Recovering 3D geometry from cameras in underwater applications involves the Refractive Structure-from-Motion problem where the non-linear distortion of light induced by a change of medium density invalidates the single viewpoint assumption. The pinhole-plus-distortion camera projection model suffers from a systematic geometric bias since refractive distortion depends on object distance. This leads to inaccurate camera pose and 3D shape estimation. To account for refraction, it is possible to use the axial camera model or to explicitly consider one or multiple parallel refractive interfaces whose orientations and positions with respect to the camera can be calibrated. Although it has been demonstrated that the refractive camera model is well-suited for underwater imaging, Refractive Structure-from-Motion remains particularly difficult to use in practice when considering the seldom studied case of a camera with a flat refractive interface. Our method applies to the case of underwater imaging systems whose entrance lens is in direct contact with the external medium. By adopting the refractive camera model, we provide a succinct derivation and expression for the refractive fundamental matrix and use this as the basis for a novel two-view reconstruction method for underwater imaging. For validation we use synthetic data to show the numerical properties of our method and we provide results on real data to demonstrate its practical application within laboratory settings and for medical applications in fluid-immersed endoscopy. We demonstrate our approach outperforms classic two-view Structure-from-Motion method relying on the pinhole-plus-distortion camera model.

Accounting for 26% of all new cancer cases worldwide, breast cancer remains the most common form of cancer in women. Although early breast cancer has a favourable long-term prognosis, roughly a third of patients suffer from a suboptimal aesthetic outcome despite breast conserving cancer treatment. Clinical-quality 3D modelling of the breast surface therefore assumes an increasingly important role in advancing treatment planning, prediction and evaluation of breast cosmesis. Yet, existing 3D torso scanners are expensive and either infrastructure-heavy or subject to motion artefacts. In this paper we employ a single consumer-grade RGBD camera with an ICP-based registration approach to jointly align all points from a sequence of depth images non-rigidly. Subtle body deformation due to postural sway and respiration is successfully mitigated leading to a higher geometric accuracy through regularised locally affine transformations. We present results from 6 clinical cases where our method compares well with the gold standard and outperforms a previous approach. We show that our method produces better reconstructions qualitatively by visual assessment and quantitatively by consistently obtaining lower landmark error scores and yielding more accurate breast volume estimates.

Recovering 3D scene geometry from underwater images involves the Refractive Structure-from-Motion (RSfM) problem, where the image distortions caused by light refraction at the interface between different propagation media invalidates the single view point assumption. Direct use of the pinhole camera model in RSfM leads to inaccurate camera pose estimation and consequently drift. RSfM methods have been thoroughly studied for the case of a thick glass interface that assumes two refractive interfaces between the camera and the viewed scene. On the other hand, when the camera lens is in direct contact with the water, there is only one refractive interface. By explicitly considering a refractive interface, we develop a succinct derivation of the refractive fundamental matrix in the form of the generalised epipolar constraint for an axial camera. We use the refractive fundamental matrix to refine initial pose estimates obtained by assuming the pinhole model. This strategy allows us to robustly estimate underwater camera poses, where other methods suffer from poor noise-sensitivity. We also formulate a new four view constraint enforcing camera pose consistency along a video which leads us to a novel RSfM framework. For validation we use synthetic data to show the numerical properties of our method and we provide results on real data to demonstrate performance within laboratory settings and for applications in endoscopy.