Iterative trocar-constrained laparoscope viewpoint search for enhanced surface coverage in 3D reconstruction

Autonomy is a growing trend in robot-assisted minimally invasive surgery. Autonomous systems require geometric information about the surgical environment, obtained from images and 3D reconstruction. The long-term goal of this work is to improve the completeness of endoscope-based 3D reconstruction by first creating a sparse 3D model and then guiding the laparoscope toward areas missing from the reconstruction. Guidance of rigid laparoscopes is challenging because the trocar, the entry point into the body, limits the degrees of freedom. Therefore, we propose an iterative geometric laparoscope viewpoint search approach, which considers the trocar point, the camera's field of view, and the robot's inverse kinematics. The validation, using ex vivo organ datasets containing prepared holes in a reconstructed point cloud, showed a success rate of 85%, in which viewpoints could be improved for the corresponding prepared holes. In contrast to existing methods applying interpolation to improve surface coverage, our method aims to cover feasible regions of interest with the camera. We achieved a reconstruction error of 1-2 mm with a relative improvement of the surface coverage of up to 6.3%. The computation time for the brute-force approach is 10 s on average per region of interest and could be reduced to 6 ms by applying a nonlinear optimization solver.