Spectral Reflectivity Recovery from Tristimulus Values using 3D Extrapolation with 3D Interpolation (vol 18, pg 507, 2014)

Journal of the Optical Society of Korea Vol. 18, No. 5, October 2014, pp. 507-516 ISSN: 1226-4776(Print) / ISSN: 2093-6885(Online) DOI: http://dx.doi.org/10.3807/JOSK.2014.18.5.507 Spectral Reflectivity Recovery from Tristimulus Values Using 3D Extrapolation with 3D Interpolation Bog G. Kim 1 , John S. Werner 2 , Michael Siminovitch 3 , Kostantinos Papamichael 3 , Jeongwon Han , and Soobeen Park * Department of Physics, Pusan National University, Busan 609-735, Korea Department of Ophthalmology and Vision Science, University of California, Davis, CA 95817, USA Design Department, California Lighting Technology Center, University of California, Davis, CA 95618, USA Department of Housing and Interior design, Pusan National University, Busan 609-735, Korea (Received June 5, 2014 : revised August 22, 2014 : accepted September 5, 2014) We present a hybrid method for spectral reflectivity recovery, using 3D extrapolation as a supplemental method for 3D interpolation. The proposed 3D extrapolation is an extended version of 3D interpolation based on the barycentric algorithm. It is faster and more accurate than the conventional spectral-recovery techniques of principal-component analysis and nonnegative matrix transformation. Four different extrapolation techniques (based on nearest neighbors, circumcenters, in-centers, and centroids) are formulated and applied to recover spectral reflectivity. Under the standard conditions of a D65 illuminant and 1964 10° observer, all reflectivity data from 1269 Munsell color chips are successfully reconstructed. The superiority of the proposed method is demonstrated using statistical data to compare coefficients of correlation and determination. The proposed hybrid method can be applied for fast and accurate spectral reflectivity recovery in image processing. Keywords : Color measurement, Extrapolation, Inverse problem, Spectral reflectivity OCIS codes : (100.3190) Inverse Problems; (300.6550) Spectroscopy, visible; (330.1690) Color; (330.1710) Color, measurement (330.1715) Color, rendering and metamerism I. INTRODUCTION Recently there has been considerable interest in spectral reflectivity recovery methods in the field of color science [1-7] because of their fundamental importance, as well as their technological significance. In general, the color of an object is determined by the illumination conditions and the reflectivity of the surface material [8-10]. The light spectrum reflected by the material is passed through the eye and quantified by tristimulus values [8-10]. The spectral behavior of a colored object is known to be the fingerprint of the color, which is independent of the applied light source and the observer (for nonfluorescent materials). Spectral reflectivity recovery is also important for multispectral image processing, color consistency, color reconstruction, and color image pro- cessing [1-3]. Recovering the spectral reflectivity from known tristimulus values is an inverse problem for a given illumination condition [1, 7, 8]. In general, the solution to such an inverse problem is ill-posed, meaning that an exact and accurate solution is not easy to find. The solution also depends on the noise and initial conditions [11-13]. Two major methods for spectral reflectivity recovery are the pseudo-inverse technique [2-6, 14-17] and the interpolation technique [7, 18-20]. In the pseudo-inverse technique, principal-component analysis [2-6, 14-16] and nonnegative matrix transformation [7, 17, 21-23] are developed with various adaptation techniques. These are partially successful at reflectivity recovery, but finding an appropriate adaptation set requires extensive computation time, and the adaptation algorithm itself suffers from a locali- zation problem. A three-dimensional (3D) interpolation technique is often applied to minimize calculations when approximating mathemati- cally defined complex functions, or to produce intermediate results from sparse data points [11, 24]. Both situations can be directly employed when we convert images from *Corresponding author: sobpark@pusan.ac.kr Color versions of one or more of the figures in this paper are available online.