Geometric optimization for 3D pose estimation of quadratic surfaces

Our task is 3D pose estimation for on-line application in industrial robotics and machine vision. It involves the estimation of object position and orientation relative to a known model. Since most man made objects can be approximated by a small set of quadratic surfaces, in this paper we focus on pose estimation of such surfaces. Our optimization is of an error measure between the CAD model and the measured data. Most existing algorithms are sensitive to noise and occlusion or only converge linearly. Our optimization involves iterative cost function reduction on the smooth manifold of the Special Euclidean Group, SE₃. The optimization is based on locally quadratically convergent Newton-type iterations on this constraint manifold. A careful analysis of the underlying geometric constraint is required.