Pose detection of 3-D objects using images sampled on SO(3), spherical harmonics, and wigner-D matrices

Determining the pose of three-dimensional objects from two-dimensional images has become an important issue in industrial automation applications. Eigendecomposition represents one computationally efficient method for dealing with this class of problems. One major drawback of using the eigendecomposition technique is the expensive off-line computation required to calculate the optimal subspace. This off-line computational expense may preclude the use of eigendecomposition for industrial applications where time is of the essence. In this work, we address this issue by proposing a computationally efficient algorithm for estimating the eigendecomposition to a user specified accuracy. In particular, we sample the rotation group SO(3) in a manner that allows us to take advantage of the correlation in SO(3) and transform the data from the spatial domain to the spectral domain. We then present an algorithm to estimate the eigendecomposition in this domain, thus relieving the computational burden. Experimental results are presented to compare the proposed algorithm to the true eigendecomposition, as well as assess the computational savings.