Relative Pose Estimation from Image Correspondences under a Remote Center of Motion Constraint

Abstract

This letter proposes an algorithm to estimate the relative pose between two image view-points assuming that a camera is moving under a remote center of motion constraint. This is useful in minimally invasive robotic surgery, where the motion of a laparoscopic camera is constrained by the keyhole insertion point. Our method uses point correspondences between the two images and does not require any knowledge about the position of the remote center of motion. The pipeline consists of a 4-point minimal closed-form solver, used within a robust RANSAC framework to filter outlier correspondences, followed by a Levenberg-Marquardt refinement step. Our method compares favorably against the classic relative pose solution for unconstrained motion (5-point algorithm) both with synthetic data and a real footage of endoscopic robotic surgery.