Illuminant Power Spectrum
This chapter provides an overview of the standard illuminants and their relation to the correlated colour temperature (CCT). It also examines the estimation of the illuminant power spectrum. To this end, we examine the CIE standard illuminants and the mod
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Illuminant Power Spectrum
In order to retrieve the spectra of a material, it is first necessary to remove the effect of the illuminants in the scene. The main challenge here stems from the fact that the output of the imager depends on the amount of light that passes through the lens of the camera, not the object reflectance (the ratio of reflected to incoming light impinging on the object surface). Note that whereas irradiance is determined by the light source and viewer directions and the material properties of the surface under study, reflectance is a characteristic of the material. This is well known in remote sensing, where material identification is, in general, a classification problem (Chang et al. 2003). In spectral imaging, we are often confronted with the need to recover the reflectance invariant to illuminant, viewer directions and sensor choice. Thus, for scene analysis, the problem should be treated as one arising from complex geometric settings found in real-world scenes, with one or more illuminants of different sorts (neon tubes, incandescent light bulbs, sunlight) and inter-reflections between object surfaces, some of them translucent or transparent. Moreover, for reliable scene analysis, methods should be applicable to highly textured surfaces and scenes with multiple illuminants. In this regard, the case of multiple illuminants, when their directions are known, is also interesting from a scholarly point of view, since the angular variables for isotropic reflection depend solely on the surface normal (Horn and Brooks 1989). The multi-image case, such as that pertaining to stereo vision, where the light source directions are not known, may be a worthy vehicle for application of large-scale optimisation methods to process all the spatial and spectral domain parameters simultaneously in order to recover the illuminant directions, surface shape and photometric parameters.
5.1 Standard Illuminants In the visible spectrum, the CIE has defined a number of standard illuminant power spectra corresponding to commonly used light sources (Wyszecki and Stiles 2000). A. Robles-Kelly, C.P. Huynh, Imaging Spectroscopy for Scene Analysis, Advances in Computer Vision and Pattern Recognition, DOI 10.1007/978-1-4471-4652-0_5, © Springer-Verlag London 2013
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Illuminant Power Spectrum
Fig. 5.1 Left-hand panel: characteristic vectors of the CIE D illuminant. Right-hand panel: power spectra of the D65 illuminant and the Planckian black body radiator
These standard illuminants are denoted by letters; the A, B and C series were defined in 1931 and the D series in 1964. The A series is aimed at representing typical, domestic, tungsten-filament lighting. The A series follows Planck’s law for a black body spectral radiance of the form LA (λ) =
c1 λ−5 c2 exp( λT )−1
(5.1)
where T = 2856 K, c1 = 3.74183 × 10−16 W m2 and c2 = 1.4388 × 10−2 mK. Note that c2 acts as a normalisation factor which has been chosen to achieve a spectral power of 100 at 560 nm. The B and C series correspond to direct and shaded sunligh
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