## A Signal-Processing Framework for Reflection (2004)

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Venue: | ACM TRANSACTIONS ON GRAPHICS |

Citations: | 34 - 4 self |

### BibTeX

@ARTICLE{Ramamoorthi04asignal-processing,

author = {Ravi Ramamoorthi and Pat Hanrahan},

title = {A Signal-Processing Framework for Reflection},

journal = {ACM TRANSACTIONS ON GRAPHICS},

year = {2004},

volume = {23},

pages = {1004--1042}

}

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### Abstract

... In this paper, we formalize these notions, showing that the reflected light field can be thought of in a precise quantitative way as obtained by convolving the lighting and BRDF, i.e. by filtering the incident illumination using the BRDF. Mathematically, we are able to express the frequency-space coe#cients of the reflected light field as a product of the spherical harmonic coe#- cients of the illumination and the BRDF. These results are of practical importance in determining the well-posedness and conditioning of problems in inverse rendering---estimation of BRDF and lighting parameters from real photographs. Furthermore, we are able to derive analytic formulae for the spherical harmonic coe#cients of many common BRDF and lighting models. From this formal analysis, we are able to determine precise conditions under which estimation of BRDFs and lighting distributions are well posed and well-conditioned. Our mathematical analysis also has implications for forward rendering---especially the e#cient rendering of objects under complex lighting conditions specified by environment maps. The results, especially the analytic formulae derived for Lambertian surfaces, are also relevant in computer vision in the areas of recognition, photometric stereo and structure from motion.