The orientation, or pose, of an object is a fundamental property that helps to define the geometrical relationship between the object and its environment. In addition, knowledge of object orientation can also facilitate interpretive and decision-making tasks in a variety of practical domains, including industrial, meteorological, and medical applications. Determining object pose, however, remains an open research question in the fields of graphics and visualization. This article describes a novel yet intuitively simple approach, which we call topological goniometry, to directly determine the pose of a three-dimensional object from 3D data. The topology of interest is that of two-sided surfaces in a three-manifold, and includes objects whose shaped are unaffected by elastic transformations. Algorithmically, topological goniometry is composed of the following major steps. The first analyzes the global topology in order to generate a distribution of 3D coordinate triplets in the proximity of the desired pose axis. Using this set of 3D points, that second step then invokes a "3D Walk" algorithm that considers 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 generalized 3D curve. The methods are illustrated with a variety of synthetically created models that exhibit duct-like shapes, and are further tested by introducting noise as well as deformations to these models. The approach is also applied to a number of real discrete data obtained from meteorological and medical domains. The results suggest that the appproach is applicable to both real and synthetic datasets and is shown to be robust, computationally efficient, and applicable to a variety of problems. The approach can incorporate context- or application-dependent information about the object of interest by using a set of constraints that guide the process of orientation determination. This article describes the approach, its implementation, and the results obtained with numerous applications.

Categories and Subject Descriptors