Tracker-endoscope calibration for colonoscopy

This thesis presents work in nonlinear optimization, linear algebra, and computer vision, for the purpose of calibrating a dual-sensor colonoscopy setup. The relative orientation and offset between the reference frame of a magnetic tracker and endoscope are determined automatically, allowing the position and orientation of the endoscope tip to be inferred directly from the tracker readings. The goal of this research is to enable 3D reconstruction of the colon for use in cancer screening. Colorectal cancer is the third most common form of cancer and second leading cause of cancer-related death in the Western world. Polyps, diverticula and depressed lesions are threats that may be undetected in standard exams[43]. In this thesis, a dual-sensor calibration method is presented that makes possible the application of computer vision algorithms to colonoscopy. Such techniques can be used to locate lesions that may be otherwise difficult to detect. The calibration algorithm has three stages: camera calibration, linear approximation, and nonlinear optimization. Calibration is used to determine the intrinsic, extrinsic, and distortion parameters of the endoscope. As endoscopes feature large fisheye distortion, accurate calibration of the distortion parameters is needed since distortion correction must be applied before any computer vision algorithms can be used. The intrinsic and extrinsic parameters of the endoscope are then used in the linear approximation stage. In the second stage the camera positions and orientations relative to the tracker base and the calibration grid are equated, forming a system of nonlinear equations. Rotations are parameterized as nine variable matrices to create a linear overdetermined system. An LDLT decomposition solves for the tracker-camera transformation. Due to the excess of degrees of freedom, the rotations produced are not orthonormal; this is solved by post-processing with an SVD. The third step is nonlinear optimization. Here we use our implementation of a state-of-the art trust region based global minimizer. As we no longer need a linear parameterization, rotations are parameterized in axis-angle format. The optimization routines treat quantities determined in calibration as ground truth, with the initial guess for the variable assignment provided by the linear approximation.