Abstract
Moments are statistical measures used to obtain relevant information
about a certain object under study (e.g., signals, images or waveforms),
e.g., to describe the shape of an object to be recognized by a pattern
recognition system. Invariant moments (e.g., the Hu invariant set)
are a special kind of these statistical measures designed to remain
constant after some transformations, such as object rotation, scaling,
translation, or image illumination changes, in order to, e.g., improve
the reliability of a pattern recognition system. The classical moment
invariants methodology is based on the determination of a set of
transformations (or perturbations) for which the system must remain
unaltered. Although very well established, the classical moment invariants
theory has been mainly used for processing single static images (i.e.
snapshots) and the use of image moments to analyze images sequences
or video, from a dynamic point of view, has not been sufficiently
explored and is a subject of much interest nowadays. In this paper,
we propose the use of variant moments as an alternative to the classical
approach. This approach presents clear differences compared to the
classical moment invariants approach, that in specific domains have
important advantages. The difference between the classical invariant
and the proposed variant approach is mainly (but not solely) conceptual:
invariants are sensitive to any image change or perturbation for
which they are not invariant, so any unexpected perturbation will
affect the measurements (i.e. is subject to uncertainty); on the
contrary, a variant moment is designed to be sensitive to a specific
perturbation, i.e., to measure a transformation, not to be invariant
to it, and thus if the specific perturbation occurs it will be measured;
hence any unexpected disturbance will not affect the objective of
the measurement confronting thus uncertainty. Furthermore, given
the fact that the proposed variant moments are orthogonal (i.e. uncorrelated)
it is possible to considerably reduce the total inherent uncertainty.
The presented approach has been applied to interesting open problems
in computer vision such as shape analysis, image segmentation, tracking
object deformations and object motion tracking, obtaining encouraging
results and proving the effectiveness of the proposed approach.
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