Error analysis of surface normals determined by radiometry

Surface normals can be computed from three images of a workpiece taken under three distinct lighting conditions without requiring surface continuity. Radiometric methods are susceptible to systematic errors such as: errors in the measurement of light source orientations; mismatched light source irradiance; detector nonlinearity; the presence of specular reflection or shadows; the spatial and spectral distribution of incident light; surface size, material, and microstructure; and the length and properties of the light source to target path. Typically, a 1° error in surface orientation of a Lambertian workpiece is caused by a 1 percent change in image intensity due to variations in incident light intensity or a 1° change in orientation of a collimated light source. Tests on a white nylon sphere indicate that by using modest error prevention and calibration schemes, surface angles off the camera axis can be computed within 5°, except at edge pixels. Equations for the sensitivity of surface normals to major error sources have been derived. Results of surface normal estimation and edge extraction experiments on various non-Lambertian and textured workpieces are also presented.