Here, three classes of structures acquire descriptions: boundaries, surfaces and surface clusters. The structures are interrelated and at times their descriptions depend on their relationships with other entities. We have identified a variety of descriptions, some of which are listed below. Those numbered have been implemented and their computations are described in the given section. Those that are viewpoint invariant are signaled by a "(V)" annotation.
These three dimensional descriptions are reminiscent of the types of features used in traditional two dimensional pattern recognition approaches to computer vision (e.g. [14], pages 254-261). With these, one attempts to measure enough object properties to partition the feature space into distinct regions associated with single object classes. These techniques have been successful for small model bases containing simple, distinct unobscured two dimensional objects, because the objects can then be partially and uniquely characterized using object-independent descriptions. Unfortunately, three dimensional scenes are more complicated because the feature values may change as the object's orientation changes, and because of occlusion.
The description processes discussed below extract simple global properties of curves and surfaces. The processes assume constant shape, but the actual features are not always uniform, resulting in descriptions that are not always exact (e.g. the chair back is not a perfect cylinder, though it is described as such). However, the segmentation assumptions produce features with the correct shape class (e.g. locally ellipsoidal), and so a first-order global characterization is possible. This property is exploited to approximately characterize the features.
To estimate the global properties, global methods are used, as shown below. In retrospect, I feel that some of the methods are less theoretically ideal or practically stable than desired, and perhaps other approaches (e.g. least-squared error) might be better. That being said, the algorithms are generally simple and fast, using a few measurements from the data feature to estimate the desired property. There is a modest error, associated with most of the properties, but this is small enough to allow model invocation and hypothesis construction to proceed without problems.