›› 2013, Vol. 28 ›› Issue (3): 454-467.doi: 10.1007/s11390-013-1347-z

Special Issue: Artificial Intelligence and Pattern Recognition

• Graphics, Visualization, and Image Processing • Previous Articles     Next Articles

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

Wen-Yong Zhao1 (赵文勇), Shao-Lin Chen1 (陈绍林), Yuan Zheng1 (郑媛), and Si-Long Peng1,2 (彭思龙)   

  1. 1. National ASIC Design and Engineering Center, Institute of Automation, Chinese Academy of Sciences Beijing 100190, China;
    2. College of Control Engineering, Northeastern University at Qinhuangdao, Qinhuangdao 066004, China
  • Received:2012-05-07 Revised:2012-11-27 Online:2013-05-05 Published:2013-05-05
  • Contact: 10.1007/s11390-013-1347-z
  • Supported by:

    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.

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 S2. 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.

[1] Basri R, Jacobs D W. Lambertian reflectance and linear subspaces. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2003, 25(2): 218-233.

[2] Ramamoorthi R, Hanrahan P. An efficient representation for irradiance environment maps. In Proc. the 28th Conf. Computer Graphics and Interactive Techniques, August 2001, pp.497-500.

[3] Ramamoorthi R, Hanrahan P. On the relationship between radiance and irradiance: Determining the illumination from images of a convex Lambertian object. Journal of the Optical Society of America A, Optics, Image Science and Vision, 2001, 18(10): 2448-2459.

[4] Wen Z, Liu Z, Huang T S. Face relighting with radiance environment maps. In Proc. IEEE Computer Society Conference on Computer Vision and Pattern Recognition, June 2003, Vol.2, pp.158-165.

[5] Zhang L, Samaras D. Face recognition from a single training image under arbitrary unknown lighting using spherical harmonics. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2006, 28(3): 351-363.

[6] Qing L, Shan S, Gao W. Face recognition with harmonic delighting. In Proc. Asian Conference on Computer Vision, Jan. 2004, pp.824-829.

[7] Johnson M K, Farid H. Exposing digital forgeries in complex lighting environments. IEEE Transactions on Information Forensics and Security, 2007, 2(3): 450-461.

[8] Mahajan D, Ramamoorthi R, Curless B. A theory of frequency domain invariants: Spherical harmonic identities for BRDF/lighting transfer and image consistency. IEEE Trans. Pattern Analysis and Machine Intelligence, 2008, 30(2): 197213.

[9] Blanz V, Vetter T. A morphable model for the synthesis of 3D faces. In Proc. the 26th Annual Conference on Computer Graphics and Interactive Techniques, Aug. 1999, pp.187-194.

[10] Duffin R J, Schae?er A C. A class of nonharmonic fourier series. Trans. American Mathematical Society, 1952, 72(2): 341-366.

[11] Kovacevic J, Chebira A. Life beyond bases: The advent of frames (part I). IEEE Signal Processing Magazine, 2007, 24(4): 86-104.

[12] Kovacevic J, Chebira A. Life beyond bases: The advent of frames (part II). IEEE Signal Processing Magazine, 2007, 24(5): 115-125.

[13] Christensen O. An Introduction to Frames and Riesz Bases. Boston: Birkh?auser, 2002.

[14] Eldar Y C, Bolcskei H. Geometrically uniform frames. IEEE Transactions on Information Theory, 2003, 49(4): 993-1006.

[15] Daubechies I. Ten Lectures on Wavelets. Society for Industrial and Applied Mathematics, 1992.

[16] Ivanic J, Ruedenberg K. Rotation matrices for real spherical harmonics. Direct determination by recursion. The Journal of Physical Chemistry, 1996, 100(15): 6342-6347.

[17] Jackson J D. Classical Electrodynamics (3rd edition). Wiley, 1998.

[18] Sternberg S. Group Theory and Physics. Cambridge Univ. Press, 1995.

[19] Kosmann-Schwarzbach Y. Groups and Symmetries. Springer, 2010.

[20] Meyer B. On the symmetries of spherical harmonics. Canadian J. Mathematics, 1954, 135: 135-157.

[21] Sim T, Baker S, Bsat M. The CMU pose, illumination, and expression (PIE) database. In Proc. the 5th IEEE Int. Conf. Automatic Face and Gesture Recognition, May 2002, pp.4651.

[22] Brunelli R, Messelodi S. Robust estimation of correlation with applications to computer vision. Pattern Recognition, 1995, 28(6): 833-841.
No related articles found!
Full text



[1] Zhang Bo; Zhang Ling;. An Algorithm for Finding D-Time Table[J]. , 1992, 7(1): 62 -67 .
[2] Harald E. Otto;. UNDO, An Aid for Explorative Learning?[J]. , 1992, 7(3): 226 -236 .
[3] Xu Meirui; Liu Xiaolin;. A VLSI Algorithm for Calculating the Tree to Tree Distance[J]. , 1993, 8(1): 68 -76 .
[4] Pan Zhigeng; Shi Jiaoying; Hu Bingfeng;. DGLa: A Distributed Graphics Language[J]. , 1994, 9(2): 97 -106 .
[5] Yao Shu; Zhang Bo;. Situated Learning of a Behavior-Based Mobile Robot Path Planner[J]. , 1995, 10(4): 375 -379 .
[6] Hu Shimin;. A Subdivision Scheme for Rational Triangular Bézier Surfaces[J]. , 1996, 11(1): 9 -16 .
[7] LIN Hua; LU Mi; Jesse Z.FANG;. A Direct Approach for Finding Loop Transformation Matrices[J]. , 1996, 11(3): 237 -256 .
[8] Xu Meihe; Tang Zesheng;. Surface Reconstruction for Cross Sectional Data[J]. , 1996, 11(5): 471 -479 .
[9] Yi Bo; Tao Xianping; G.Cioni; A.Colagrossi;. Intuitive Minimal Abduction in Sequent Calculi[J]. , 1998, 13(3): 209 -219 .
[10] ZHENG Fang; XU Mingxing; MOU Xiaolong; WU Jian; WU Wenhu; FANG Ditang;. HarkMan—A Vocabulary-Independent Keyword Spotter for Spontaneons Chinese Speech[J]. , 1999, 14(1): 18 -26 .

ISSN 1000-9000(Print)

CN 11-2296/TP

Editorial Board
Author Guidelines
Journal of Computer Science and Technology
Institute of Computing Technology, Chinese Academy of Sciences
P.O. Box 2704, Beijing 100190 P.R. China
E-mail: jcst@ict.ac.cn
  Copyright ©2015 JCST, All Rights Reserved