  Recent advances 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,
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. A fully-calibrated method enables the use of
arbitrary laser setups, while a partially-calibrated method reduces the need
for calibration by only assuming parallelism on the laser beams, with no
constraints on the camera. The proposed methods have several advantages with
respect to the existing methods. The need for laser alignment with the optical
axis of the camera is removed, together with the extremely error-prone manual
identification of image points on the 3D model.
  The performance of the methods and their applicability was evaluated on both
data generated from a realistic 3D model and 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. In the real scenario, the computation of 6 independent model scale
estimates using our fully-calibrated approach, produced values with standard
deviation of 0.3%.
