The revised Kubelka-Munk theory is examined theoretically and experimentally. Systems of dyed paper sheets are simulated, and the results are compared with other models. The results show that the revised Kubelka-Munk model yields significant errors in predicted dye-paper mixture reflectances, and is not self-consistent. The absorption is noticeably overestimated. Theoretical arguments show that...

This paper provides a theoretical connection between two different mathematical models dedicated to the reflectance and the transmittance of diffusing layers. The Kubelka–Munk model proposes a continuous description of scattering and absorption for two opposite diffuse fluxes in a homogeneous layer (continuous two-flux model). On the other hand, Kubelka’s layering model describes the multiple r...

We propose a spectral prediction model for predicting the reflectance and transmittance of recto-verso halftone prints. A recto-verso halftone print is modeled as a diffusing substrate surrounded by two inked interfaces in contact with air (or with another medium). The interaction of light with the print comprises three components: (a) the attenuation of the incident light penetrating the print...

Parmi les modèles de prédiction couleur courants, celui de Kubelka et Munk occupe une position centrale. En dépit de son caractère phénoménologique et de sa simplicité, il conduit à des résultats intéressants, et est toujours employé dans les systèmes d’aide à la formulation d’encres, de peintures et de teintures. Après un bref rappel du modèle, une nouvelle formulation mathématique basée sur u...

A generally applicable theoretical model describing light propagating through turbid media is proposed. The theory is a generalization of the revised Kubelka-Munk theory, extending its applicability to accommodate a wider range of absorption influences. A general expression for a factor taking into account the effect of scattering on the total photon path traversed in a turbid medium is derived...

This paper presents various extensions of the so-called two-flux models for prediction of reflectance and transmittance of diffusing media, i.e. the Kubelka-Munk model, introduced in [HDI062], and the extension of Kubelka-Munk for stacks of diffusing layers. A first matrix formulation of the Kubelka-Munk differential equations leads to a matrix framework based on transfer matrices, which can be...

A fundamental problem in color image processing is the integration of the physical laws of light reflection into image processing results, the problem known as photometric invariance. The derivation of object properties from color images yields the extraction of geometric and photometric invariants from color images. Photometric invariance is to be derived from the physics of reflection. In thi...

The color of the blends of pre-colored fibers depends on the ratio of each fiber in the blends. Some theories have been introduced for color matching of blends of pre-colored fibers. Most however, are restricted in scope and accuracy. Kubelka and Munk presented the most applicable theory, which is still used in industry. In this work, the classical Kubelka-Munk method for color prediction of a ...

A spectral-projected gradient method and an extension of the Kubelka-Munk theory are applied to obtain the relevant parameters of the theory from measured diffuse reflectance spectra of pigmented samples illuminated with visible diffuse radiation. The initial estimate of the spectral dependence of the parameters, required by a recursive spectral-projected gradient method, was obtained by use of...

We present a pair of coupled partial differential equations to describe the evolution of the average total intensity and intensity flux of a wave field inside a randomly layered medium. These equations represent a modification of the Kubelka-Munk equations, or radiative transfer. Our modification accounts for wave interference (e.g., localization), which is neglected in radiative transfer. We n...