Abstract
Line segment sampling has recently been adopted in many rendering algorithms for better handling of a wide range of effects such as motion blur, defocus blur and scattering media. A question naturally raised is how to generate line segment samples with good properties that can effectively reduce variance and aliasing artifacts observed in the rendering results. This paper studies this problem and presents a frequency analysis of line segment sampling. The analysis shows that the frequency content of a line segment sample is equivalent to the weighted frequency content of a point sample. The weight introduces anisotropy that smoothly changes among point samples, line segment samples and line samples according to the lengths of the samples. Line segment sampling thus makes it possible to achieve a balance between noise (point sampling) and aliasing (line sampling) under the same sampling rate. Based on the analysis, we propose a line segment sampling scheme to preserve blue-noise properties of samples which can significantly reduce noise and aliasing artifacts in reconstruction results. We demonstrate that our sampling scheme improves the quality of depth-of-field rendering, motion blur rendering, and temporal light field reconstruction.
Supplemental Material
Available for Download
Supplemental material.
- Akenine-Möller, T., Munkberg, J., and Hasselgren, J. 2007. Stochastic rasterization using time-continuous triangles. In GH, 7--16. Google Scholar
Digital Library
- Balzer, M., Schlömer, T., and Deussen, O. 2009. Capacity-constrained point distributions: a variant of lloyd's method. ACM Trans. Graph. 28, 3 (July), 86:1--86:8. Google Scholar
Digital Library
- Barringer, R., Gribel, C. J., and Akenine-Möller, T. 2012. High-quality curve rendering using line sampled visibility. ACM Trans. Graph. 31, 6 (Nov.), 162:1--162:10. Google Scholar
Digital Library
- Bowers, J., Wang, R., Wei, L.-Y., and Maletz, D. 2010. Parallel poisson disk sampling with spectrum analysis on surfaces. ACM Trans. Graph. 29, 6 (Dec.), 166:1--166:10. Google Scholar
Digital Library
- Bridson, R. 2007. Fast poisson disk sampling in arbitrary dimensions. In ACM SIGGRAPH 2007 sketches, ACM, New York, NY, USA, SIGGRAPH '07. Google Scholar
Digital Library
- Cheslack-Postava, E., Wang, R., Akerlund, O., and Pellacini, F. 2008. Fast, realistic lighting and material design using nonlinear cut approximation. ACM Trans. Graph. 27, 5 (Dec.), 128:1--128:10. Google Scholar
Digital Library
- Cohen, M. F., Shade, J., Hiller, S., and Deussen, O. 2003. Wang tiles for image and texture generation. ACM Trans. Graph. 22, 3 (July), 287--294. Google Scholar
Digital Library
- Cook, R. L. 1986. Stochastic sampling in computer graphics. ACM Trans. Graph. 5, 1 (Jan.), 51--72. Google Scholar
Digital Library
- Dunbar, D., and Humphreys, G. 2006. A spatial data structure for fast poisson-disk sample generation. ACM Trans. Graph. 25, 3 (July), 503--508. Google Scholar
Digital Library
- Durand, F., Holzschuch, N., Soler, C., Chan, E., and Sillion, F. X. 2005. A frequency analysis of light transport. ACM Trans. Graph. 24, 3 (July), 1115--1126. Google Scholar
Digital Library
- Ebeida, M. S., Davidson, A. A., Patney, A., Knupp, P. M., Mitchell, S. A., and Owens, J. D. 2011. Efficient maximal poisson-disk sampling. ACM Trans. Graph. 30, 4 (July), 49:1--49:12. Google Scholar
Digital Library
- Ebeida, M. S., Mitchell, S. A., Patney, A., Davidson, A. A., and Owens, J. D. 2012. A simple algorithm for maximal poisson-disk sampling in high dimensions. Comp. Graph. Forum 31, 2pt4 (May), 785--794. Google Scholar
Digital Library
- Egan, K., Tseng, Y.-T., Holzschuch, N., Durand, F., and Ramamoorthi, R. 2009. Frequency analysis and sheared reconstruction for rendering motion blur. ACM Trans. Graph. 28, 3 (July), 93:1--93:13. Google Scholar
Digital Library
- Egan, K., Hecht, F., Durand, F., and Ramamoorthi, R. 2011. Frequency analysis and sheared filtering for shadow light fields of complex occluders. ACM Trans. Graph. 30, 2 (Apr.), 9:1--9:13. Google Scholar
Digital Library
- Fattal, R. 2011. Blue-noise point sampling using kernel density model. ACM Trans. Graph. 30, 4 (July), 48:1--48:12. Google Scholar
Digital Library
- Gribel, C. J., Doggett, M., and Akenine-Möller, T. 2010. Analytical motion blur rasterization with compression. In HPG, 163--172. Google Scholar
Digital Library
- Gribel, C. J., Barringer, R., and Akenine-Möller, T. 2011. High-quality spatio-temporal rendering using semi-analytical visibility. ACM Trans. Graph. 30, 4 (July), 54:1--54:12. Google Scholar
Digital Library
- Hachisuka, T., Jarosz, W., Weistroffer, R. P., Dale, K., Humphreys, G., Zwicker, M., and Jensen, H. W. 2008. Multidimensional adaptive sampling and reconstruction for ray tracing. ACM Trans. Graph. 27, 3 (Aug.), 33:1--33:10. Google Scholar
Digital Library
- Havran, V., Bittner, J., Herzog, R., and Seidel, H.-P. 2005. Ray maps for global illumination. In EGSR, 43--54. Google Scholar
Digital Library
- Jarosz, W., Zwicker, M., and Jensen, H. W. 2008. The beam radiance estimate for volumetric photon mapping. Comp. Graph. Forum 27, 2 (Apr.), 557--566.Google Scholar
Cross Ref
- Jarosz, W., Nowrouzezahrai, D., Sadeghi, I., and Jensen, H. W. 2011. A comprehensive theory of volumetric radiance estimation using photon points and beams. ACM Trans. Graph. 30, 1 (Feb.), 5:1--5:19. Google Scholar
Digital Library
- Jarosz, W., Nowrouzezahrai, D., Thomas, R., Sloan, P. P., and Zwicker, M. 2011. Progressive photon beams. ACM Trans. Graph. 30, 6 (Dec.). Google Scholar
Digital Library
- Jensen, H. W., and Buhler, J. 2002. A rapid hierarchical rendering technique for translucent materials. ACM Trans. Graph. 21, 3 (July), 576--581. Google Scholar
Digital Library
- Jones, T. R., and Perry, R. N. 2000. Antialiasing with line samples. In EGRW, 197--206. Google Scholar
Digital Library
- Kopf, J., Cohen-Or, D., Deussen, O., and Lischinski, D. 2006. Recursive wang tiles for real-time blue noise. ACM Trans. Graph. 25, 3 (July), 509--518. Google Scholar
Digital Library
- Lagae, A., and Dutré, P. 2005. A procedural object distribution function. ACM Trans. Graph. 24, 4 (Oct.), 1442--1461. Google Scholar
Digital Library
- Lagae, A., and Dutré, P. 2008. A comparison of methods for generating Poisson disk distributions. Computer Graphics Forum 27, 1 (March), 114--129.Google Scholar
Cross Ref
- Lehtinen, J., Aila, T., Chen, J., Laine, S., and Durand, F. 2011. Temporal light field reconstruction for rendering distribution effects. ACM Trans. Graph. 30, 4 (July), 55:1--55:12. Google Scholar
Digital Library
- Li, H., Wei, L.-Y., Sander, P. V., and Fu, C.-W. 2010. Anisotropic blue noise sampling. ACM Trans. Graph. 29, 6 (Dec.), 167:1--167:12. Google Scholar
Digital Library
- Lloyd, S. 1983. An optimization approach to relaxation labeling algorithms. Image and Vision Computing 1, 2 (May), 85--91.Google Scholar
Cross Ref
- McCool, M., and Fiume, E. 1992. Hierarchical poisson disk sampling distributions. In GI, 94--105. Google Scholar
Digital Library
- Mehta, S. U., Wang, B., and Ramamoorthi, R. 2012. Axis-aligned filtering for interactive sampled soft shadows. ACM Trans. Graph. 31, 6 (Nov.), 163:1--163:10. Google Scholar
Digital Library
- Mitchell, D. P. 1987. Generating antialiased images at low sampling densities. SIGGRAPH Comput. Graph. 21, 4 (Aug.), 65--72. Google Scholar
Digital Library
- Mitchell, D. P. 1991. Spectrally optimal sampling for distribution ray tracing. SIGGRAPH Comput. Graph. 25, 4 (July), 157--164. Google Scholar
Digital Library
- Nehab, D., and Shilane, P. 2004. Stratified point sampling of 3D models. In PBG, 49--56. Google Scholar
Digital Library
- Novák, J., Nowrouzezahrai, D., Dachsbacher, C., and Jarosz, W. 2012. Progressive virtual beam lights. Comp. Graph. Forum 31, 4 (June), 1407--1413. Google Scholar
Digital Library
- Novák, J., Nowrouzezahrai, D., Dachsbacher, C., and Jarosz, W. 2012. Virtual ray lights for rendering scenes with participating media. ACM Trans. Graph. 31, 4 (July), 60:1--60:11. Google Scholar
Digital Library
- Ostromoukhov, V., Donohue, C., and Jodoin, P.-M. 2004. Fast hierarchical importance sampling with blue noise properties. ACM Trans. Graph. 23, 3 (Aug.), 488--495. Google Scholar
Digital Library
- Ostromoukhov, V. 2007. Sampling with polyominoes. ACM Trans. Graph. 26, 3 (July). Google Scholar
Digital Library
- Öztireli, A. C., and Gross, M. 2012. Analysis and synthesis of point distributions based on pair correlation. ACM Trans. Graph. 31, 6 (Nov.), 170:1--170:10. Google Scholar
Digital Library
- Öztireli, A. C., Alexa, M., and Gross, M. 2010. Spectral sampling of manifolds. ACM Trans. Graph. 29, 6 (Dec.), 168:1--168:8. Google Scholar
Digital Library
- Pang, W.-M., Qu, Y., Wong, T.-T., Cohen-Or, D., and Heng, P.-A. 2008. Structure-aware halftoning. ACM Trans. Graph. 27, 3 (Aug.), 89:1--89:8. Google Scholar
Digital Library
- Ramamoorthi, R., Mahajan, D., and Belhumeur, P. 2007. A first-order analysis of lighting, shading, and shadows. ACM Trans. Graph. 26, 1 (Jan.). Google Scholar
Digital Library
- Soler, C., Subr, K., Durand, F., Holzschuch, N., and Sillion, F. 2009. Fourier depth of field. ACM Trans. Graph. 28, 2 (May), 18:1--18:12. Google Scholar
Digital Library
- Sun, X., Zhou, K., Lin, S., and Guo, B. 2010. Line space gathering for single scattering in large scenes. ACM Trans. Graph. 29, 4 (July), 54:1--54:8. Google Scholar
Digital Library
- Tzeng, S., Patney, A., Davidson, A., Ebeida, M. S., Mitchell, S. A., and Owens, J. D. 2012. High-quality parallel depth-of-field using line samples. In HPG, 23--31. Google Scholar
Digital Library
- Wei, L.-Y., and Wang, R. 2011. Differential domain analysis for non-uniform sampling. ACM Trans. Graph. 30, 4 (July), 50:1--50:10. Google Scholar
Digital Library
- Wei, L.-Y. 2008. Parallel poisson disk sampling. ACM Trans. Graph. 27, 3 (Aug.), 20:1--20:9. Google Scholar
Digital Library
- Wei, L.-Y. 2010. Multi-class blue noise sampling. ACM Trans. Graph. 29 (July), 79:1--79:8. Google Scholar
Digital Library
- White, K. B., Cline, D., and Egbert, P. K. 2007. Poisson disk point sets by hierarchical dart throwing. In RT, 129--132. Google Scholar
Digital Library
- Zhou, Y., Huang, H., Wei, L.-Y., and Wang, R. 2012. Point sampling with general noise spectrum. ACM Trans. Graph. 31, 4 (July), 76:1--76:11. Google Scholar
Digital Library
Index Terms
Line segment sampling with blue-noise properties
Recommendations
Spoke-Darts for High-Dimensional Blue-Noise Sampling
Blue noise sampling has proved useful for many graphics applications, but remains underexplored in high-dimensional spaces due to the difficulty of generating distributions and proving properties about them. We present a blue noise sampling method with ...
Blue-noise dithered sampling
SIGGRAPH '16: ACM SIGGRAPH 2016 TalksThe visual fidelity of a Monte Carlo rendered image depends not only on the magnitude of the pixel estimation error but also on its distribution over the image. To this end, state-of-the-art methods use high-quality stratified sampling patterns, which ...
Multi-class blue noise sampling
SIGGRAPH '10: ACM SIGGRAPH 2010 papersSampling is a core process for a variety of graphics applications. Among existing sampling methods, blue noise sampling remains popular thanks to its spatial uniformity and absence of aliasing artifacts. However, research so far has been mainly focused ...





Comments