REPRODUCIBLE REPRODUCTIONS Color , light , and digital images

We believe that our perception of an object reveals its true nature. However, the image is the result of particular lighting conditions, and the physiology of the eye. In this paper we investigate how to characterize an object independent of its environment. Such that two independent measurements yield the same answer, independent of the lighting and the camera. At the most basic level this problem deals with the scattering of light. Light with a particular wavelength and polarization hits and object at a particular point under a given angle. Part of the light is absorbed, part is scattered over a wide range of scattering angles. The smallest unit in which this problem can be decomposed is the chance of scattered light at a certain angle and polarization, given the incident light at a certain angle and polarization. The wavelength of the scattered light can be different from the wavelength of the incident light, however, for all practical purposes we can assume that both are the same. Once these core features are known, we can reconstruct the appearance of an object under all lighting conditions, for different observers. This requires us to move away from the human as the ultimate gauge, as the humans are unable to distinguish separate wavelengths, except in the crudest manner of red, green, and blue averaged color luminances. Much of color theory is devoted to this particular, more or less physiological aspect, of image reproduction. Gloss and structure are usually considered unwanted features in image reproduction, however, they are as much features of an object as the color that remains when the lighting conditions are optimized in the sense that the apparent gloss and structure is minimized. Rather than seeking the lighting conditions that minimize the surface effects, we seek to characterize the scattering, such that the analysis of the image can extend beyond the color features of the original, and problems of surface structure and gloss are documented for future study. We already mentioned the degrees of freedom which characterize the scattering process from which the more complex situations of lighting and imaging can be reconstructed. Note that these do not depend on any model for the lighting, the object, or the camera or observer. These are basic physical and reproducible processes. They involve the wavelength, polarization, and the angle of both the incident light and the reflected light. Gloss, and specular reflections, are usually associated incident and reflective angles which are close together, and a small wavelength dependence such that the color associated with gloss is the color of the lighting. The core measurement would involve hitting the object with monochromatic light from a given angle and measuring the reflected light at another angle. The measured light, given the amount of incident light would be an invariant and reproducible observation. However, generally, in different experiments different angles, and different wavelengths might be used, which makes a direct, one-to-one comparison impossible. Therefore it is a common procedure to use the scattering data to generate smooth functions for all angles and wavelengths, such that different experiments yield the same basic quantities. These are often referred to as multipole expansions. Another feature of making this fitting part of the experimental analysis is that integrated quantities, such as our physiological eye characteristics are easily determined. For a given class of objects, such as paintings, the first task is to find out how many, and which independent measurements are required to characterize the object sufficiently. It might well be that a substantial number of measurements are required under small angles to characterize the detailed structure of gloss. It might also be that a precise angular-spatial correlation is necessary to disentangle all the features that resulted from the structure of the surface. A priori, there is little else than preliminary measurements that can tell us how detailed the actual