On optimally combining pieces of information, with application to estimating 3-d complex-object position from range data.

New asymptotic methods are introduced that permit computationally simple Bayesian recognition and parameter estimation for many large data sets described by a combination of algebraic, geometric, and probabilistic models. The techniques introduced permit controlled decomposition of a large problem into small problems for separate parallel processing where maximum likelihood estimation or Bayesian estimation or recognition can be realized locally. These results can be combined to arrive at globally optimum estimation or recognition. The approach is applied to the maximum likelihood estimation of 3-D complex-object position. To this end, the surface of an object is modeled as a collection of patches of primitive quadrics, i.e., planar, cylindrical, and spherical patches, possibly augmented by boundary segments. The primitive surface-patch models are specified by geometric parameters, reflecting location, orientation, and dimension information. The object-position estimation is based on sets of range data points, each set associated with an object primitive. Probability density functions are introduced that model the generation of range measurement points. This entails the formulation of a noise mechanism in three-space accounting for inaccuracies in the 3-D measurements and possibly for inaccuracies in the 3-D modeling. We develop the necessary techniques for optimal local parameter estimation and primitive boundary or surface type recognition for each small patch of data, and then optimal combining of these inaccurate locally derived parameter estimates in order to arrive at roughly globally optimum object-position estimation.

Bayesian recognition of local 3-d shape by approximating image intensity functions with quadric polynomials.

The recognition in image data of viewed patches of spheres, cylinders, and planes in the 3-D world is discussed as a first step to complex object recognition or complex object location and orientation estimation. Accordingly, an image is partitioned into small square windows, each of which is a view of a piece of a sphere, or of a cylinder, or of a plane. Windows are processed in parallel for recognition of content. New concepts and techniques include approximations of the image within a window by 2-D quadric polynomials where each approximation is constrained by one of the hypotheses that the 3-D surface shape seen is either planar, cylindrical, or spherical; a recognizer based upon these approximations to determine whether the object patch viewed is a piece of a sphere, or a piece of a cylinder, or a piece of a plane; lowpass filtering of the image by the approximation. The shape recognition is computationally simple, and for large windows is approximately Bayesian minimum-probability-of-error recognition. These classifications are useful for many purposes. One such purpose is to enable a following processor to use an appropriate estimator to estimate shape, and orientation and location parameters for the 3-D surface seen within a window.