On Image Analysis by the Methods of Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
A survey of moment-based techniques for unoccluded object representation and recognition
CVGIP: Graphical Models and Image Processing
Moment-based texture segmentation
Pattern Recognition Letters
IEEE Transactions on Pattern Analysis and Machine Intelligence
Clustering Algorithms
New computational methods for full and subset Zernike moments
Information Sciences—Informatics and Computer Science: An International Journal - Mining stream data
ACM Computing Surveys (CSUR)
A new class of Zernike moments for computer vision applications
Information Sciences: an International Journal
Exact and Speedy Computation of Legendre Moments on Binary Images
WIAMIS '07 Proceedings of the Eight International Workshop on Image Analysis for Multimedia Interactive Services
A unified methodology for the efficient computation of discrete orthogonal image moments
Information Sciences: an International Journal
Zernike velocity moments for sequence-based description of moving features
Image and Vision Computing
Toward a generalized theory of uncertainty (GTU)--an outline
Information Sciences: an International Journal
A new feature extractor invariant to intensity, rotation, and scaling of color images
Information Sciences: an International Journal
A systematic method for efficient computation of full and subsets Zernike moments
Information Sciences: an International Journal
Information Sciences: an International Journal
Content-based facial image retrieval using constrained independent component analysis
Information Sciences: an International Journal
Fast computation of exact Zernike moments using cascaded digital filters
Information Sciences: an International Journal
A hybrid color distance for image segmentation
HAIS'11 Proceedings of the 6th international conference on Hybrid artificial intelligent systems - Volume Part II
3D markerless motion tracking in real-time using a single camera
IDEAL'11 Proceedings of the 12th international conference on Intelligent data engineering and automated learning
Circle detection using electro-magnetism optimization
Information Sciences: an International Journal
Concurrency and Computation: Practice & Experience
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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.