Technical report | Sparse Reconstruction of a Scene and Camera Poses from the Scene Images with MATLAB®

Abstract

This report addresses the description and implementation of numerical algorithms for the reconstruction of world points representing a scene, and pinhole camera poses from the scene images. The Image Processing and Computer Vision System toolboxes of MATLAB are used for detecting, extracting and matching features in images. A camera graph is introduced to indicate which image pairs to process, and a homography graph is derived as a sub-graph of the line graph of the camera graph to parametrize three-dimensional transition homographies.

Executive Summary

This report addresses the description and implementation of numerical algorithms for the reconstruction of world points representing a scene, and pinhole camera poses from the scene images. The Image Processing and Computer Vision System toolboxes of MATLAB are used for detecting, extracting and matching features in images. A camera graph is introduced to indicate which image pairs to process, and a homography graph is derived as a sub-graph ofthe line graph of the camera graph to parametrize three-dimensional transition homographies.

The estimated transition homographies are applied to world points and cameras, locally reconstructed from image pairs, to bring them to a global frame of homogeneous coordinates. Then potentially duplicate points are eliminated using an introduced metric between two projective points with respect to cameras, and a visibility relation for Bundle Adjustment is computed. This approach properly addresses the common situation when a point disappears from a camera view and reappears later. Compatibility cocycle conditions for keypoint matching relations over the camera graph cycles and for transition homographies over the homography graph cycles are discussed.