Empirical modeling for non-Lambertian reflectance based on full-waveform laser detection

Abstract

Empirical models are proposed for recalculating non-Lambertian reflectance based on the transmitted pulses and returned pulses that are recorded by a lab-built full-waveform laser detection sys-tem. The experiments were implemented on three objects, which were gray-cement concrete, red dull paper, and glazed indoor tile. The pulse energy was calculated based on the pulse waveforms in two ways, integral of the waveform (IW) method and multiplying peak by the full width at half maximum of the waveform (PF) method. The newly introduced empirical parameters semi-ellipsoid distribution ratio (SEDR) of the semi-ellipsoid model and ellipsoid distribution ratio (EDR) of the ellipsoid model were put forward to evaluate the degree of the non-Lambertian reflectance of material surface, instead of Lambertian-based factor that is the cosine of the incidence angle. We conclude that the bigger values of SEDR and EDR indicate more significant deviation from Lambertian for material surface. The modified reflectance results estimated by using the semi-ellipsoid model display better approximations than those obtained from Phong cosine. Moreover, it is obvious that the modified reflectance using a combined method of PF and modified semi-ellipsoid model out-weighs the results estimated by other manners. 1 Introduction The characterization of reflective properties of materials can be realized by defining the function that determines how reflected radiance is distributed in terms of the distribution of incident radiance. This function is the bidirectional reflec-tance distribution function (BRDF). 1 BRDF as a model is useful for different kinds of reflection descriptions and depends only on the characteristics of the material surface. The completely diffuse bihemispherical albedo can be derived through integration of the BRDF for the entire solar and viewing hemisphere, 2 while the direct beam directional hemispherical albedo can be calculated through integration of the BRDF for a particular illumination geometry. 3 To esti-mate remotely sensed albedo, reflectance measurements must be interpreted with the help of BRDF models for retrieving the required variables from the actual observa-tions. In general, BRDF models can be classified into one or two of these categories: theoretical model (physical-based model), data-driven model, and empirical model (phenom-enological model). Theoretical models try to accurately explain light scattering by using physics laws. The typical theoretical model was the microfacet model, which was the basis for the individual models such as Torrance-Sparrow BRDF, 4,5 Cook-Torrance, 6 Oren-Nayar BRDF, 7 and so on. They usually lead to complex expressions and high com-putational effort. These theoretical models result in a very difficult nonlinear optimization problem; thus they are not normally employed in rendering systems. In contrast, data-driven techniques use the measured data for rendering, which describe reflectance directly based from the tabulated data.