The Method of Normalization to Determine Invariants

The determination of invariant characteristics is an important problem in pattern recognition. Many invariants are known, which have been obtained either by normalization or by other methods. This paper shows that the method of normalization is much more general and allows one to derive a lot of sets of invariants from the second list as well. To this end, the normalization method is generalized and is presented in such a way that it is easy to apply, thus unifying and simplifying the determination of invariants. Furthermore, this paper discusses the advantages and disadvantages of the invariants obtained by normalization. Their main advantage is that the normalization process provides us with a standard position of the object. Because of the generality of the method, also new invariants are obtained such as normalized moments more stable than known ones, Legendre descriptors and Zernike descriptors to affine transformations, two-dimensional Fourier descriptors and affine moment invariants obtained by combining Hu's moment invariants and normalized moments.

[1]  Erland Jungert.  Qualitative spatial reasoning from the observer's point of view-towards a generalization of symbolic projection , 1994, Pattern Recognit..

[2]  P. M. Payton,et al.  Projective invariants for curves in two and three dimensions , 1992 .

[3]  Demetri Psaltis,et al.  Image Normalization by Complex Moments , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[4]  Roland T. Chin,et al.  On Image Analysis by the Methods of Moments , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[5]  M. Lee.  Using moments to reduce object recognition to a one-dimensional search , 1990, [1990] Proceedings. 10th International Conference on Pattern Recognition.

[6]  Kalle Åström.  Affine and Projective Normalization of Planar Curves and Regions , 1994, ECCV.

[7]  Thomas H. Reiss,et al.  Recognizing Planar Objects Using Invariant Image Features , 1993, Lecture Notes in Computer Science.

[8]  Herbert Süße,et al.  Ein allgemeiner Zugang zur Berechnung von Invarianten , 1993, DAGM-Symposium.

[9]  Wesley E. Snyder,et al.  Application of Affine-Invariant Fourier Descriptors to Recognition of 3-D Objects , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[10]  K. Arbter.  Affininvariante Fourierdeskriptoren ebener Kurven. , 1990 .

[11]  Herbert Süße,et al.  Invariant Standrad Positions of Ordered Sets of Points , 1995, CAIP.

[12]  J. M. Galvez,et al.  Normalization and shape recognition of three-dimensional objects by 3D moments , 1993, Pattern Recognit..

[13]  Hudai Dirilten,et al.  Pattern Matching Under Affine Transformations , 1977, IEEE Transactions on Computers.

[14]  Andrew Blake,et al.  Isoperimetric Normalization of Planar Curves , 1994, IEEE Trans. Pattern Anal. Mach. Intell..

[15]  Gösta H. Granlund,et al.  Fourier Preprocessing for Hand Print Character Recognition , 1972, IEEE Transactions on Computers.

[16]  Ming-Kuei Hu,et al.  Visual pattern recognition by moment invariants , 1962, IRE Trans. Inf. Theory.

[17]  K. Wang.  Affine-invariant moment method of three dimensional object identification. , 1977 .

[18]  Ernest L. Hall,et al.  Three-Dimensional Moment Invariants , 1980, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[19]  M. Teague.  Image analysis via the general theory of moments , 1980 .

[20]  King-Sun Fu,et al.  Shape Discrimination Using Fourier Descriptors , 1977, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[21]  Jan Flusser,et al.  Pattern recognition by affine moment invariants , 1993, Pattern Recognit..

[22]  Andrew Zisserman,et al.  Geometric invariance in computer vision , 1992 .

[23]  Azriel Rosenfeld,et al.  From pixels to features: J C Simon (ed). Published by Nort-Holland, Netherlands. 1989. 416 pp. $94.75 , 1990 .

[24]  Isaac Weiss,et al.  Geometric invariants and object recognition , 1993, International Journal of Computer 11263on.

[25]  Eamon B. Barrett,et al.  General methods for determining projective invariants in imagery , 1991, CVGIP Image Underst..

[26]  Ralph Roskies,et al.  Fourier Descriptors for Plane Closed Curves , 1972, IEEE Transactions on Computers.

[27]  Anthony P. Reeves,et al.  Three-Dimensional Shape Analysis Using Moments and Fourier Descriptors , 1988, IEEE Trans. Pattern Anal. Mach. Intell..

[28]  K. Voss,et al.  A General Method to Determine Invariants , 1994 .

[29]  R. C. Papademetriou,et al.  Reconstructing with moments , 1992, Proceedings., 11th IAPR International Conference on Pattern Recognition. Vol. III. Conference C: Image, Speech and Signal Analysis,.

[30]  John A. Orr,et al.  Applications of Tensor Theory to Object Recognition and Orientation Determination , 1985, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[31]  Thomas H. Reiss,et al.  The revised Fundamental Theorem of Moment Invariants , 1991, IEEE Trans. Pattern Anal. Mach. Intell..