Abstract
Lens effects are crucial visual elements in the synthetic imagery, but rendering lens effects with complex full lens models is time-consuming. This paper proposes a polynomial regression-based approach for constructing a sparse and accurate polynomial lens model. Terms of a polynomial are built adaptively in a bottom-up approach. Depending on the distribution of aberrations, this approach partitions the light field and builds separate polynomial models for local light fields. A line pupil-based sampling method is presented to accelerate the generation of camera rays. In addition, a new Monte Carlo estimator is derived to support general Monte Carlo rendering. Experiments show that this approach significantly reduces the time cost of constructing a polynomial lens model in comparison to state-of-the-art methods, while achieving high imaging accuracy.
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References
Hullin, M.B., Hanika, J., Heidrich, W.: Polynomial optics: a construction kit for efficient ray-tracing of lens systems. Comput. Graph. Forum 31(4), 1375–1383 (2012)
Hanika, J., Dachsbacher, C.: Efficient Monte Carlo rendering with realistic lenses. Comput. Graph. Forum 33(2), 323–332 (2014)
Schrade, E., Hanika, J., Dachsbacher, C.: Sparse high-degree polynomials for wide-angle lenses. Comput. Graph. Forum 35(4), 89–97 (2016)
Potmesil, M., Chakravarty, I.: A lens and aperture camera model for synthetic image generation. ACM SIGGRAPH Comput. Graph. 15(3), 297–305 (1981)
Kolb, C., Mitchell, D., Hanrahan, P.: A realistic camera model for computer graphics. In: Proceedings of SIGGRAPH ’95. SIGGRAPH ’95. ACM, New York, pp. 317–324 (1995)
Gauss, C.F.: Dioptrische untersuchungen. Dioptrische Untersuchungen, by Gauss, Carl Friedrich 1 (1841)
Heidrich, W., Slusallek, P., Seidel, H.P.: An image-based model for realistic lens systems in interactive computer graphics. Graphics Interface ’97, pp 68–75 (1997)
Lee, S., Eisemann, E., Seidel, H.P.: Real-time lens blur effects and focus control. ACM Trans. Graph 29(4), 65:1–65:7 (2010)
Hullin, M., Eisemann, E., Seidel, H.P., Lee, S.: Physically-based real-time lens flare rendering. ACM Trans. Graph 30(4), 108:1–108:10 (2011)
Steinert, B., Dammertz, H., Hanika, J., Lensch, H.P.: General spectral camera lens simulation. Comput. Graph. Forum 30(6), 1643–1654 (2011)
Wu, J., Zheng, C., Hu, X., Xu, F.: Rendering realistic spectral bokeh due to lens stops and aberrations. Vis. Comput. 29(1), 41–52 (2013)
Zheng, N., Hagen, N., Brady, D.J.: Analytic-domain lens design with proximate ray tracing. JOSA A 27(8), 1791–1802 (2010)
Hopkins, G.W.: Proximate ray tracing and optical aberration coefficients. JOSA 66(5), 405–410 (1976)
Lee, S., Eisemann, E.: Practical real-time lens-flare rendering. Comput. Graph. Forum 32(4), 1–6 (2013)
Tropp, J.A., Gilbert, A.C.: Signal recovery from random measurements via orthogonal matching pursuit. IEEE Trans. Inf. Theory 53(12), 4655–4666 (2007)
Pudil, P., Novovičová, J., Kittler, J.: Floating search methods in feature selection. Pattern Recognit. Lett. 15(11), 1119–1125 (1994)
Todorovski, L., Ljubič, P., Džeroski, S.: Inducing polynomial equations for regression. In: European Conference on Machine Learning. Springer, Berlin, pp. 441–452 (2004)
Jekabsons, G., Lavendels, J.: Polynomial regression modelling using adaptive construction of basis functions. In: Proceedings of IADIS International Conference, Applied Computing, pp. 269–276 (2008)
Smith, W.J.: Modern Lens Design, 2nd edn. McGraw-Hill New York, Maidenhead (2005)
Guyon, I., Elisseeff, A.: An introduction to variable and feature selection. J. Mach. Learn. Res. 3, 1157–1182 (2003)
Pharr, M., Jakob, W., Humphreys, G.: Physically Based Rendering: From Theory to Implementation, 3rd edn. Morgan Kaufmann, Burlington (2016)
Jakob, W., Marschner, S.: Manifold exploration: a Markov chain Monte Carlo technique for rendering scenes with difficult specular transport. ACM Trans. Graph. 31(4), 58:1–58:13 (2012)
Kelemen, C., Szirmay-Kalos, L., Antal, G., Csonka, F.: A simple and robust mutation strategy for the metropolis light transport algorithm. Comput. Graph. Forum 21(3), 531–540 (2002)
Lafortune, E.P., Willems, Y.D.: Bi-directional path tracing. In: Proceedings of Third International Conference on Computational Graphics and Visualization Techniques (Compugraphics ’93), pp. 145–153 (1993)
Hachisuka, T., Jensen, H.W.: Stochastic progressive photon mapping. ACM Trans. Graph. 28(5), 14:11–14:18 (2009)
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This work was supported in part by the research grant (ref. 9140A21010115HT05003). The camera lens data are courtesy of Emanuel Schrade et al.
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Zheng, Q., Zheng, C. Adaptive sparse polynomial regression for camera lens simulation. Vis Comput 33, 715–724 (2017). https://doi.org/10.1007/s00371-017-1402-9
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DOI: https://doi.org/10.1007/s00371-017-1402-9