The Generalized Relative Pose and Scale Problem: View-Graph Fusion via 2D-2D Registration

Abstract

It is well-known that the relative pose problem can be
\ngeneralized to non-central cameras. We present a further
\ngeneralization, denoted the generalized relative pose
\nand scale problem. It has surprising importance for classical
\nproblems such as solving similarity transformations
\nfor view-graph concatenation in hierarchical structure from
\nmotion and loop-closure in visual SLAM, both posed as a
\n2D-2D registration problem. The relative pose problem and
\nall its generalizations constitute a family of similar symmetric
\neigenvalue problems, which allow us to compress data
\nand find a geometrically meaningful solution by an efficient
\nsearch in the space of rotations. While the derivation of a
\ncompletely general closed-form solver appears intractable,
\nwe make use of a simple heuristic global energy minimization
\nscheme based on local minimum suppression, returning
\noutstanding performance in practically relevant scenarios.
\nEfficiency and reliability of our algorithm are demonstrated
\non both simulated and real data, supporting our claim of superior
\nperformance with respect to both generalized 2D-3D
\nand 3D-3D registration approaches. By directly employing
\nimage information, we avoid the common noise in point
\nclouds occuring especially along the depth direction.