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Lighting Estimation of a Convex Lambertian Object Using Redundant Spherical Harmonic Frames

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Abstract

An explicit lighting estimation from a single image of Lambertian objects is influenced by two factors: data incompletion and noise contamination. Measurement of lighting consistency purely using the orthogonal spherical harmonic basis cannot achieve an accurate estimation. We present a novel signal-processing framework to represent the lighting field. We construct a redundant spherical harmonic frame with geometric symmetry on the sphere S 2. Spherical harmonic frames are defined over the generating rotation matrices about symmetry axes of finite symmetry subgroups of SO(3), and the generating functions are spherical harmonic basis functions. Compared with the orthogonal spherical harmonic basis, the redundant spherical harmonic frames not only describe the multidirectional lighting distribution intuitively, but also resist the noise theoretically. Subsequently, we analyze the relationship of the irradiance to the incoming radiance in terms of spherical harmonic frames, and reconstruct the lighting function filtered by the Lambertian BRDF (bidirectional reflectance distribution function). The experiments show that the frame coefficients of spherical harmonic frames can better characterize the complex lighting environments finely and robustly.

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Authors and Affiliations

  1. National ASIC Design and Engineering Center, Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China

    Wen-Yong Zhao, Shao-Lin Chen, Yuan Zheng & Si-Long Peng

  2. College of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao, 066004, China

    Si-Long Peng

Authors
  1. Wen-Yong Zhao
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  2. Shao-Lin Chen
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  3. Yuan Zheng
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  4. Si-Long Peng
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Corresponding author

Correspondence to Wen-Yong Zhao.

Additional information

The work was supported by the National Natural Science Foundation of China under Grant No. 60972126, the Joint Funds of the National Natural Science Foundation of China under Grant No. U0935002/L05, the Beijing Municipal Natural Science Foundation of China under Grant No. 4102060, and the Key Program of National Natural Science Foundation of China under Grant No. 61032007.

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Zhao, WY., Chen, SL., Zheng, Y. et al. Lighting Estimation of a Convex Lambertian Object Using Redundant Spherical Harmonic Frames. J. Comput. Sci. Technol. 28, 454–467 (2013). https://doi.org/10.1007/s11390-013-1347-z

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  • DOI: https://doi.org/10.1007/s11390-013-1347-z

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