One-shot color mapping of a ray direction field for obtaining three-dimensional profiles integrating deep neural networks

Abstract

A method for simultaneously and instantly obtaining both a three-dimensional (3D) surface and its inclination angle distribution from a single image captured by an imaging system equipped with a coaxial multicolor filter that integrates deep neural networks (DNNs) is proposed. The imaging system can obtain a light-ray direction in the field of view through one-shot color mapping. Light rays reflected from a 3D surface, even if it has microscale height variations with a small inclination angle distribution, can be assigned different colors depending on their directions by the imaging system. This enables the acquisition of the surface inclination angle distribution. Assuming a smooth and continuous 3D surface, it is possible to reconstruct the surface from a single captured image using DNNs. The DNNs can provide the height variations of the 3D surface by solving a nonlinear partial differential equation that represents the relationship between height variation and the direction of light rays. This method is validated analytically and experimentally using microscale convex surfaces.