 2020: I will be offering two scientific team projects in Spring/Summer 2020, one on StyleGAN, which is a generative adversarial network architecture for generating images, and a second one on how to augment physical simulations (e.g. of a pendulum or a bouncing ball) with neural networks to remove some of the idealizations that are typically made for these (e.g. neglect of friction or highly simplistic elasticity models). Please get in touch with me if you are interested in one of the projects. Due to the dynamics of the current health situation the format is not clear yet. Please regularly check the university website for updates or contact me via email.
- March 2020: I will be teaching WR I: Einführung in das Wissenschaftliche Rechnen and WR IV: Tensor analysis, vector calculus and applications in Spring/Summer 2020. Due to the dynamics of the current health situation the format of the courses is not clear yet. Please regularly check the course websites as well as the university website for updates or contact me via email.
- February 2020: My work on Local Fourier Slice Photography will appear in ACM Transactions of Graphics. I will also present it at Siggraph 2020. Resources are available on the project page.
- November 2019: I gave a talk on the construction of divergence free wavelets at the Geophysical Fluid Dynamics Group at FU Berlin. Slides are available here.
- September 2019: In the fall / winter term I am teaching Scientific Computing II on dynamical systems, GPU programming on general purpose computing using GPUs (with a general introduction to parallel programming), and, together with Jan Heiland, a seminar on geometric formulations and discretizations of fluid mechanics. Please see the LSF or get in touch if you have questions on the courses.
- September 2019: A list of some possible B.Sc. or M.Sc. topics I am interested in supervising can be found here.
- September 2019: I gave a seminar talk at NOAA in Boulder on our weather and climate simulation project.
- August 2019: I gave a seminar talk at NOAA in Boulder on our weather and climate simulation project.
- July 2019: I gave a talk at the Workshop on Stochastic Parameterizations and Their Use in Data Assimilation in London.
- I will be teaching Introduction to Scientific Computing, Tensor Analysis, and, together with Jan Heiland, a seminar on geometric formulations and discretizations of fluid mechanics.
- February 2019: My work on divergence free wavelets is now available on the publisher's website. A reference implementation can be found on the project page.
- February 2019: Our abstract A Local Spectral Exterior Calculus for the Primitive Equations has been accepted as an oral to the EGU general assembly in Vienna in April. Our collaborators Themis Sapsis and Boyko Dodov will also present other parts of our project on a combined analytic / data-driven weather and climate simulation.
- February 2019: I just uploaded a pre-preprint on Local Fourier Slice Photography that enables post-capture refocus of light fields directly from a compressed wavelet representation.
- November 2018: I just uploaded a preprint on Psiec, a local spectral exterior calculus. It provides a discretization of Cartan's exterior calculus of differential forms based on wavelets. The work also contains a Fourier domain description of exterior calculus in R^n.
- October 2018: I am co-organizing a session on hybrid data-based/dynamical modeling of environmental flows at the European Geosciences Union meeting in Vienna in April. Please consider submitting your work.
- September 2018: I'm teaching GPU programming and Advanced Image Synthesis this term.
- September 2018: My work on divergence free wavelets will appear in Journal of Mathematical Fluid Mechanics. A reference implementation is available on the project page.
- September 2018: A Local Fourier Slice Equation will appear in Optics Express. Please see the project page for our reference implementation.
- June 2018: Some photos from FiumeFest are now available.
- June 2018: We are organizing a workshop on the occasion of Eugene Fiume's 60th birthday. It will be held in Vancouver, BC, on August 17th (Friday after Siggraph). Please get in touch if you would like to be a part of it.
- Joint work with Fabian Martins, Clauson Carvalho da Silva, and Katharina Zähringer on PIV measurements in complex flow beds has been accepted to Journal of Advanced Optics and Photonics. Details coming soon.
- May 2018: I gave a talk about divergence free wavelets at Themis Sapsis' Sandlab at MIT.
- May 2018: I just uploaded two manuscripts to the ArXiv. Polar Wavelets in Space establishes closed form spatial representations for polar wavelets in two and three dimensions. We also provide two applications that demonstrate the numerical benefits of our result. Divergence Free Polar Wavelets introduces a tight frame of divergence free wavelets that provides an extension of polar wavelets to the vector-valued setting. The wavelets have many desirable properties and, among other things, we prove that in two dimensions the wavelets attain, with an appropriate angular localization, the same quasi-optimal approximation rates for piecewise smooth signal that curvelets provide in the scalar setting. We also provide numerical experiments that verify that these theoretical properties also provide practical advantages. A third manuscript on a sparse Fourier slice theorem is coming soon.
- January 2018: Slides from a talk I gave at Peter Benner's group at the Max Planck Institute for Dynamics of Complex Technical Systems about my research.
- September 2017: Some remarks on Monte Carlo integration and the curse of dimensionality..
- June 2017: Work by Philipp Petersen, Martin Schäfer and myself on bendlets, a new shearlet-like transform whose frame functions are sheared, to adapt to the local normal direction of a curve, and also bent, to adapt to the local curvature, was accepted to Applied and Computational Harmonic Analysis.
- May 2017: I will present some work on anti-aliasing at EGSR 2017 in Helsinki
- October 2016: Clauson Carvalho da Silva joined my group as a Ph.D. student. Welcome!
- September 2016: I was visiting George Drettakis' group at INRIA Sophia-Antipolis (slides).
- September 2016: I gave a talk at Nvidia reseach about my work. Slides are available here.
- September 2016: I will be teaching a course on GPU programming this fall.
- September 2016: Acagamics and myself are offering a course on advanced game development this fall.

My research is centered around the development of quantitatively effective image synthesis techniques that ensure computational efficiency, such as optimal or close to optimal convergence rate, and reliable error bounds for the computed image. These techniques are of importance for example for augmented reality, where virtual and real content are superimposed and inconsistencies or delays are immediately apparent, and for visualizations in design and engineering, where informed design decisions are only possible with reliable imagery. My work towards this objective leads me to many interesting questions at the intersection of computer science, mathematical physics, and applied mathematics.

As a basis for quantitatively effective image synthesis techniques I developed in the last years novel foundations for light transport simulation. An important aspect of this programme was a formulation of light transport theory using the language of geometric mechanics. This elucidates the structure of light transport theory and clarifies its connections to other models of light in physics. I also developed a reformulation of the correspondence between pointwise samples, i.e. the information available from ray tracing, and continuous functions, such as the images we would like to compute. The central ingredient for this reformulation are reproducing kernel bases that provide a rigorous yet numerically practical characterization of point samples.

Building on these foundations, I recently developed an image synthesis technique that employs, in a precise technical sense, a (quasi-)optimal number of samples on the image plane. Important questions I am currently addressing are how this technique can be extended to the full light transport problem, how the curse of dimensionality can be broken using non-probabilistic techniques, and how optimal techniques can be obtained for dynamic scenes.

Next to image synthesis, I am also interested in the simulation of phenomena such as fluids and elasticity, and in questions in applied mathematics and mathematical physics.

Representative publications:

C. Lessig, P. Petersen, and M. Schäfer, Bendlets: A second-order shearlet transform with bent elements, Appl. Comput. Harmon. Anal., 2017.

C. Lessig, M. Desbrun, and E. Fiume, A Constructive Theory of Sampling for Image Synthesis Using Reproducing Kernel Bases, ACM Trans. Graph. (Proceedings SIGGRAPH 2014), 33(4), 1–14, 2014.

C. Lessig and A. L. Castro, The Geometry of Phase Space Lifts: From Maxwell's Equations to Radiative Transfer Theory, in Geometry, Mechanics and Dynamics: the Legacy of Jerry Marsden, Springer, 2014.

C. Lessig, Modern Foundations of Light Transport Simulation, Ph.D dissertation, University of Toronto, Toronto, 2012.

C. Lessig, T. de Witt, and E. Fiume, Efficient and Accurate Rotation of Finite Spherical Harmonics Expansions, J. Comp. Phys., 231(2), 243–250, 2012.

C. Lessig and E. Fiume, SOHO: Orthogonal and Symmetric Haar Wavelets on the Sphere, ACM Trans. Graph., 27(1) 2008.

2016 - present

Juniorprofessor (assistant professor) at Otto-von-Guericke Universität Magdeburg

2013 - 2016

Post-doc with Marc Alexa in the computer graphics group at TU Berlin

2012 - 2013

Post-doc with Mathieu Desbrun in the Department of Computing+Mathematical Sciences at the California Institute of Technology

2007 - 2012

Ph.D. student with Eugene Fiume at the University of Toronto (Thesis: Modern Foundations of Light Transport Simulation)

2005 - 2007

M.Sc. student with Eugene Fiume at the University of Toronto (Thesis: Symmetric and Orthogonal Wavelets on the Sphere)

2005 - 2007

Summer intern in the developer technology group at NVIDIA working with Mark Harris

2001 - 2005

Fall 2017

GPU Programming, OVGU Magdeburg.

Fall 2017

Advanced Image Synthesis, OVGU Magdeburg.

Spring 2017

Team Project: Post-Processing for Rendering, OVGU Magdeburg.

Spring 2017

Mathematical Methods for Computer Graphics, OVGU Magdeburg.

Fall 2016

GPU Programming, , OVGU Magdeburg

October 2015

Mathematical Methods for Computer Graphics, University of Toronto.

Fall/Winter 2015

Introduction to Scientific Computing, TU Berlin.

Fall/Winter 2014

Introduction to Scientific Computing, TU Berlin.

Spring/Summer 2014

Computer Graphics 2 (Geometric Representations), TU Berlin.

February 2014

Mathematical Methods for Computer Graphics, University of Toronto.

Fall/Winter 2013

Introduction to Scientific Computing, TU Berlin.

Spring/Summer 2013

Algorithms and Data Structures, TU Berlin.

Fall/Winter 2011

Computer Graphics 1, TU Berlin.

Spring/Summer 2011

Advanced Image Synthesis, TU Berlin.

The course on mathematical methods for computer graphics, which I taught in the last years at the University of Toronto, is an educational project of particular interest to me. Many students with an undergraduate education in computer science lack the mathematical background that is required for research in computer graphics (and related fields such as computer vision and machine learning) and these students hence have to pick up the mathematical tools and concepts required for their research during their Ph.D program. Currently this takes place in an ad-hoc and piecemeal manner. While this provides immediate motivation for the mathematics, it also makes it difficult for students to obtain a comprehensive understanding and to see common principles and structures—aspects that are essential to build on concepts. My course addresses this by teaching the mathematical foundations and methods that are required for computer graphics research. It thereby tries to make the underlying ideas apparent without neglecting abstraction and rigour.

As part of the Jerry Marsden memorial program at the Fields institute in Toronto I taught, together with Alex Castro and Henry Jacobs, an introductory course on geometric mechanics. Material from this course can be found here.

While I was at the University of Toronto I also co-supervised M.Sc. and Ph.D. students.

C. Lessig, Controlling and Sampling Visibility Information on the Image Plane, Eurographics Symposium on Rendering 2017, 2017.

X. Wang, D. Lindlbauer, C. Lessig, and M. Alexa, Accuracy of Monocular Gaze Tracking on 3D Geometry, ETVIS 2015: Workshop on Eye Tracking and Visualization, 2015.

G. Mason, C. Lessig, and M. Desbrun, Discretization of Hamiltonian Incompressible Fluids, in 17th US National Conference of Theoretical and Applied Mathematics, 2014.

C. Lessig and A. L. Castro, The Geometry of Phase Space Lifts: From Maxwell's Equations to Radiative Transfer Theory, in Geometry, Mechanics and Dynamics: the Legacy of Jerry Marsden, Springer, 2014; also presented at the SIAM Annual conference 2013.

T. de Witt, C. Lessig, and E. Fiume, Fluid Simulation Using Laplacian Eigenfunctions, ACM Trans. Graph., 31(1), 1–11, 2012.

C. Lessig and E. Fiume, On the Effective Dimension of Light Transport, Comput. Graph. Forum (Proceedings of EGSR 2010), 29(4), 1399–1403, 2010.

C. Lessig and P. Bientinesi, On Parallelizing the MRRR Algorithm for Data-Parallel Coprocessors, in Proceedings of PPAM 2010: Part I, 396–402, 2010.

H.-F. Pabst, J. P. Springer, A. Schollmeyer, R. Lenhardt, C. Lessig, and B. Fröhlich, Ray Casting of Trimmed NURBS Surfaces on the GPU, in The 2006 IEEE Symposium on Interactive Ray Tracing, 2006.

C. Lessig, D. Nowrouzezahrai, and K. Singh, GPU-Accelerated Ray Casting of Node-Based Implicit Surfaces, in Siggraph 2006 Posters, 2006.

M. Moehring, C. Lessig, and O. Bimber, Video See-Through and Optical Tracking with Consumer Cell Phones, in Siggraph 2004 Sketches and Applications, 2004.

M. Moehring, C. Lessig, and O. Bimber, Video See-Through AR on Consumer Cell-Phones, in Third IEEE and ACM International Symposium on Mixed and Augmented Reality, 2004, pp. 252–253.

We show that radiance, the central quantity in classical radiometry, is only meaningful in the context of measurements but not when transport is considered. Read more.

We provide an introduction to the central concepts and ideas of geometric mechanics aimed at the non-specialist. Read more.

Based on the work by Ng et al. [2004], we explore the influence of sampling strategies and signal approximation on the quality of rendered images. Read more.

We explore the practicality of Spherical Radial Basis Functions for the representation of surface light fields. Different kernel functions and strategies for obtaining the basis representation of signals are explored. Read more.

We demonstrate ray casting of quadratic surface at real-time frame rates even for complex scenes. Our implementation shows that the technique can be easily integrated into existing modeling packages. Read more.

Model of a industrial milling machine which exploits the scripting capabilities of modern modeling packages to enable an interactive exploration of the machine. Read more.

We use the compute power of state-of-the-art GPUs to ray cast volume data sets from medical imaging. Improvements in recent hardware enable us to achieve significantly better performance than previous work. See more.

We built a virtual showcase for the Deutsche Museum in Bonn, which explains the most important aspects of photosynthesis. See more.