Part I of this paper investigates the diierences | conceptually and algorithmically | between aane and projective frameworks for the tasks of visual recognition and reconstruction from perspective views. It is shown that an aane invariant exists between any view and a xed view chosen as a reference view. This implies that for tasks for which a reference view can be chosen, such as in alignment ...

We deene a new invariant for symbolic Z 2-actions, the projective fundamental group. This invariant is the limit of an inverse system of groups, each of which is the fundamental group of a space associated with the Z 2-action. The limit group measures a kind of long-distance order that is manifested along loops in the plane, and roughly speaking bears the same relation to the mixing properties ...

The geometrical description of an object can be separated into two parts: a) the registration information and b) the ‘shape’ (which is invariant under registration transformation). A common choice of registration is the group of Euclidean similarity transformations, and then the geometrical properties that are invariant under this group of transformations are known as ‘similarity shape’. In thi...

In this paper we propose to use invariant signatures of polygonal approximations of smooth curves for projective object recognition. Similar signatures have been proposed previously as simple and robust signatures. However, they were known to be sensitive to the curve sampling scheme and density, and worked well mainly for in-trinsically polygonal shapes. This paper proposes a re-sampling metho...

In this paper we find a discrete moving frame and their associated invariants along projective polygons in RP, and we use them to describe invariant evolutions of projective N -gons. We then apply a reduction process to obtain a natural Hamiltonian structure on the space of projective invariants for polygons, establishing a close relationship between the projective N -gon invariant evolutions a...

In Image-Based Modeling, which reconstructs 3-dimensional structures and extracts a texture from 2-dimensional images, one of the greatest problems is to match feature points of two images. The well-known template matching is used for automatically relating individual points in different images. However, since it matches each image in which a viewpoint position differs, incorrect feature points...

The paper deals with features of a 2-D point set which are invariant with respect to a projective transform. First, projective invariants for "ve-point sets, which are simultaneously invariant to the projective transform and to permutation of the points, are derived. They are expressed as functions of "ve-point cross-ratios. Then, the invariants for more than "ve points are derived. The algorit...