Three-dimensional reconstruction of endoscope images by a fast shape from shading method

Abstract

Three-dimensional (3D) reconstruction from images has been one of the fundamental problems in the domain of computer vision. Shape from shading (SFS) is an approach to obtain the shape of an object from a single intensity image. This paper presents a 3D reconstruction approach for endoscope images using a fast SFS method. A new image irradiance equation of endoscope images is established based on the facts that the image is formed under perspective camera projection and the surface is illuminated by a near point light source. The light source is assumed to be located at the optical center of the camera and the attenuation of the illumination is taken into account. Then the image irradiance equation is derived as a nonlinear partial differential equation (PDE), which is associated with a static Hamilton–Jacobi equation considering the boundary conditions. The viscosity solution of the resulting Hamilton–Jacobi equation is approximated by using a new iterative fast marching method. The proposed approach is evaluated on both synthetic and real medical endoscope images and the experimental results show that the proposed approach is fast and accurate.