# AN INCREMENTAL WEIGHTED LEAST SQUARES APPROACH TO SURFACE LIGHTS FIELDS

### Greg Coombe, Anselmo Lastra

#### 2006

#### Abstract

An Image-Based Rendering (IBR) approach to appearance modelling enables the capture of a wide variety of real physical surfaces with complex reflectance behaviour. The challenges with this approach are handling the large amount of data, rendering the data efficiently, and previewing the model as it is being constructed. In this paper, we introduce the Incremental Weighted Least Squares approach to the representation and rendering of spatially and directionally varying illumination. Each surface patch consists of a set of Weighted Least Squares (WLS) node centers, which are low-degree polynomial representations of the anisotropic exitant radiance. During rendering, the representations are combined in a non-linear fashion to generate a full reconstruction of the exitant radiance. The rendering algorithm is fast, efficient, and implemented entirely on the GPU. The construction algorithm is incremental, which means that images are processed as they arrive instead of in the traditional batch fashion. This human-in-the-loop process enables the user to preview the model as it is being constructed and to adapt to over-sampling and under-sampling of the surface appearance.

#### References

- Buehler, C., et al., 2001. Unstructured Lumigraph Rendering. in SIGGRAPH 2001.
- Carr, J.C., et al., 2001. Reconstruction and Representation of 3D Objects with Radial Basis Functions. in SIGGRAPH. 2001.
- Chen, W.-C., et al., 2002. Light Field Mapping: Efficient Representation and Hardware Rendering of Surface Light Fields. in SIGGRAPH. 2002.
- Coombe, G., et al., 2005. Online Construction of Surface Light Fields. in Eurographics Symposium on Rendering.
- Debevec, P.E., C.J. Taylor, and J. Malik, 1996. Modeling and Rendering Architecture from Photographs: A Hybrid Geometry- and Image-Based Approach. in SIGGRAPH. 1996.
- Debevec, P.E., Y. Yu, and G.D. Borshukov, 1998. Efficient View-Dependent Image-Based Rendering with Projective Texture-Mapping. in Eurographics Rendering Workshop. Vienna, Austria.
- Furukawa, R., et al., 2002. Appearance based object modeling using texture database: acquisition, compression and rendering. Proceedings of the 13th Eurographics workshop on Rendering. 257-266.
- Gardner, A., et al. 2003. Linear Light Source Reflectometry. in SIGGRAPH 2003.
- Geman, S., E. Bienenstock, and R. Doursat, 1992. Neural Networks and the Bias/Variance Dilemma. Neural Computation, 4: p. 1-58.
- Gortler, S.J. et al., 1996. The Lumigraph, in SIGGRAPH 96 Conference Proceedings, p. 43--54.
- Hillesland, K., S. Molinov, and R. Grzeszczuk, 2003. Nonlinear Optimization Framework for Image-Based Modeling on Programmable Graphics Hardware. in SIGGRAPH. 2003.
- Lafortune, E.P.F., et al., 1997. Non-Linear Approximation of Reflectance Functions. in SIGGRAPH 97.
- Lensch, H.P.A. et al., 2001. Image-Based Reconstruction of Spatially Varying Materials. in Eurographics Workshop on Rendering.
- Levoy, M. and P. Hanrahan, 1996. Light Field Rendering. in SIGGRAPH. 96.
- Malzbender, T., D. Gelb, and H. Wolters, 2001. Polynomial Texture Maps. in SIGGRAPH 2001.
- Matusik, W. et al., 2003. A Data-Driven Reflectance Model. SIGGRAPH, 2003.
- Matusik, W., M. Loper, and H. Pfister. 2004. Progressively-Refined Reflectance Functions from Natural Illumination. in Eurographics Symposium on Rendering.
- McAllister, D.K., A.A. Lastra, and W. Heidrich. 2002. Efficient Rendering of Spatial Bi-directional Reflectance Distribution Functions. in Graphics Hardware 2002. Saarbruecken, Germany.
- Moody, J.E. and C. Darken, 1989. Fast learning in networks of locally-tuned processing units. Neural Computation, 1: p. 281-294.
- Mueller, G., et al. 2004. Acquisition, Synthesis and Rendering of Bidirectional Texture Functions. in Eurographics State of the Art Reports.
- Nealen, A., 2004. An As-Short-As-Possible Introduction to Least Squares, Weighted Least Squares and Moving Least Squares Methods for Scattered Data Approximation and Interpolation.
- Nishino, K., Y. Sato, and K. Ikeuchi. 1999. Eigen-Texture Method: Appearance Compression Based on 3D Model in Proceedings of CVPR-99.
- Ohtake, Y., et al. 2003. Multi-level Partition of Unity Implicits. in SIGGRAPH 2003.
- Ramamoorthi, R. and S. Marschner, 2002. Acquiring Material Models by Inverse Rendering, in SIGGRAPH 2002 Course Materials.
- Remington, K.A. and R. Pozo, 1996. NIST Sparse BLAS User's Guide. National Institute of Standards and Technology.
- Schirmacher, H., W. Heidrich, and H.-P. Seidel, 1999. Adaptive Acquisition of Lumigraphs from Synthetic Scenes in Computer Graphics Forum.
- Shepard, D., 1968. A two-dimensional interpolation function for irregularly-spaced data. in Proceedings of the 1968 23rd ACM national conference.
- Shirley, P. and K. Chiu, 1997. A Low Distortion Map Between Disk And Square. Journal of Graphics Tools, 2(3): p. 45-52.
- Wendland, H., 1995. Piecewise polynomial,positive definite and compactly supported radial basis functions of minimal degree. Advances in Computational Mathematics, 4: p. 389-396.
- Wendland, H., 2005. Scattered Data Approximation. Cambridge Monographs on Applied and Computational Mathematics, ed. P.G. Ciarlet, et al. Cambridge University Press.
- Wood, D., et al. 2000. Surface Light Fields for 3D Photography. in SIGGRAPH. 2000.
- Yu, Y. et al., 1999. Inverse Global Illumination: Recovering Reflectance Models of Real Scenes from Photographs. in Siggraph 99. Los Angeles.
- Zickler, T. et al., 2005. Reflectance Sharing: Image-based Rendering from a Sparse Set of Images in Eurographics Symposium on Rendering.

#### Paper Citation

#### in Harvard Style

Coombe G. and Lastra A. (2006). **AN INCREMENTAL WEIGHTED LEAST SQUARES APPROACH TO SURFACE LIGHTS FIELDS** . In *Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,* ISBN 972-8865-39-2, pages 84-91. DOI: 10.5220/0001358700840091

#### in Bibtex Style

@conference{grapp06,

author={Greg Coombe and Anselmo Lastra},

title={AN INCREMENTAL WEIGHTED LEAST SQUARES APPROACH TO SURFACE LIGHTS FIELDS},

booktitle={Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,},

year={2006},

pages={84-91},

publisher={SciTePress},

organization={INSTICC},

doi={10.5220/0001358700840091},

isbn={972-8865-39-2},

}

#### in EndNote Style

TY - CONF

JO - Proceedings of the First International Conference on Computer Graphics Theory and Applications - Volume 1: GRAPP,

TI - AN INCREMENTAL WEIGHTED LEAST SQUARES APPROACH TO SURFACE LIGHTS FIELDS

SN - 972-8865-39-2

AU - Coombe G.

AU - Lastra A.

PY - 2006

SP - 84

EP - 91

DO - 10.5220/0001358700840091