Invariants of objects and their images under surjective maps

Abstract

We examine the relationships between the differential invariants of objects and of their images under a surjective map. We analyze both the case when the underlying transformation group is projectable and hence induces an action on the image, and the case when only a proper subgroup of the entire group acts projectably. In the former case, we establish a constructible isomorphism between the algebra of differential invariants of the images and the algebra of fiber-wise constant (gauge) differential invariants of the objects. In the latter case, we describe residual effects of the full transformation group on the image invariants. Our motivation comes from the problem of reconstruction of an object from multiple-view images, with central and parallel projections of curves from three-dimensional space to the two-dimensional plane serving as our main examples.

Equi-affine differential invariants for invariant feature point detection

“…The computation of projective invariants is being investigated. Related works connect the differential invariants of 3D curves and their 2D projections through the method of moving frames [30,31].…”

A Feature Extraction Algorithm of Affine Invariant based on Region Partition

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