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Reflectance Modelling

In computer vision, the modelling of surface reflectance is a topic of pivotal importance for purposes of shape analysis and pattern recognition. In relation to photometric invariants, a number of physically meaningful parameters of reflectance models are material intrinsic and therefore potentially useful for pattern recognition tasks. Reflectance models are designed to capture the influence of the illumination condition, the surface geometry and the material properties under study on the observed image irradiance. Reflectance, which is the fraction of incident light reflected from the surface, is dependent on the surface and material properties. The geometric properties include, but are not limited to, the roughness scale and the structure and shape of the constituent micro-facets of the surface. Furthermore, the spectral distribution of surface reflectance is characteristic of the material and could provide useful information for material classification. Traditionally, reflectance models can be classified into three broad categories, including empirical, physics-based and phenomenological (semi-empirical). Although empirical reflectance models may not be based on a physics theory, they aim to fit the empirical measurements of real-world data. In 1924, Opik (1924) designed an empirical model to estimate the reflection behaviour of the moon. In 1941, Minnaert (1941) modified Opik’s model to obtain a reflectance function that was dependent on the polar angles of incidence and reflection, and the surface roughness. This was designed to obey the Helmholtz reciprocity principle (Helmholtz 1924), but did not originate from a theory in physics. Instead, it aimed to predict the light reflection behaviour of realistic non-Lambertian surfaces such as the moon. Phong’s model (Phong 1975) achieved rendering realism by an interpolation over the vertex surface normals of polygons constituting the surface being rendered. Ward (1992) introduced a physically plausible, yet computationally simple model for the rendering of surfaces with anisotropic reflectance. In this chapter, we focus our attention on physics-based and phenomenological models. Physics-based models employ the light scattering theory for modelling surface reflectance. In this category, Kirchhoff’s theory of the scattering of electromagnetic waves was first adopted by Beckmann to develop physics-based reflectance A. Robles-Kelly, C.P. Huynh, Imaging Spectroscopy for Scene Analysis, Advances in Computer Vision and Pattern Recognition, DOI 10.1007/978-1-4471-4652-0_4, © Springer-Verlag London 2013

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4 Reflectance Modelling

Fig. 4.1 The right-handed local coordinate system defined for each surface point under study. The origin is located at the given point, and the z-axis is aligned with the local surface normal N . The  and is reflected by the surface in the direction V . In incident light comes from the direction L the above coordinate system, the incident direction is parameterised by a zenith angle θi formed with the surface norm