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A signal-processing framework for reflection

Authors:

Ravi Ramamoorthi,

Pat HanrahanAuthors Info & Claims

ACM Transactions on Graphics (TOG), Volume 23, Issue 4

Pages 1004 - 1042

https://doi.org/10.1145/1027411.1027416

Published: 01 October 2004 Publication History

Abstract

We present a signal-processing framework for analyzing the reflected light field from a homogeneous convex curved surface under distant illumination. This analysis is of theoretical interest in both graphics and vision and is also of practical importance in many computer graphics problems---for instance, in determining lighting distributions and bidirectional reflectance distribution functions (BRDFs), in rendering with environment maps, and in image-based rendering. It is well known that under our assumptions, the reflection operator behaves qualitatively like a convolution. 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 coefficients of the reflected light field as a product of the spherical harmonic coefficients of the illumination and the BRDF. These results are of practical importance in determining the well-posedness and conditioning of problems in <i> inverse rendering</i>---estimation of BRDF and lighting parameters from real photographs. Furthermore, we are able to derive analytic formulae for the spherical harmonic coefficients 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 <i>forward rendering</i>---especially the efficient 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 <i>computer vision</i> in the areas of recognition, photometric stereo and structure from motion.

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Index Terms

A signal-processing framework for reflection
1. Computing methodologies
  1. Artificial intelligence
    1. Computer vision
  2. Computer graphics
    1. Image manipulation
      1. Image processing

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cover image ACM Transactions on Graphics

ACM Transactions on Graphics Volume 23, Issue 4

October 2004

145 pages

ISSN:0730-0301

EISSN:1557-7368

DOI:10.1145/1027411

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Copyright © 2004 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Published: 01 October 2004

Published in TOG Volume 23, Issue 4

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Yamashita KNobuhara SNishino K(2024)DeepShaRM: Multi-View Shape and Reflectance Map Recovery Under Unknown Lighting2024 International Conference on 3D Vision (3DV)10.1109/3DV62453.2024.00038(761-769)Online publication date: 18-Mar-2024
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https://dl.acm.org/doi/10.1145/3528233.3530725
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