Affine moment invariants

The affine transform is general linear transformation of space coordinates of the image:

u = a0 + a1x + a2y
v = b0 + b1x + b2y.

The affine moment invariants are features for pattern recognition computed from moments of objects on images that do not change their value in affine transformation. The geometric moment of order p + q of the image f is defined

.

We can normalize them with respect to translation, then we obtain central moments

,

where xt=m10/m00 and yt=m01/m00 are coordinates of the centroid. The ratios

are then invariant to translation and scaling.

The invariants then can be generated by the graph method or computationally equivalent tensor method.

Independent affine moment invariants of 2D images up to the order 12

 

Contact person: Tomáš Suk

 

Publications:

  1. Flusser Jan, Suk Tomáš, Zitová Barbara: 2D and 3D Image Analysis by Moments, John Wiley & Sons, (Chichester 2016) Download contents
  2. Suk Tomáš, Flusser Jan:  Affine Moment Invariants Generated by Graph Method , Pattern Recognition vol.44, 9 (2011) Download PDF 
  3. Flusser Jan, Suk Tomáš, Zitová Barbara: Moments and Moment Invariants in Pattern Recognition, Wiley & Sons Ltd., 2009
  4. Suk Tomáš, Flusser Jan: Affine Moment Invariants Generated by Automated Solution of the Equations, Proceedings of the 19th International Conference on Pattern Recognition, ICPR 2008, (Tampa, US, 8.12.2008-11.12.2008), Download PDF
  5. Suk Tomáš, Flusser Jan: The Independence of the Affine Moment Invariants, Information Optics, p. 387-396, Eds: Cristobal G., International Workshop on Information Optics. WIO'06 /5./, (Toledo, ES, 05.06.2006-07.06.2006), Download PDF
  6. Suk Tomáš, Flusser Jan: Tables of Affine Moment Invariants Generated by the Graph Method, ÚTIA AV ČR, (Praha 2005)Research Report 2156, Download PDF
  7. Suk Tomáš, Flusser Jan: Affine normalization of symmetric objects, Proceedings of the 7th International Conference on Advanced Concepts for Intelligent Vision Systems vol.3708, - (2005), p. 100-107, Advanced Concepts for Intelligent Vision Systems 2005 /7./, (Antwerp, BE, 20.09.2005-23.09.2005), Download PDF
  8. Suk Tomáš, Flusser Jan: Graph method for generating affine moment invariants, Proceedings of the 17th International Conference on Pattern Recognition. ICPR 2004, p. 192-195, International Conference on Pattern Recognition. ICPR 2004 /17./, (Cambridge, GB, 23.08.2004-26.08.2004), Download PDF
  9. Flusser Jan, Suk Tomáš: Affine moment invariants: a new tool for character recognition, Pattern Recognition Letters vol.15, p. 433-436, Download PS
  10. Flusser Jan, Suk Tomáš:A moment-based approach to registration of images with affine geometric distortion, IEEE Transactions on Geoscience and Remote Sensing and IEEE Transactions on Geoscience Electronics vol.32, 2 (1994), p. 382-387, Download PDF
  11. Flusser Jan, Saic Stanislav, Suk Tomáš: Registration of images with affine geometric distortion by means of moment invariants, Image and Signal Processing for Remote Sensing, p. 843-852, Eds: Desachy J., SPIE, (Bellingham 1994), European Symposium on Satellite Remote Sensing, (Roma, IT, 26.09.1994-30.09.1994)
  12. Flusser Jan, Suk Tomáš, Šimberová Stanislava: An Experimental Study on Uniqueness of the Affine Moment Invariants, Czech Pattern Recognition Workshop '93, p.
  13. 119-125, Eds: Hlaváč V., Pajdla T., Czechoslovak Pattern Recognition Society, (Praha 1993), Czech Pattern Recognition Workshop '93, (Temešvár, CZ, 04.11.1993-06.11.1993)
  14. Flusser Jan, Suk Tomáš:Pattern Recognition by Affine Moment Invariants, Pattern Recognition vol.26, 1 (1993), p. 167-174, Download PDF
  15. Flusser Jan, Suk Tomáš:Rozpoznávání objektů pomocí afinních momentových invariantů, ÚTIA ČSAV, (Praha 1991)Research Report 1726

 

Relevant publications by other authors:

 

  1. D. Shen and H. H. S. Ip, Generalized affine invariant image normalization, IEEE Trans. Pattern Analysis and Machine Intelligence, vol. 19, no. 5, pp. 431–440, 1997.
  2. D. Hilbert, Theory of Algebraic Invariants. Cambridge University Press, 1993.
  3. T. H. Reiss, Recognizing Planar Objects using Invariant Image Features, vol. 676 of LNCS. Berlin: Springer, 1993.
 

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