Three-dimensional surface reconstruction from reflectance direction fields with orthogonal multicolor filters

Abstract

A three-dimensional (3D) freeform surface reconstruction method is proposed, specifically designed to handle complex surfaces, even those with steep inclinations. This method utilizes a one-shot color mapping imaging system to obtain reflectance direction fields using a stripe multicolor filter positioned in two orthogonal orientations. This imaging system can capture reflectance directions that are identifiable by corresponding colors. The multicolor filter consists of multiple stripe regions, each with a different transmission spectrum. Theoretically, an equation that describes the relationship between reflectance direction fields and the reflective 3D surface can be derived based on geometrical optics. By solving this equation using a deep neural network (DNN) as a gradient descent method without any training data, the 3D surface can be accurately reconstructed, even for surfaces with steep inclinations. The effectiveness of this method is validated through numerical demonstrations on several 3D surfaces, including complex ones with concave and convex areas, as well as steep inclinations.