Multiscale slope analysis and functional correlation with gloss reflectance from photographic papers

Abstract

A novel multiscale 3D topographic characterization for slope is introduced. Slope is considered as a crucial parameter linking area-scale and 3D curvature analyses. Relationships between surface topography and gloss reflectance in photographic papers are used for an example application. Directional angles, characterizing slopes, are calculated two ways: normals to triangular facets (method 1), and eigenvectors of a covariance matrix based on nine points (method 2). Slope is the steepness of surface inclinations associated with the orientation of local surface features (facets). The impact of slope on gloss reflectance supports the use of pertinent geometric characterizations, i.e., alignment of geometric characterizations with the physical nature of the topographic interaction phenomena. Topographies of 24 photographic papers, were measured with a laser scanning confocal microscope and their gloss reflectance was measured with a micro-TRI-gloss gloss meter. Analyses of slope distributions with bivariate dispersion measures of directional angles and their trigonometric functions revealed strong correlations (R2 > 0.6) between slope distributions and gloss. Bivariate median deviation of secant or tangent of directional angles, demonstrated consistently high correlations across scales, magnifications, and filtrations. This study supports pertinent and useful characterizations grounded in the physics of topographic interaction phenomena to provide insights into relationships between surface topography, e.g., slope and gloss reflectance in photographic papers. This nuanced understanding has potential applications for other applications as well.