Spherical harmonics vs. Haar wavelets: basis for recovering illumination from cast shadows

The problem of estimating an illumination distribution from images is called inverse lighting. For inverse lighting, three approaches have been developed based on specular reflection components, diffuse reflection components, and cast shadows. The present study provides theoretical insights as to why the approach based on cast shadows works in a reliable manner, and discusses what kind of basis functions are appropriate to be used for recovering illumination from cast shadows. First, we formalize the approach based on cast shadows by using spherical harmonics. Then, we analyze the approach in the frequency domain and show the advantages and the limitations of the approach. Second, motivated by the observations in the frequency domain, we propose an efficient method using Haar wavelets that provide compact supports and sparsity of coefficients. Finally, we report the results of experiments that compared the method using spherical harmonics and the method using Haar wavelets.

[1]  Pat Hanrahan,et al.  A signal-processing framework for inverse rendering , 2001, SIGGRAPH.

[2]  Jan Kautz,et al.  Precomputed radiance transfer for real-time rendering in dynamic, low-frequency lighting environments , 2002 .

[3]  Takahiro Okabe,et al.  Support Vector Machines for Object Recognition under Varying Illumination , 2003 .

[4]  Katsushi Ikeuchi,et al.  Illumination from Shadows , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  Katsushi Ikeuchi,et al.  Acquiring a Radiance Distribution to Superimpose Virtual Objects onto Real Scene , 2001, MVA.

[6]  Peter Schröder,et al.  Spherical wavelets: efficiently representing functions on the sphere , 1995, SIGGRAPH.

[7]  D. Healy,et al.  Computing Fourier Transforms and Convolutions on the 2-Sphere , 1994 .

[8]  Pat Hanrahan,et al.  All-frequency shadows using non-linear wavelet lighting approximation , 2003, ACM Trans. Graph..

[9]  William H. Press,et al.  Numerical recipes in C , 2002 .

[10]  Katsushi Ikeuchi,et al.  Appearance sampling for obtaining a set of basis images for variable illumination , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[11]  Ronen Basri,et al.  Lambertian Reflectance and Linear Subspaces , 2003, IEEE Trans. Pattern Anal. Mach. Intell..

[12]  David Salesin,et al.  Wavelets for computer graphics: a primer. 2 , 1995, IEEE Computer Graphics and Applications.

[13]  Michael F. Cohen,et al.  Hierarchical and variational geometric modeling with wavelets , 1995, I3D '95.

[14]  David J. Kriegman,et al.  From Few to Many: Illumination Cone Models for Face Recognition under Variable Lighting and Pose , 2001, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Takahiro Okabe,et al.  Object recognition based on photometric alignment using RANSAC , 2003, 2003 IEEE Computer Society Conference on Computer Vision and Pattern Recognition, 2003. Proceedings..

[16]  P. Hanrahan,et al.  On the relationship between radiance and irradiance: determining the illumination from images of a convex Lambertian object. , 2001, Journal of the Optical Society of America. A, Optics, image science, and vision.

[17]  Amnon Shashua,et al.  On Photometric Issues in 3D Visual Recognition from a Single 2D Image , 2004, International Journal of Computer Vision.

[18]  Katsushi Ikeuchi,et al.  Determining reflectance parameters and illumination distribution from a sparse set of images for view-dependent image synthesis , 2001, Proceedings Eighth IEEE International Conference on Computer Vision. ICCV 2001.

[19]  Yang Wang,et al.  Estimation of Multiple Illuminants from a Single Image of Arbitrary Known Geometry , 2002, ECCV.

[20]  Stephen Lin,et al.  Multiple-cue illumination estimation in textured scenes , 2003, Proceedings Ninth IEEE International Conference on Computer Vision.

[21]  Steve Marschner,et al.  Inverse Lighting for Photography , 1997, CIC.