Specularity removal for shape-from-shading
Frank Chi-Hung Tong · Summit (Simon Fraser University) · 1987
Specularity reflecting surfaces confuse traditional shape-from-shading algorithms because the variation in image intensity within a specularity does not directly relate to the cosine of the incident angle, as it would for a simple Lambertian reflector.To overcome this problem.color is introduced and a method of removing the specular component of the intensity variation is proposed based on a dichromatic model of surface reflection.Unlike Shafer's method for specularity removal, which is restricted to uniformly colored surface patches, our algorithm uses information from several differently colored regions.The problem of segmenting an image into color regions is successfully avoided as the specular component is calculated and removed using local operations only.The image resulting from specularity removal preserves the relative intensity of the diffuse component so it can then be input to a shape-from-shading algorithm.Our shape-from-shading algorithm is based on variational calculus.Without assuming the location of the scene illurninant, and allowing background illumination, the algorithm computes the shape from the diffuse component image in a more general setting than the existing algorithms do.In the thesis, the algorithm is formulated into a local relaxation scheme which allows a parallel network implementation.iii Spcculm Removal for Shape-from-Shading To my parents.Ded icuf ion Specular Runovd for Shape-fromshading 'The notion of surface smoothness is formulated in various ways.In Horn's work [~rHo85], smoothness is realized as a minimization of the gradient of the surface.In another work [HoBr86], a more sophisticated formulation is used.A smooth surface is considered as an integrable one, i.e. z x j .= -Z j , .where Z is thede~th~map of-the image.'The reflected intensity is at a constant ratio to the illuminating intensity.'The reflected intensity is independent of the viewing angle.They are also known as Lambertian reflectors.'when light strikes a surface, part of it is reflected at the air-material interface due to the difference in the refractive indices across the interface.See [Shaf84b] 'when light traverses the bulk of a surface, it undergoes scattering, absorption, and reemission by the colorant particles on the way.The degree of interaction differs with the wavelength of the light.When the light reemerges from the surface, it shows a different spectrum with respect to the incident light.The ratio between the reflected and the incident spectra is called the surface reflectance.See [Shaf84b].' known aepriori.Brooks and Horn, in [~rHo85], treated the intensity and direction of the light in different chromaticities.12A variational problem is a one in which it seeks to extremize a functional so that the pro.blem is forced to the optimal solution.Some constraints are usually incorporated into the functional to restrict the set of candidate solutions to a plausible one.I3A variational problem is said to be well-posed if extremization of the functional would lead to a unique solution.