In this paper, we present a method to recover the parameters governing the reflection of light from a surface making use of a single hyperspectral image. To do this, we view the image radiance as a combination of specular and diffuse reflection components and present a cost functional which can be used for purposes of iterative least squares optimisation. This optimisation process is quite general in nature and can be applied to a number of reflectance models widely used in the computer vision and graphics communities. We elaborate on the use of these models in our optimisation process and provide a variant of the Beckmann–Kirchhoff model which incorporates the Fresnel reflection term. We show results on synthetic images and illustrate how the recovered photometric parameters can be employed for skin recognition in real world imagery, where our estimated albedo yields a classification rate of 95.09±4.26% as compared to an alternative, whose classification rate is of 90.94±6.12%. We also show quantitative results on the estimation of the index of refraction, where our method delivers an average per-pixel angular error of 0.15°. This is a considerable improvement with respect to an alternative, which yields an error of 9.9°. 
An optimisation approach to the recovery of reflection parameters from a single hyperspectral image