Orthogonality and optimality of view-graph-based information sets

Establish whether the view-graph-based data association constructed from pose graph edges (sequential, loop closure, and extrinsic edges) constitutes an ideal complete and orthogonal information set for visual pose estimation in Structure-from-Motion; formally define orthogonality between visual images in this context and prove or refute the claimed optimality of the view-graph information set.

Background

The paper proposes constructing a non-redundant view graph using pose graph priors (sequential, loop closure, and extrinsic edges) to guide feature matching and triangulation. This strategy aims to provide a complete yet non-redundant set of constraints that improves efficiency and accuracy compared to radius-based pairing.

In the trajectory refinement experiments, the authors argue that indiscriminately using all available matches is suboptimal and suggest that an ideal information set would be both complete and orthogonal. They note, however, that the orthogonality of visual images is difficult to formalize and that they cannot definitively prove their view-graph set attains this ideal, identifying a theoretical gap between empirical performance and formal guarantees.