Image encoding, labeling and reconstruction from differential geometry
Erhardt Barth, Terry Caelli, and Christoph Zetzsche
ABSTRACT In this paper we consider how the representation
of images as surfaces, and their characterizations via surface differential
forms, can be related to the concept of redundancy in the intensity signal.
In contrast to common approaches, the basic surface types (planar, parabolic,
elliptic/hyperbolic) are not seen as equal-priority classes, but as corresponding
to different degrees of redundancy. This leads to a new approach to image
representation and region labeling based upon generalized curvature measures.
Furthermore, we employ different reconstruction algorithms to show that
elliptic surface patches carry the significant information in natural images.
Based upon deterministic and stochastic relaxation techniques, these algorithms
allow one to reconstruct the original image from (i) "elliptic intensities"
only and (ii) curvature measures which are zero for nonelliptic regions.
Reprint Request.
Efficient
visual representation and reconstruction from generalised curvature measures
is
a brief, preliminary version of this paper.