Sensitivity of reflected radiance to surface normal orientation

Given the illumination and the surface normal at a point on a convex surface, the effect of small changes in surface normal direction on observed reflected radiance is examined. A signal-processing framework suitable for the hemispherical geometry of the problem is applied to discuss surface reflection in terms of convolving incident illumination with the reflectance function. Depending on the surface material´s reflection properties as well as on the incident illumination distribution, normal direction deviation may or may not be noticeable. Expressions are derived to quantitatively evaluate the amount of change in reflected radiance. Different scenarios exemplify the results. The presented theoretical results have implications for shape-from-shading techniques as well as for scene-based compression methods.