Monocular 3D scene reconstruction at absolute scale

Abstract

In this article we propose a method for combining geometric and real-aperture methods for monocular three-dimensional (3D) reconstruction of static scenes at absolute scale. Our algorithm relies on a sequence of images of the object acquired by a monocular camera of fixed focal setting from different viewpoints. Object features are tracked over a range of distances from the camera with a small depth of field, leading to a varying degree of defocus for each feature. Information on absolute depth is obtained based on a Depth-from-Defocus approach. The parameters of the point spread functions estimated by Depth-from-Defocus are used as a regularisation term for Structure-from-Motion. The reprojection error obtained from bundle adjustment and the absolute depth error obtained from Depth-from-Defocus are simultaneously minimised for all tracked object features. The proposed method yields absolutely scaled 3D coordinates of the scene points without any prior knowledge about scene structure and camera motion. We describe the implementation of the proposed method both as an offline and as an online algorithm. Evaluating the algorithm on real-world data, we demonstrate that it yields typical relative scale errors of a few per cent. We examine the influence of random effects, i.e. the noise of the pixel grey values, and systematic effects, caused by thermal expansion of the optical system or by inclusion of strongly blurred images, on the accuracy of the 3D reconstruction result. Possible applications of our approach are in the field of industrial quality inspection; in particular, it is preferable to stereo cameras in industrial vision systems with space limitations or where strong vibrations occur.