View variation of point set and line segment features

摘要

The recognition of 3D objects becomes much more difficult as the relative viewing position becomes less constrained. For an image feature to be effective in the discrimination of 3D objects, it is useful if the distribution of the feature values over permissible views tends to be narrow. This paper is a study of the variation of point-set and line-segment features with respect to view. It is first established that there is no general-case view-invariant defined for any number of points, given true perspective, weak perspective or orthographic projection models.rnThe remainder of the paper focuses on feature variation under weak perspective, a commonly used projection model in 3D recognition. Its special-case invariants are explained in terms of the invariance of linear dependence relations with respect to linear transformation. The variation with respect to view is then studied for an important set of 2D 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 fraction of views (over a view sphere) and the range of values assumed by a feature over these views. This relationship is a function of both the feature and the particular configuration of 3D line segments; an analysis and series of graphs are presented for each of the features and for a few configurations of 3D line segments.