Fast eigenspace decomposition of correlated images.

We present a computationally efficient algorithm for the eigenspace decomposition of correlated images. Our approach is motivated by the fact that for a planar rotation of a two-dimensional (2-D) image, analytical expressions can be given for the eigendecomposition, based on the theory of circulant matrices. These analytical expressions turn out to be good first approximations of the eigendecomposition, even for three-dimensional (3-D) objects rotated about a single axis. In addition, the theory of circulant matrices yields good approximations to the eigendecomposition for images that result when objects are translated and scaled. We use these observations to automatically determine the dimension of the subspace required to represent an image with a guaranteed user-specified accuracy, as well as to quickly compute a basis for the subspace. Examples show that the algorithm performs very well on a number of test cases ranging from images of 3-D objects rotated about a single axis to arbitrary video sequences.

A multiscale stochastic image model for automated inspection.

We develop a novel multiscale stochastic image model to describe the appearance of a complex three-dimensional object in a two-dimensional monochrome image. This formal image model is used in conjunction with Bayesian estimation techniques to perform automated inspection. The model is based on a stochastic tree structure in which each node is an important subassembly of the three-dimensional object. The data associated with each node or subassembly is modeled in a wavelet domain. We use a fast multiscale search technique to compute the sequential MAP (SMAP) estimate of the unknown position, scale factor, and 2-D rotation for each subassembly. The search is carried out in a manner similar to a sequential likelihood ratio test, where the process advances in scale rather than time. The results of this search determine whether or not the object passes inspection. A similar search is used in conjunction with the EM algorithm to estimate the model parameters for a given object from a set of training images. The performance of the algorithm is demonstrated on two different real assemblies.