A three-point solution with scale estimation ability for two-view flat-refractive underwater photogrammetry

Abstract

Underwater photogrammetry can efficiently document complex environments with limited accessibility. As the establishment of reference control networks is involved, using the relative two-view relation, which requires neither knowledge nor estimation of object-space coordinates, offers an attractive solution. In this paper, we study the two-view relation of underwater photogrammetry flat refractive geometry. Through its axial camera form, we show that the necessary correspondences to establish the relative orientation can be reduced to only three points. We also show that all six relative pose parameters can be estimated directly, where the baseline is estimated to its scale, with no external control. For the estimation, we propose direct models, and in seeking optimal minimization forms, we develop a closed-form expression for the epipolar curve. Thereby, we shed light on the epipolar geometry of the flat-refractive imaging system. For a complete evaluation, we also analyze the limits of the baseline estimation to its actual scale. In addition to our scale estimation ability, results show improved accuracy in the relative orientation parameters by order of magnitude or more compared to the state-of-the-art. Experiments demonstrate how our proposed model yields sub-millimeter levels of internal 3-space accuracy without introducing external knowledge.