VIEW VARIATION OF POINT-SET AND LINE-SEGMENT FEATURES

The recognition of 3-D objects becomes much more difficult as the position of the viewer relative to the object becomes less constrained. Part of this difficulty comes from the fact that many important features of an object's image vary with view. This paper is a study of the variation, with respect to view, of 2-D features defined for projections of 3-D point sets and line segments. It is first established that general-case view-invariants do not exist for any number of points, given true perspective, weak perspective or orthographic projection models. The remainder of the paper focuses on feature variation under the weak perspective approximation. Though there are no general-case weak-perspective invariants, there are special-case invariants of practical importance. The special-case weak-perspective invariants cited in the literature are derived from linear dependence relations and the invariance of this type of relation to linear transformation. The variation with respect to view is then studied for an important set of 2-D line segment features: the relative orientation, size, and position of one line segment with respect to another. The analysis includes an important evaluation criterion for feature utility in terms of view-variation: the relationship between the fraction of views (over a view sphere) and the range or values assumed by a feature over these views. This relationship is a function of both the feature and the particular configuration of 3-D line segments; an analysis and series of graphs are presented for each of the features and for different configurations of 3-D line segments. Finally, the use of this information in objection recognition is demonstrated in difficult discrimination tasks.