Generalization of Lambert's reflectance model

Lambert's model for body reflection is widely used in computer graphics. It is used extensively by rendering techniques such as radiosity and ray tracing. For several real-world objects, however, Lambert's model can prove to be a very inaccurate approximation to the body reflectance. While the brightness of a Lambertian surface is independent of viewing direction, that of a rough surface increases as the viewing direction approaches the light source direction. In this paper, a comprehensive model is developed that predicts body reflectance from rough surfaces. The surface is modeled as a collection of Lambertian facets. It is shown that such a surface is inherently non-Lambertian due to the foreshortening of the surface facets. Further, the model accounts for complex geometric and radiometric phenomena such as masking, shadowing, and interreflections between facets. Several experiments have been conducted on samples of rough diffuse surfaces, such as, plaster, sand, clay, and cloth. All these surface demonstrate significant deviation from Lambertian behavior. The reflectance measurements obtained are in strong agreement with the reflectance predicted by the model.

[1]  M. Minnaert.  The reciprocity principle in lunar photometry , 1941 .

[2]  N. Orlova.  PHOTOMETRICAL RELIEF OF THE LUNAR SURFACE , 1961 .

[3]  B. Hapke,et al.  PHOTOMETRIC STUDIES OF COMPLEX SURFACES, WITH APPLICATIONS TO THE MOON , 1963 .

[4]  P. Beckmann,et al.  The scattering of electromagnetic waves from rough surfaces , 1963 .

[5]  J. M. Coulson,et al.  Heat Transfer , 2018, Finite Element Method for Solids and Structures.

[6]  P. Beckmann.  Shadowing of random rough surfaces , 1965 .

[7]  P. Oetking.  Photometric studies of diffusely reflecting surfaces with applications to the brightness of the Moon , 1966 .

[8]  R. Wagner.  Shadowing of Randomly Rough Surfaces , 1967 .

[9]  Bruce G. Smith.  Lunar surface roughness - Shadowing and thermal emission. , 1967 .

[10]  K. Torrance,et al.  Theory for off-specular reflection from roughened surfaces , 1967 .

[11]  D. Buhl,et al.  Reradiation and thermal emission from illuminated craters on the lunar surface , 1968 .

[12]  R. Hering,et al.  Apparent radiation properties of a rough surface , 1969 .

[13]  F. E. Nicodemus,et al.  Geometrical considerations and nomenclature for reflectance , 1977 .

[14]  James F. Blinn,et al.  Models of light reflection for computer synthesized pictures , 1977, SIGGRAPH.

[15]  Turner Whitted,et al.  An improved illumination model for shaded display , 1979, CACM.

[16]  W. Frei,et al.  Digital Correction of Solar Illumination and Viewing Angle Artifacts in Remotely Sensed Images , 1981 .

[17]  Robert L. Cook,et al.  A Reflectance Model for Computer Graphics , 1987, TOGS.

[18]  J. Koenderink,et al.  Geometrical modes as a general method to treat diffuse interreflections in radiometry , 1983 .

[19]  A. Ishimaru,et al.  Backscattering enhancement of random discrete scatterers , 1984 .

[20]  A. Ishimaru,et al.  Retroreflectance from a dense distribution of spherical particles , 1984 .

[21]  Donald P. Greenberg,et al.  The hemi-cube: a radiosity solution for complex environments , 1985, SIGGRAPH.

[22]  J. Kajiya.  Anisotropic reflection models , 1985, SIGGRAPH 1985.

[23]  Nelson L. Max,et al.  Bidirectional reflection functions from surface bump maps , 1987, SIGGRAPH.

[24]  Roy Hall,et al.  Illumination and Color in Computer Generated Imagery , 1988, Monographs in Visual Communication.

[25]  Pierre Poulin,et al.  A model for anisotropic reflection , 1990, SIGGRAPH.

[26]  Pierre Poulin,et al.  A Model for Anisotropic Reeection , 1990 .

[27]  Donald P. Greenberg,et al.  A comprehensive physical model for light reflection , 1991, SIGGRAPH.

[28]  Stephen H. Westin,et al.  Predicting reflectance functions from complex surfaces , 1992, SIGGRAPH.

[29]  J. Howell,et al.  Thermal radiation heat transfer - Third edition , 1992 .

[30]  B. Hapke,et al.  The Opposition Effect of the Moon: The Contribution of Coherent Backscatter , 1993, Science.

[31]  Pat Hanrahan,et al.  Reflection from layered surfaces due to subsurface scattering , 1993, SIGGRAPH.

[32]  G. Rybicki.  Radiative transfer , 2019, Climate Change and Terrestrial Ecosystem Modeling.