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If the ambient illumination is known, then the lighting matrix A is known If the number of sensors equals the number of degrees of freedom in the surface reflectivity, p = n, then the lighting matrix can be inverted to obtain the coefficients of the surface spectral reflectivity CTat each point in the image which characterizes the color of the corresponding points on the scene surfaces If the ambient illumination is not known, then solving the problem will require more sensors than the number of degrees of freedom in surface reflectance Since it was assumed that the ambient illumination is the same for all points in the scene, the information at multiple scene points can be used to estimate the ambient illumination Suppose p = n + 1 From s different spatial locations, sp = s(n + 1) different measurements can be obtained There are sn unknowns for the surface reflectance and m unknowns for the ambient light spectrum It is necessary to sample at s > m locations to have more data than unknowns This analysis suggests that the problem of color constancy can be solved without knowing the ambient illumination if there are n + 1 sensors The matrix A maps an n-dimensional surface space into an (n + 1)dimensional sensor space For example, if p = 3 and n = 2, then the subspace is a plane in a three-dimensional space This suggests the following two-step algorithm for determining surface reflectivity independent of scene illumination: 1 Determine the plane (subspace) spanning the data points in the sensor space to recover the ambient light vector E

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2 Determine the lighting matrix A from the ambient light vector E and invert it to obtain the surface reflectivity vector CT

This chapter has barely scratched the surface of the topic of color vision The intention has been to introduce the minimum number of formulas and

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Corrosion protection for steel reinforcing bars is provided by masonry cover over the steel Additional corrosion protection may be provided by coating the bars with either zinc or epoxy ASTM A 767 defines two classes of zinc coating, where Class I requires a thicker application of zinc than Class II, as shown in Table 35 Coating damage that occurs during fabrication or handling to the point of shipment is required to be repaired with a zinc-rich formulation in accordance with ASTM A 780 Standard Practice for Repair of Hot Dip Galvanized Coatings Sheared ends of reinforcing bars are required to be repaired in the same manner ASTM A 775 defines only one category of epoxy coating, but provides several performance requirements for that coating The requirements for the epoxy coating on steel reinforcing bars are shown in Table 36

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concepts required to generalize the material on shading ( 9) to cover colored light, reflectance, and imaging The brief presentation on color terminology and the CIE color model provides an introduction to color theory sufficient to allow the reader to pursue the topic in other sources The presentation of the HSI color model gives the reader some glimpse of the transformations that can be applied to multispectral imagery to allow the segmentation and edge detection algorithms covered elsewhere in this text to be used The key concept in segmenting multispectral imagery is to find a transformation that reduces the dimensionality (number of channels) and makes it easy to use thresholds to determine core regions Image processing algorithms have been developed for correcting differences in the color capabilities of various displays and printers, and realistic graphics renderings require approximations to the spectral distributions for ambient illumination and spectral reflectivity There are many image enhancement techniques that use color to highlight interesting features in images Since this text is not concerned with the generation, reproduction, or enhancement of images, many interesting topics in color imagery have been omitted; the reader is encouraged to pursue the topic in the many excellent texts on image processing and computer graphics that are widely available

accounts of color theory [81] Image processing texts provide extensive coverage of color representations, including the CMY color model used in color printing and the YIQ color model used in broadcast television The HSI color model and the derivation of the formulas for converting RGB values to HSI values was adapted from Gonzalez and Woods [91] The material on color constancy was adapted from the work of Maloney and Wandell (see Wandell [246])

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