Norberto Ezquerra
Abstract
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.
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Index Terms
- An approach to 3D pose determination
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Reviews
Paolo E. Sabella
A methodology for determining the pose or orientation of a 3D object is presented. By a process the authors call topological goniometry, a generalized curve in three-dimensional space, referred to as the pose axis, is constructed to represent the object's pose. The pose axis is constructed by fitting a curve through the cluster of the midpoints of normal vectors extended inward from the baricenter of each polygon until they intersect another polygon. The algorithm involves heuristics such as only considering normal vectors that intersect within a predetermined distance, and selecting a scale factor and region of search when fitting the curve. The ability to determine the pose of an object is useful in analyzing surfaces extracted from meteorological data and 3D medical imagery. Although these extracted features enhance understanding of acquired data, there is no quantitative measure of how accurately the algorithm performs. To this end, 3D synthetic models were generated and the pose axis computed was compared to that computed when the models were degraded and subjected to noise; the authors used the area of the surface generated between the theoretical pose axis and the pose axis actually calculated as the measure of error. Unfortunately, the results are not conclusive, except perhaps to indicate the insensitivity of the algorithm to noise. This method appears to be a robust technique for computing a medial axis. Although it can be enhanced by incorporating application-dependent constraints and heuristics, this is a limitation as well as an advantage.
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