Recovering the Reduced Scattering and Absorption Coefficients of Turbid Media from a Single Image

This study introduces a physics-based inverse rendering method for determining the reduced scattering and absorption coefficients of turbid materials with arbitrary shapes, using a single image as input. The approach enables fully spectrally-resolved reconstruction of the wavelength-dependent behaviour of the optical properties while also circumventing the specialised sample preparation required by established measurement techniques. Our approach employs a numerical solution of the Radiative Transfer Equation based on an inverse Monte Carlo framework, utilising an improved Levenberg–Marquardt algorithm. By rendering the edge effects accurately, particularly translucency, it becomes possible to differentiate between scattering and absorption from just one image. Importantly, the errors induced by only approximate prior knowledge of the phase function and refractive index of the material were quantified. The method was validated through theoretical studies on three materials spanning a range of optical parameters, initially using a simple cube geometry and later extended to more complex shapes. Evaluated via the CIE ΔE2000 colour difference, forward renderings based on the recovered properties were indistinguishable from those preset, which were obtained from integrating sphere measurements on real materials. The recovered optical properties showed less than 4% difference relative to these measurements. This work demonstrates a versatile approach for optical material characterisation, with significant potential for digital twin creation and soft-proofing in manufacturing.