Structure from Motion on a Sphere

TL;DR

This paper introduces a specialized structure-from-motion method for cameras rotating on a sphere, providing a minimal and efficient essential matrix solution for scene reconstruction with unique camera orientations.

Contribution

It presents a novel minimal solver for the essential matrix in spherical camera motion, enabling efficient scene reconstruction and object scanning.

Findings

Efficient minimal solution for essential matrix with three point correspondences.

Application of the method in scene modeling and object scanning.

Effective pipeline combining rotation averaging and bundle adjustment.

Abstract

We describe a special case of structure from motion where the camera rotates on a sphere. The camera's optical axis lies perpendicular to the sphere's surface. In this case, the camera's pose is minimally represented by three rotation parameters. From analysis of the epipolar geometry we derive a novel and efficient solution for the essential matrix relating two images, requiring only three point correspondences in the minimal case. We apply this solver in a structure-from-motion pipeline that aggregates pairwise relations by rotation averaging followed by bundle adjustment with an inverse depth parameterization. Our methods enable scene modeling with an outward-facing camera and object scanning with an inward-facing camera.