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Chapter 11:
Spectrum Decomposition and Reconstruction
It has been shown that the illuminant and object spectra could be approximated to a very high degree of accuracy by linearly combining a few principal components. As early as 1964, Judd, MacAdam, and Wyszecki reported that various daylight illuminations could be approximated by three components (see Section 1.5) and Cohen showed that the spectra of Munsell color chips could be accurately represented by a few principal components. Using principal component analysis (PCA), Cohen reported that the first basis vector alone accounted for 92.72% of the cumulative variance, and merely three or four vectors accounted for 99% variance or better. As a result, principal-component analysis became an extremely powerful tool for the computational color technology community. These findings led to the establishment of a finite-dimensional linear model. Combining with the rich contents of linear algebra and matrix theory, the model provides powerful applications in color science and technology. Many color scientists and researchers have contributed to the building and applying of this model to numerous color-image processing areas such as color transformation, white-point conversion, metameric pairing, indexing of metamerism, object spectrum reconstruction, illuminant spectrum reconstruction, color constancy, chromatic adaptation, and targetless scanner characterization. In this chapter, we present several methods for spectrum decomposition and reconstruction, including orthogonal projection, smoothing inverse, Wiener inverse, and principal component analysis. Principal components from several publications are compiled and evaluated by using a set of fourteen spectra employed for the color rendering index. Their similarities and differences are discussed. New methods of spectrum reconstruction directly from tristimulus values are developed and tested.
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