Motion and Structure from Feature Correspondences: A Review

We present a review of algorithms and their performance for determining three-dimensional (3D) motion and structure of rigid objects when their corresponding features are known at different times or are viewed by different cameras. Three categories of problems are considered, depending upon whether the features are two(2D) or three-dimensional (3D) and the type of correspondence: A) 3D to 3D (i.e., locations of corresponding features in 3D space are known at two different times), b) 2D to 3D (i.e., locations of features in 3D space and their projection on the camera plane are known), and c) 2D to 2D (i.e., projections of features on the camera plane are known at two different times). Features considered include points, straight lines, curved lines, and corners. Emphasis is on problem formulation, efficient algorithms for solution, existence and uniqueness of solutions. and sensitivity of solutions to noise in the observed data. Algorithms described have been used in a variety of applications. Some of these are: A) positioning and navigating 3D objects in a 3D world, b) camera calibration, i.e., determining location and orientation of a camera by observing 3D features whose location is known, c) estimating motion and structure of moving objects relative to a camera. We mention some of the mathematical techniques borrowed from algebraic geometry, projective geometry, and homotopy theory that are required to solve these problems, list unsolved problems, and give some directions for future research.