Improvements in structure-from-motion techniques are enabling many scientific fields to benefit from the routine creation of detailed 3D models. However, for a large number of applications, only a single camera is available for the image acquisition, due to cost or space constraints in the survey platforms. Monocular structure-from-motion raises the issue of properly estimating the scale of the 3D models, in order to later use those models for metrology. The scale can be determined from the presence of visible objects of known dimensions, or from information on the magnitude of the camera motion provided by other sensors, such as GPS.

This paper addresses the problem of accurately scaling 3D models created from monocular cameras in GPS-denied environments, such as in underwater applications. Motivated by the common availability of underwater laser scalers, we present two novel approaches which are suitable for different laser scaler configurations. A fully unconstrained method enables the use of arbitrary laser setups, while a partially constrained method reduces the need for calibration by only assuming parallelism on the laser beams and equidistance with the camera. The proposed methods have several advantages with respect to existing methods. By using the known geometry of the scene represented by the 3D model, along with some parameters of the laser scaler geometry, the need for laser alignment with the optical axis of the camera is eliminated. Furthermore, the extremely error-prone manual identification of image points on the 3D model, currently required in image-scaling methods, is dispensed with.

The performance of the methods and their applicability was evaluated both on data generated from a realistic 3D model and on data collected during an oceanographic cruise in 2017. Three separate laser configurations have been tested, encompassing nearly all possible laser setups, to evaluate the effects of terrain roughness, noise, camera perspective angle and camera-scene distance on the final estimates of scale. In the real scenario, the computation of 6 independent model scale estimates using our fully unconstrained approach, produced values with a standard deviation of

. By comparing the values to the only other possible method currently usable for this dataset, we showed that the consistency of scales obtained for individual lasers is much higher for our approach ( compared to ).