On Image Analysis by the Methods of Moments
IEEE Transactions on Pattern Analysis and Machine Intelligence
3-D Moment Forms: Their Construction and Application to Object Identification and Positioning
IEEE Transactions on Pattern Analysis and Machine Intelligence
The revised Fundamental Theorem of Moment Invariants
IEEE Transactions on Pattern Analysis and Machine Intelligence
Graphical Models and Image Processing
Digital Pattern Recognition by Moments
Journal of the ACM (JACM)
Reconstruction of Three-Dimensional Objects through Matching of Their Parts
IEEE Transactions on Pattern Analysis and Machine Intelligence
Moment Forms Invariant to Rotation and Blur in Arbitrary Number of Dimensions
IEEE Transactions on Pattern Analysis and Machine Intelligence
On Characterization of Discrete Triangles by Discrete Moments
DGCI '02 Proceedings of the 10th International Conference on Discrete Geometry for Computer Imagery
On discrete triangles characterization
Computer Vision and Image Understanding
Matching and normalization of affine deformed image from regular moments
Pattern Recognition Letters
Pattern Recognition
Extension of Moment Features' Invariance to Blur
Journal of Mathematical Imaging and Vision
International Journal of Computer Vision
Measuring Cubeness of 3D Shapes
CIARP '09 Proceedings of the 14th Iberoamerican Conference on Pattern Recognition: Progress in Pattern Recognition, Image Analysis, Computer Vision, and Applications
Person identification from human walking sequences using affine moment invariants
ICRA'09 Proceedings of the 2009 IEEE international conference on Robotics and Automation
2-D ultrasound probe complete guidance by visual servoing using image moments
IEEE Transactions on Robotics
Projective invariants of co-moments of 2D images
Pattern Recognition
Decoupled image-based visual servoing for cameras obeying the unified projection model
IEEE Transactions on Robotics
Affine moment invariants generated by graph method
Pattern Recognition
Tunable cubeness measures for 3D shapes
Pattern Recognition Letters
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The proof of the generalized fundamental theorem of moment invariants (GFTMI) [1] is presented for n-dimensional pattern recognition. In 1962, Hu [2] formulated the fundamental theorem of moment invariants (FTMI) for two-dimensional pattern recognition, that is subjected to general linear transformation. In 1970, I showed that the FTMI was in fact incorrect, and the corrected FTMI (CFTMI) was formulated [3], which was generalized by us for n-dimensional case in 1974 [1] without proof. On the basis of GFTMI, the moment invariants of affine transformation and subgroups of affine transformation are constructed. Using these invariants, the conceptual mathematical theory of recognition of geometric figures, solids, and their n-dimensional generalizations is worked out. By means of this theory, it is possible for the first time to analyze scenes consisting not only of polygons and polyhedra, as so far, but also scenes consisting of geometric figures and solids with curved contours and surfaces, respectively. In general, it is the author's opinion that this theory is a useful step toward the essential development of robot vision and toward creating machine intelligence驴to make machines able to think by means of geometric concepts of different generalities and dimensions, and by associations of these concepts.