I am a postdoctoral fellow in the computer graphics group at TU Berlin. My research is rooted in the quest for quantitatively effective image synthesis techniques, although I often also pursue other interesting questions in computer graphics and computational science. In my work I employ and contribute to concepts and tools in computer science, mathematical physics, and applied mathematics.

*July 2016:*I will start as a junior professor at the Otto-von-Guericke-Universität Magdeburg, not far from Berlin, in August 2016. If you are interested in working with me as a Ph.D. student on cutting edge research on rendering and / or geometry processing please get in touch. Candidates with a background in mathematics or physics are particularly encouraged to apply (even with limited background in computer graphics).*July 2016:*Philipp Petersen, Martin Schäfer and myself just uploaded our manuscript on bendlets, a second order shearlet transform whose elements are sheared, to adapt to the local normal direction, and bent, to adapt to the local curvature, to ArXiv.*July 2015:*I recently gave a talk in the image group at the University of Copenhagen about my research. Thanks to Kenny Erleben to organizing the visit. Slides can be found here.*August 2014:*I obtained the first image synthesis technique that is quantitatively effective in that it employs an (almost-)optimal number of samples and allows the quantification of error in the computed image. I announced this result in my Siggraph talk and we are currently working on a write-up.*April 2014:*Our paper on reproducing kernel bases got accepted to Siggraph.

My research is motivated by the development of quantitatively effective image synthesis techniques, which are of importance for example in computer aided design and mixed reality movie production. Working towards this objective leads me to many interesting questions at the intersection of computer science, mathematical physics, and applied mathematics.

In the last years, I developed alternative mathematical and computational foundations for light transport simulation. An important aspect was a formulation of light transport using the language of geometric mechanics, elucidating the structural aspects of the theory and also clarifying its physical origins. I also addressed the correspondence between pointwise samples, which is the only information that is available from ray tracing, and the continuous solutions that are of interest. As a rigorous yet numerically practical tool to establish the correspondence I introduced the concept of reproducing kernel bases.

Building on these alternative foundations, I was recently able to obtain the first image synthesis technique that is quantitatively effective and employs a (quasi-)optimal number of samples while permitting to quantify the error in the generated image. Important questions I would like to address in the next years are how the curse of dimensionality can be broken in the context of of quantitatively effective image synthesis techniques and how these can be extended to dynamic scenes.

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

Representative publications:

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.

I am currently a postdoctoral fellow in Marc Alexa's computer graphics group at TU Berlin. Prior to that I was a postdoctoral fellow in the Department of Computing+Mathematical Sciences at the California Institute of Technology where I worked with Mathieu Desbrun. I obtained my Ph.D. from the University of Toronto under Eugene Fiume for a thesis on Modern Foundations of Light Transport Simulation. My M.Sc. is also from the University of Toronto for which I constructed Symmetric and Orthogonal Haar Wavelets on the Sphere. While in graduate school I also interned for a few summers in the developer technology at NVIDIA, working with Mark Harris. I did my undergraduate studies at the Bauhaus Universität Weimar where I graduated with distinction for a thesis on Interactive Ray Casting and Ray Tracing on Programmable Graphics Hardware. More information about me can be found in my curriculum vitae.

- Ph.D.: Modern Foundations of Light Transport Simulation, with Eugene Fiume, University of Toronto, April 2012.
- M.Sc.: Symmetric and Orthogonal Wavelets on the Sphere, with Eugene Fiume, University of Toronto, June 2007.
- B.Sc.: Interactive Ray Casting and Ray Tracing on Programmable Graphics Hardware, with Bernd Fröhlich, Bauhaus Universität Weimar, January 2005.

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 (MPGI4), TU Berlin.

Spring/Summer 2013

Algorithms and Data Structures (MPGI2), 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 is an educational project of particular interest to me. It arose from my experience in teaching computer graphics courses and from my involvement in student supervision. Currently, missing mathematical knowledge is provided or learned in an ad-hoc manner when needed. While this immediately motivates the mathematics it also makes it for students difficult to obtain a comprehensive understanding and to see common principles and structures---aspects that are essential to build on concepts. I therefore believe that it is beneficial to teach the mathematical foundations and methods that are required for contemporary computer graphics outside of a specific subject, while remaining sufficiently applied and practical and providing enough applications to be immediately relevant to the students. This was for me the motivation to develop and teach a course on mathematical methods for computer graphics.

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 in graduate school, I was many times teaching assistant for the introductory computer graphics course. I was also teaching assistant for Computational Reality, Illusion and Deception and Computers and Society. Please refer to my curriculum vitae for details.

I also co-supervise(d) M.Sc. and Ph.D. students at the University of Toronto.

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.