A Probabilistic Graphical Model Approach to the Structure-and-Motion Problem
This addresses a fundamental problem in computer vision for 3D reconstruction, but it is incremental as it applies existing probabilistic graphical model techniques to a known bottleneck.
The paper tackles the structure-and-motion problem in computer vision by formulating it with probabilistic graphical models, using Gaussian random variables and sigma point parameterizations to linearize nonlinear relationships, and reports promising results in simulations and real-world data.
We present a means of formulating and solving the well known structure-and-motion problem in computer vision with probabilistic graphical models. We model the unknown camera poses and 3D feature coordinates as well as the observed 2D projections as Gaussian random variables, using sigma point parameterizations to effectively linearize the nonlinear relationships between these variables. Those variables involved in every projection are grouped into a cluster, and we connect the clusters in a cluster graph. Loopy belief propagation is performed over this graph, in an iterative re-initialization and estimation procedure, and we find that our approach shows promise in both simulation and on real-world data. The PGM is easily extendable to include additional parameters or constraints.