### Abstract

Surface reflectance functions (SRFs) and spectral power distributions (SPDs) of illuminants are typically modeled as elements in an N-dimensional linear function subspaces. Each SRF and SPD is represented by an N-vector and the mapping between SRF and SPD functions and an N-dimensional vector assigns N-dimensional "color" codes representing surface and light information. The N basis functions are chosen so that SRFs and SPDs can be accurately reconstructed from their N-dimensional vector codes. Typical rendering applications assume that the resulting mapping is an isomorphism where vector operations of addition, scalar multiplication and component-wise multiplication on the N-vectors can be used to model physical operations such as superposition of lights, light-surface interactions and inter-reflection. When N is small, this implicit isomorphism can fail even though individual SPDs and SRFs can still be accurately reconstructed by the codes. The vector operations do not mirror the physical. However, if the choice of basis functions is restricted to characteristic functions (that take on only the values 0 and 1) then the resulting map between SPDs/SRFs and N-vectors is an isomorphism that preserves the physical operations needed in rendering. The restriction to bases composed of characteristic functions can only reduce the goodness of fit of the linear function subspace to actual surfaces and lights. We will investigate how to select characteristic function bases of any dimension N (number of basis functions) and evaluate how accurately a large set of Munsell color chips can approximated as a function of dimension.

Original language | English (US) |
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Title of host publication | 5th European Conference on Colour in Graphics, Imaging, and Vision and 12th International Symposium on Multispectral Colour Science 2010, CGIV 2010/MCS'10 |

Pages | 560-565 |

Number of pages | 6 |

State | Published - 2010 |

Event | 5th European Conference on Colour in Graphics, Imaging, and Vision and 12th International Symposium on Multispectral Colour Science 2010, CGIV 2010/MCS'10 - Joensuu, Finland Duration: Jun 14 2010 → Jun 17 2010 |

### Publication series

Name | 5th European Conference on Colour in Graphics, Imaging, and Vision and 12th International Symposium on Multispectral Colour Science 2010, CGIV 2010/MCS'10 |
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### Other

Other | 5th European Conference on Colour in Graphics, Imaging, and Vision and 12th International Symposium on Multispectral Colour Science 2010, CGIV 2010/MCS'10 |
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Country | Finland |

City | Joensuu |

Period | 6/14/10 → 6/17/10 |

### ASJC Scopus subject areas

- Computer Graphics and Computer-Aided Design
- Computer Vision and Pattern Recognition