Recovering absolute scale for Structure from Motion using the law of free fall

Abstract Reconstructions of objects (or scenes) using Structure from Motion (SfM) based on monocular camera or multiple uncalibrated cameras are only possible up to an unknown scale. Most of existing approaches for recovering absolute scale for SfM rely on additional constraints in absolute scale quantified by either metric data of the object (or scene) or motion data of the camera(s). This paper presented a novel approach for recovering absolute scale for SfM based on motion constraints defined by a relative free fall motion between the camera and the object. The proposed approach is strict because the adopted relative free fall motion is directly reconstructed by SfM and is therefore not complicated by the intrinsic problem that the motion of the camera recorded by external sensors cannot truly represent the motion of the center of perspective of the camera. Experiments of the proposed approach based on a widely used SfM-MVS pipeline had derived scale factors with relative errors smaller than 5%, yet returned camera motions that did not approximate with a reasonable degree of accuracy to what the law of free fall predicted. It is suggested that this deviation is owing to that SfM processes are not constrained by physical laws, and might be moderated by fusing kinematic constraints of free fall motion into bundle adjustment. In addition, uncertainties related to camera properties and experiment designs should also be reduced so that the proposed closed-form analytical solution for recovering absolute scale can work properly in practice. To our knowledge, this paper for the first time shows the potential of recovering absolute scale for geometric SfM reconstruction using a universal physical law.