PnS: a Perspective-n-Spheres Algorithm for Laparoscope Calibration in Minimally Invasive Surgery

Abstract

Accurate endoscope localization is a key element for Computer-Assisted Laparoscopic Surgery (CALS). External localizers track the endoscope pose and reconstruct the camera geometry through a calibration matrix. Perspective-n-Points (PnP) methods estimate this matrix from a set of paired point coordinates, given by the simultaneous position of a spherical marker on the image (2D coordinates) and in the external localizer frame (3D coordinates). In this paper, the PnP calibration is restated as an iterative Perspective-n-Spheres (PnS) problem: the spherical geometry of the marker is taken into account when computing the projection of its 3D center into the 2D image plane. Using calibration residuals as evaluation matrix, the proposed PnS provides better results compared to the State-of-the-Art (SoA) PnP methods. Furthermore, results show that the calibration yields different estimates due to different camera poses in the working volume. This is assumed to result from a lack of absolute precision in the marker localization across the external localizer workspace.