AN APPROACH TO 3D POSE DETERMINATION

The orientation, or pose, of an object is a fundamental property that helps to define the geometrical relationship between the object and it s environment. In addition, knowledge of object orientation can also f acilitate interpretive and decision-making tasks in a variety of pract ical domains, including industrial, meteorological, and medical applic ations. Determining object pose, however, remains an open research que stion in the fields of graphics and visualization. This article descri bes a novel yet intuitively simple approach, which we call topological goniometry, to directly determine the pose of a three-dimensional obj ect from 3D data. The topology of interest is that of two-sided surfac es in a three-manifold, and includes objects whose shapes are unaffect ed by elastic transformations. Algorithmically, topological goniometry is composed of the following major steps. The first analyzes the glob al topology in order to generate a distribution of 3D coordinate tripl ets in the proximity of the desired pose axis. Using this set of 3D po ints, the second step then invokes a ''3D Walk'' algorithm that consid ers the local topology to produce a generalized curve representing an estimate of the object's axis of pose. The resultant pose axis is thus not constrained to lie along a straight line but can be a generalized 3D curve. The methods are illustrated with a variety of synthetically created models that exhibit duct-like shapes, and are further tested by introducing noise as well as deformations to these models. The appr oach is also applied to a number of real discrete data obtained from m eteorological and medical domains. The results suggest that the approa ch is applicable to both real and synthetic datasets and is shown to b e robust, computationally efficient, and applicable to a variety of pr oblems. The approach can incorporate context- or application-dependent information about the object of interest by using a set of constraint s that guide the process of orientation determination. This article de scribes the approach, its implementation, and the results obtained wit h numerous applications.