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.

Robot-assisted laparoscopic prostatectomy (RALP) is a treatment for prostate cancer that involves complete or nerve sparing removal prostate tissue that contains cancer. After removal the bladder neck is successively sutured directly with the urethra. The procedure is called urethrovesical anastomosis and is one of the most dexterity demanding tasks during RALP. Two suturing instruments and a pair of needles are used in combination to perform a running stitch during urethrovesical anastomosis. While robotic instruments provide enhanced dexterity to perform the anastomosis, it is still highly challenging and difficult to learn. In this paper, we presents a vision-guided needle grasping method for automatically grasping the needle that has been inserted into the patient prior to anastomosis. We aim to automatically grasp the suturing needle in a position that avoids hand-offs and immediately enables the start of suturing. The full grasping process can be broken down into: a needle detection algorithm; an approach phase where the surgical tool moves closer to the needle based on visual feedback; and a grasping phase through path planning based on observed surgical practice. Our experimental results show examples of successful autonomous grasping that has the potential to simplify and decrease the operational time in RALP by assisting a small component of urethrovesical anastomosis.

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.

We propose a method for geometric calibration of multi-focus plenoptic cameras using raw images. Multi-focus plenoptic cameras feature several types of micro-lenses spatially aligned in front of the camera sensor to generate micro-images at different magnifications. This multi-lens arrangement provides computational-photography benefits but complicates calibration. Our methodology achieves the detection of the type of micro-lenses, the retrieval of their spatial arrangement, and the estimation of intrinsic and extrinsic camera parameters therefore fully characterising this specialised camera class. Motivated from classic pinhole camera calibration, our algorithm operates on a checker-board's corners, retrieved by a custom micro-image corner detector. This approach enables the introduction of a reprojection error that is used in a minimisation framework. Our algorithm compares favourably to the state-of-the-art, as demonstrated by controlled and freehand experiments, making it a first step towards accurate 3D reconstruction and Structure-from-Motion.

We study a problem that we call Shape-from-Template, which is the problem of reconstructing the shape of a deformable surface from a single image and a 3D template. Current methods in the literature address the case of isometric deformations, and relax the isometry constraint to the convex inextensibility constraint, solved using the so-called maximum depth heuristic. We call these methods zeroth-order since they use image point locations (the zeroth-order differential structure) to solve the shape inference problem from a perspective image. We propose a novel class of methods that we call first-order. The key idea is to use both image point locations and their first-order differential structure. The latter can be easily extracted from a warp between the template and the input image. We give a unified problem formulation as a system of PDEs for isometric and conformal surfaces that we solve analytically. This has important consequences. First, it gives the first analytical algorithms to solve this type of reconstruction problems. Second, it gives the first algorithms to solve for the exact constraints. Third, it allows us to study the well-posedness of this type of reconstruction: we establish that isometric surfaces can be reconstructed unambiguously and that conformal surfaces can be reconstructed up to a few discrete ambiguities and a global scale. In the latter case, the candidate solution surfaces are obtained analytically. Experimental results on simulated and real data show that our isometric methods generally perform as well as or outperform state of the art approaches in terms of reconstruction accuracy, while our conformal methods largely outperform all isometric methods for extensible deformations.

Recovering a deformable surface's 3D shape from a single view registered to a 3D template requires one to provide additional constraints. A recent approach has been to constrain the surface to deform quasi-isometrically. This is applicable to surfaces of materials such as paper and cloth. Current `closed-form' solutions solve a convex approximation of the original problem whereby the surface's depth is maximized under the isometry constraints (this is known as the maximum depth heuristic). No such convex approximation has yet been proposed for the conformal case. We give a unified problem formulation as a system of PDEs for developable, isometric and conformal surfaces that we solve analytically. This has important consequences. First, it gives the first analytical algorithms to solve this type of reconstruction problems. Second, it gives the first algorithms to solve for the exact constraints. Third, it allows us to study the well-posedness of this type of reconstruction: we establish that isometric surfaces can be reconstructed unambiguously and that conformal surfaces can be reconstructed up to a few discrete ambiguities and a global scale. In the latter case, the candidate solution surfaces are obtained analytically. Experimental results on simulated and real data show that our methods generally perform as well as or outperform state of the art approaches in terms of reconstruction accuracy.