Christian Lessig



Christian Lessig


Email: lessig (at) isg.cs.ovgu.de

Google Scholar: profile

Office hours: Thursdays, 14:00 - 15:00, G29-215

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.


News


Research

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, 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.



Curriculum Vitae


2016 - present

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


2013 - 2016

2005 - 2007

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



Teaching


Current (Spring 2017)


Current (Spring 2017)


Fall 2016

GPU Programming, , OVGU Magdeburg


October 2015

Fall/Winter 2015
Fall/Winter 2014

Spring/Summer 2014

February 2014

Fall/Winter 2013

Spring/Summer 2013

Fall/Winter 2011

Spring/Summer 2011

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.


Publications


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.


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.


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, 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, 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.


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



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.


Miscellaneous notes and projects:.



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.