Analyzing the Effect of Angle of Incidence on the Terrestrial Laser Scanning Intensity of Broad-Leaved Surfaces Using a Piecewise Data-Driven Model

Terrestrial laser scanners provide both geometric and radiometric information, and terrestrial laser scanning (TLS) intensity is influenced by surface optical properties and the angle of incidence. This study presents a piecewise polynomial Lambert–Beckmann (PPLB) model to enhance TLS intensity characterization for broad-leaved surfaces. The PPLB model incorporates the Beckmann law, thus enabling a data-driven estimation of transition angles and enhancing the fitting flexibility across diverse leaf surfaces. TLS measurements were conducted on adaxial and abaxial leaf surfaces of five tree species using a RIEGL VZ-400 scanner. The results indicated that the TLS intensity consistently declined as the angle of incidence increased; however, different species and surfaces showed distinct angular response patterns. Across all ten tested species–surface combinations, the PPLB model achieved low root mean square error values of 0.0095–0.0183 and yielded three physically meaningful parameters: specular reflection contribution (ks), surface roughness (m), and transition angle (θT). Excluding the θT = 0° fitted result for the Golden Shower Tree abaxial surface, the estimated nonzero θT values ranged from 30° to 64°, indicating substantial variability in threshold angles among leaf surfaces beyond the commonly assumed value of 45°. These findings highlight the importance of incorporating surface-specific threshold angles for improved leaf characterization.