Terrestrial laser scanner intensity correction for the incidence angle effect on surfaces with different colours and sheens

Laser scanning intensity captures information about the reflectance of target-surfaces and is used for a variety of applications such as data registration, classification, object detection and recognition. To enhance its utility, intensity values often undergo a correction process, which reduces the influence of nuisance parameters on recorded intensity (often range and incidence angle). This study applies and tests the Torrance-Sparrow model to correct intensity for the incidence angle effect in terrestrial laser scanning. Main components of the Torrance-Sparrow model are the geometrical attenuation (G) and microfacet distribution functions (D). Four models of geometrical attenuation and microfacet distribution functions are evaluated, namely, (i) Beckmann, (ii) Trowbridge-Reitz, (iii) GGX, and (iv) shifted gamma distribution (SGD). These models provide different derivations of the functions G and D, which estimate parameters necessary for the Torrance-Sparrow model. Target-surfaces scanned from various incidence angles are used for the assessment. These are painted with eight different colours (white, yellow, red, green, blue, grey, brown, and black) and two sheens (flat and semi-gloss), which create different reflection characteristics (diffuse and specular). Numerical and visual evaluations show that all four models manage to model the specular reflection component of the semi-gloss sheen target-surfaces for all tested colours. However, in flat-sheen surfaces, the Beckmann and SGD models show inferior modelling than GGX and Trowbridge-Reitz for brown, grey, and black colours. In addition, a relative comparison of the roughness parameters and Fresnel factors showed that only the Trowbridge-Reitz model produced reasonable values, based on encountered surface characteristics. Application of the Trowbridge-Reitz model in independent point-cloud data shows how intensity values can be corrected for the incidence angle effect in real cases.