Orthogonal variant moments features in image analysis

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.