Optimal Estimation of Matching Constraints

We describe work in progress on a numerical library for estimating multi-image matching constraints, or more precisely the multi-camera geometry underlying them. The library will cover several variants of homographic, epipolar, and trifocal constraints, using various diierent feature types. It is designed to be modular and open-ended, so that (i) new feature types or error models, (ii) new constraint types or parametrizations, and (iii) new numerical resolution methods, are relatively easy to add. The ultimate goal is to provide practical code for stable, reliable, statistically optimal estimation of matching geometry under a choice of robust error models, taking full account of any nonlinear constraints involved. More immediately, the library will be used to study the relative performance of the various competing problem parametriza-tions, error models and numerical methods. The paper focuses on the overall design, parametrization and numerical optimization issues. The methods described extend to many other geometric estimation problems in vision, e.g. curve and surface tting.