Stereo Vision Based 3D Reconstruction For Surgical Navigation System

Navigation systems for surgery enable a surgeon to look through the anatomy of the patient, to see the instruement invaded into the anatomy, and to plan the path of the instruement, so that the invasion is reduced and the accuracy of operation is improved. Consequently, surgical navigation has become a hot spot in medical field. Here, we hope to develop improved 3D reconstruction algorithms for surgical navigation systems.Three dimensional (3D) reconstruction is an important technical component for the implementation of surgical navigation system. Traditionally, 3D reconstruction includes the following technical components: camera calibration, feature extraction and correspondence and triangulation. To reduce complexity, circular features and spherical features are widely used in surgical navigation systems to serve as markers, because of their wide visibility, easy availability and invulnerability to partial occlusion. Therefore, this thesis revisits the reconstruction of circular and spherical features. Although some of these techniques have been partially solved in literatures, brand‐new viewpoints and systematic analysis are suggested in this work. For example, the projective equation of a circle is proposed, naturally encoding the intrinsic camera parameters and the circle pose parameters. This proposed equation can serve as a unified framework for circle based computer vision problems, including camera calibration and pose estimation. Specifically, technical advancements have been achieved in the following four aspects.1. Camera Calibration Using Circular FeaturesIn this thesis, we proposed an algorithm to calibrate the focal length and the extrinsic parameters of a camera by using two coplanar circles. This method only needs one perspective view of two coplanar circles with arbitrary radius and topologic configuration. We develop a closed form solution for this problem, whose results can be directly used in practical vision systems with moderate noise levels or used to initialize current iteration‐based algorithm for higher accuracy and speed.2. Reconstruction of circular featureDifferent from existing methods on the basis of analytical geometry, we develop the projective equation of a circle. Based on this equation, we explore the relation between the image of the absolute conic (IAC) and the circle image and propose a closed form solution for circle pose determination from one perspective view as well. By relating the redundancy of the estimated pose parameters to the ambiguity in identifying the image of circular points (ICPs), a new geometric explanation for the reasonability of the two sets of solutions is presented and their mutual relationship is disclosed. Furthermore, we propose a reconstruction algorithm of circles with known radius from binocular stereo vision to eliminate ambiguity.3. The Projected Sphere Center Dectection and Sphere ReconstructionIn this thesis, we define the deviation between the perspective elliptical contour center (PECC) and the projected sphere center (PSC) as their Euclidian distance in the image coordinate system. We first present the closed form representation of the deviation. We qualitatively conclude that the deviation becomes significant as the sphere leaves the central area of the camera's view field and approaches the image plane. If and only if the sphere center lies on the camera optical axis, the PSC is coincident with the PECC, i.e. the deviation equals to zero. To avoid solving nonlinear equation systems, we give the projective equation of a sphere in matrix form, thus enabling us to calculate the PSC by a least square method.4. Binocular Stereo Vision Based Deformable Sheet ReconstructionA fully calibrated stereo rig is used to capture images of the deformable surface. By using the L‐infinite norm, the keypoint correspondence between the model and the image is formulated as Second Order Cone Programming (SOCP), a subclass of convex optimization problems, which can be effectively solved using the interior point method. Unlike the traditional cost function measured by the L‐2 norm, the most outstanding advantage of the proposed algorithm lies in its theoretically proved global optimum, which can be easily and efficiently identified, without any process of initialization. Experiments verify the efficiency and accuracy of our proposed algorithm.Based on these theoretical fruits, we have developed a prototype for surgical navigation by designing a stereo vision rig and implementing such algorithms as feature extraction, triangulation, multi‐object segmention and coordinate transformation. Expriments have shown that our developed system is efficient and accurate.