Self-calibration method for microfacet slope standard deviation σ in leaf BRDF microfacet model fitting

When data is fitted with the bidirectional reflectance distribution function (BRDF) microfacet model, the standard deviation σ of the microfacet slope for a Gaussian function is required. For leaves that contain strongly scattering media internally, when fitting is performed with light incident at small angles (e.g., angles of incidence ranging between 10° and 30°), there are instances where multiple fits with similar precision (σ) can yield good results (with comparable root mean square errors, RMSE). This phenomenon is especially pronounced in leaves with rough textures. Based on the leaf volumetric scattering BRDF model we proposed, the fitting results of data obtained from thirteen leaf samples revealed that an exponential (e-index) relationship exists between the difference between the volumetric scattering coefficient and the specular reflection coefficient in the model and the preset standard deviation of microfacet slopes. By utilizing this relationship, the preset range of σ (the standard deviation of microfacet slopes) can be narrowed, leading to better fitting results when data is fitted with light incident at small angles. Furthermore, in contrast to common volumetric scattering models, the coefficients of the volumetric scattering model employed in this paper demonstrate a more predictable and regular pattern of variation in response to changes in σ.