Novel Directional Blanket Covering Method for Surface Curvature Analysis at Different Scales and Directions

The curvature of surface topography is quantified in this study using a newly developed directional blanket covering curvature (DBCC) method. The novel method addresses a long-standing problem of a measurement of a local surface curvature at individual scales and directions. The curvature data are obtained using the first and second derivations of the quadratic polynomial fitted to the local surface profile extracted from the surface height image data at individual scale and direction. The range of scales is set between an instrument spatial resolution and 1/10 of the image shortest size. Using the surface curvature data, three parameters, i.e. curvature, peak and valley dimensions, are calculated as the slopes of lines fitted to data point subsets of log–log plots of surface areas (differences between dilated and eroded surface curvature matrices) against scales of calculation. The dimensions quantify directional changes in the overall curvature and the curvature of peaks and valleys at individual scales. The scale corresponds to the centre of the subset. A flat surface criterion based on the surface areas was also proposed. Using the criterion, a flat surface was identified in computer images of dome, corrugated plate and fractal surface. The DBCC method was applied to computer-generated fractal surfaces with increasing curvature complexity, sine waves with decreasing curvature at single scale and microscope images of isotropic (sandblasted) and anisotropic (ground) surfaces of titanium plates. Results showed that the method is accurate in the measurement of surface curvature and the detection of minute changes occurring in the curvature of real surfaces over a wide range of scales.