Radiometric Compensation through Inverse Light Transport Gordon Wetzstein and Oliver Bimber
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1 Radiometric Compensation through Inverse Light Transport Gordon Wetzstein and Oliver Bimber Pacific Graphics 2007 contact: Radiometric Compensation through Inverse Light Transport 1 30
2 SmartProjector - no Screens required! original image observed projection Radiometric Compensation through Inverse Light Transport 2 30
3 SmartProjector - Applications museums live-stage performances architectural visualization cultural heritage sites outdoor advertisement air plane cabin car interior Radiometric Compensation through Inverse Light Transport 3 30
4 SmartProjector - Limitations no direct mapping: refractions no direct mapping: inter-reflections Radiometric Compensation through Inverse Light Transport 4 30
5 Related Work tiled screen calibration [geometric correction and luminance matching] book: Majumder and Brown Practical Multi-Projector Display Design, AK Peters 2007 [Yang et al. 2005] unconventional projections [no screens, HDR, high-speed, super-resolution] state-of-the-art report: Bimber et al. The Visual Computing of Projector-Camera Systems, EG 2007 image-based relighting, environment matting and dual photography [forward light transport acquisition and relighting] [Debevec et al. 2000], [Masselus et al. 2003], [Sen et al. 2005], [Zonker et al. 1999] inverse illumination [indirect light removal for photography and projection] focus related projector-camera techniques [Seitz et al. 2005], [Bimber et al. 2006] [image sharpening for defocused projections] [Bimber and Emmerling 2006], [Zhang and Nayar 2006], [Brown et al. 2006] Radiometric Compensation through Inverse Light Transport 5 30
6 The 8D Reflectance Field LF = f ( u, v, ϕ, φ)? Radiometric Compensation through Inverse Light Transport 6 30
7 Forward Light Transport L o ( ) ( ) ~ ( ) ( ) x, w = L x, w + T x, w, w' L x, w' d w' o e Ω ( xi ) = Le ( xi ) + T ( xi w j ) Li ( w j ) L, j i L i o, e, incoming, outgoing, emissive light field ~ T transport function T x, w points in space / discrete samples w, w' discrete transport function directions c = T p + e 0 ( pq 1) c 0 t0 L t 0 p 0 e 0 M = M O M M + M 0 ( pq 1) c ( mn 1) t ( mn 1) t ( mn 1) p ( pq 1) e L ( mn 1) p mn camera resolution pq projector resolution c camera image T e light transport matrix projected light environment light color channel radiometric compensation? in camera space Radiometric Compensation through Inverse Light Transport 7 30
8 Light Transport Acquisition p m q mn x 1 C n pq pq x 1 P c = Tp mn Radiometric Compensation through Inverse Light Transport 8 30
9 Light Transport Acquisition p m q mn x 1 C n pq pq x 1 P c = Tp mn Radiometric Compensation through Inverse Light Transport 9 30
10 Light Transport Acquisition p m q mn x 1 C n pq pq x 1 P c = Tp mn Radiometric Compensation through Inverse Light Transport 10 30
11 Light Transport Acquisition p m q mn x 1 C n pq pq x 1 P c = Tp mn Radiometric Compensation through Inverse Light Transport 11 30
12 Light Transport Acquisition p m q mn x 1 C n pq pq x 1 P c = Tp mn Radiometric Compensation through Inverse Light Transport 12 30
13 Light Transport Acquisition video clip projected patterns camera image Radiometric Compensation through Inverse Light Transport 13 30
14 Dual Photography interchange camera and projector by transposing the light transport matrix p m q n pq x 1 C mn x 1 P pq mn c = Tp mn T pq c = T T p [Sen et al. 2005] Radiometric Compensation through Inverse Light Transport 14 30
15 Dual Photography c = Tp composition illuminated composition illumination pattern T p' = T c' dual light transport matrix T illuminated dual Radiometric Compensation through Inverse Light Transport 15 30
16 Generalized Radiometric Compensation c = Tp + e c = T p + T p + T p + e R G B R R R R G R B R c = T p + T p + T p + e R G B G G R G G G B G c = T p + T p + T p + e R G B B B R B G B B B single camera, single projector R G B cr er TR TR T R pr R G B cg e G TG TG T G p = G R G B cb e B TB TB T B p B solve with iterative non-negative least squares general setup with r cameras and k projectors c e T T T L T p = M M M M O M M 0 R 0 G 0 B ( k 1) B ( r 1) cb ( r 1) e B ( r 1) TB ( r 1) TB ( r 1) TB ( r 1) T ( k 1) L B 0 R 0 G 0 B ( k 1) B 0 0 R 0 R 0 R 0 R 0 R 0 R R 0 R 0 G 0 B ( k 1) B 0 0cG 0 e G 0TG 0TG 0TG L 0TG pg 0 R 0 G 0 B ( k 1) B 0 0cB 0 e B 0TB 0TB 0TB L 0T B pb p B Radiometric Compensation through Inverse Light Transport 16 30
17 Diffuse Scattering and Inter-Reflections Radiometric Compensation through Inverse Light Transport 17 30
18 Diffuse Scattering and Inter-Reflections [ The Chubb Chubbs, Pixar] shadows cannot be compensated with single projector Radiometric Compensation through Inverse Light Transport 18 30
19 Defocus Compensation original uncompensated compensation compensated Radiometric Compensation through Inverse Light Transport 19 30
20 Multi-projector compensation left left + right right Radiometric Compensation through Inverse Light Transport 20 30
21 Radiometric Compensation through Inverse Light Transport Interactive Compensation on the GPU reformulate problem for GPU optimized implementation pre-processing: compute inverse light transport on-line matrix-vector multiplication SVD: e p T c + = ( ) = = + + 1) ( 0 1) ( 1) ( 0 0 1) ( 1) ( 1) ( 0 0 1) ( 0 0 pq mn mn pq mn pq mn p p e c e c t t t t p e c T Μ Μ Λ Μ Ο Μ Λ, T T T U V T V U + + = Σ = Σ
22 Sample Light Transport composition dual Radiometric Compensation through Inverse Light Transport 22 30
23 Cluster Decomposition Radiometric Compensation through Inverse Light Transport 23 30
24 Compensation Results [ 9, Focus Features and 9, LLC] Radiometric Compensation through Inverse Light Transport 24 30
25 Projecting on Refractive Material Radiometric Compensation through Inverse Light Transport 25 30
26 Projecting on Refractive Material pseudo-inverse light transport matrix Radiometric Compensation through Inverse Light Transport 26 30
27 Projecting on Refractive Material [ Mike s New Car, Pixar] Radiometric Compensation through Inverse Light Transport 27 30
28 Interactive Compensation on GPU video clip 30 fps, GeForce 7900 GTX [ Mike s New Car, Pixar] Radiometric Compensation through Inverse Light Transport 28 30
29 Summary generalized theory of radiometric compensation using inverse light transport proof-of-concept: diffuse scattering and inter-reflections reflecting statuette refracting glass defocus compensation multiple overlapping projector interactive compensation on the GPU Radiometric Compensation through Inverse Light Transport 29 30
30 Limitations projection hardware resolution black level brightness contrast depth of focus physical setup environment light projection surface computational resources matrix sparsity Radiometric Compensation through Inverse Light Transport 30 30
31 Outlook view-dependent compensation [Bimber et al. 2005] incremental inverse light transport acquisition (possibly direct-indirect separation) [Nayar et al. 2006] novel transport acquisition storage processing schemes [Garg et al. 2006] Radiometric Compensation through Inverse Light Transport 31 30
32 Thank you! Questions? Radiometric Compensation through Inverse Light Transport 32 30
33 Related Work Seamless Multi-Projections Yang, R., Majumder, A, Brown, M. Camera Based Calibration Techniques for Seamless Multi-Projector Displays. ACM TOGS Majumder, A, Brown, M. Practical Multi-Projector Display Design. AK Peters 2007 Nayar, S. Peri, H., Grossberg, M., Belhumeur, P. A Projection System with Radiometric Compensation for Screen Imperfections. ProCams 2003 Bimber, O., Emmerling, A., Klemmer, T. Embedded Entertainment with Smart Projectors. IEEE Computer, 2005 Bimber, O., Iwai, D., Wetzstein, G., Grundhöfer, A. The Visual Computing of Projector-Camera Systems. EuroGraphics (STAR) 2007 Fuji, K., Grossberg, M., Nayar, S. A Projector-Camera System with Real-Time Photometric Adaptation for Dynamic Environments. IEEE CVPR 2005 Bimber, O., Wetzstein, G., Emmerling, A., Nitschke, C. Enabling View-Dependent Stereoscopic Projection in Real Environments. ISMAR 05 Grossberg, M., Peri, H., Nayar, S. Making one Object Look Like Another: Controlling Appearance using a Projector-Camera System. IEEE CVPR 2004 Ashdown, M., Okabe, T., Sato, I., Sato, Y. Robust Content-Dependent Photometric Projector Compensation, ProCams 2006 Grundhöfer, A., Bimber, O. Real-Time Adaptive Radiometric Compensation. IEEE Transactions on Visualization and Computer Graphics, to appear Bimber, O., Iwai, D., Wetzstein, G., Grundhöfer, A., The Visual Computing of Projector-Camera Systems. EuroGraphics state-of-the-art report 2007 Forward Light Transport, BRDF Acquisition and Relighting Debevec, P., Hawkins, T., Tchou, C., Duiker, H., Sarokin, W., Sagar, M. Acquiring the Reflectance Field of a Human Face. SIGGRAPH 00 Masselus, V., Peers, P., Dutré, P, Willems, Y. Relighting with 4D incident Light Fields. ACM TOGS 2003 Goesele, M., Lensch. H., Lang, J., Fuchs, C., Seidel, H. DISCO: Acquisition of Translucent Objects. SIGGRAPH 04 Peers, P., vom Berge, K., Matusik, W., Ramamoorthi, R., Lawrence, J., Rusinkiewicz, S., Dutré, P. A Compact Factored Representation of Heterogeneous Subsurface Scattering. SIGGRAPH 2006 Sen, P., Chen, B., Garg, G, Marschner, S, Horowitz, M., Levoy, M., Lensch, H. Dual Photography. SIGGRAPH 05 Focus Related Projector-Camera Techniques Bimber, O., Emmerling, A. Multi-Focal Projection: A Multi-Projector Technique for Increased Focal Depth. IEEE TVCG, 2006 Levoy, M., Chen, B., Vaish, V., Horowitz, M., McDowall, I., Bolas, M. Synthetic Aperture Confocal Imaging. SIGGRAPH 04 Zhang, L., Nayar, S. Projection Defocus Analysis for Scene Capture and Image Display. SIGGRAPH 06 Brown, M., Song, P., Cham, T. Image Pre-Conditioning for Out-of-Focus Projector Blur. CVPR 06 Inverse Illumination Seitz, S., Matsushita, Y., Kutulakos, K. A Theory of Inverse Light Transport. ICCV, 2005 Bimber, O., Grundhöfer, A., Zeidler, T., Danch, D., Kapakos, P. Compensating Indirect Scattering for Immersive and Semi-Immersive Projection Displays. IEEE VR, 2006 Radiometric Compensation through Inverse Light Transport 33 30
34 Comparison CPU - GPU pseudo-inverse is less stable than solving explicitly however, no visible difference Radiometric Compensation through Inverse Light Transport 34 30
35 Error Analysis Radiometric Compensation through Inverse Light Transport 35 30
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