Image reconstruction from a complete set of similarity invariants extracted from complex moments

Various types of moments have been used to recognize image patterns in a number of applications. However, only few works have paid attention to the completeness property of the invariant descriptor set, which is of fundamental importance from the theoretical as well as the practical points of views. This paper proposes a systematic method to extract a complete set of similarity invariants (translation, rotation and scale), by means of some linear combinations of complex moments. The problem of image reconstruction from a finite set of its moment invariants is then examined by exploiting the link between the discrete Fourier transform of an image and its complex moments. Experimental results are presented that confirm theoretical properties as well as numerical effectiveness of the method.

[1]  Faouzi Ghorbel,et al.  Robust and Efficient Fourier-Mellin Transform Approximations for Gray-Level Image Reconstruction and Complete Invariant Description , 2001, Comput. Vis. Image Underst..

[2]  J Flusser,et al.  Recognition of blurred images by the method of moments , 1996, IEEE Trans. Image Process..

[3]  Miroslaw Pawlak,et al.  On Image Analysis by Moments , 1996, IEEE Trans. Pattern Anal. Mach. Intell..

[4]  Y. Sheng,et al.  Orthogonal Fourier–Mellin moments for invariant pattern recognition , 1994 .

[5]  Richard J. Prokop,et al.  A survey of moment-based techniques for unoccluded object representation and recognition , 1992, CVGIP Graph. Model. Image Process..

[6]  Jan Flusser,et al.  Combined blur and affine moment invariants and their use in pattern recognition , 2003, Pattern Recognit..

[7]  Jan Flusser,et al.  Construction of Complete and Independent Systems of Rotation Moment Invariants , 2003, CAIP.

[8]  Faouzi Ghorbel,et al.  A complete invariant description for gray-level images by the harmonic analysis approach , 1994, Pattern Recognit. Lett..

[9]  Jan Flusser,et al.  Projective moment invariants , 2004, IEEE Transactions on Pattern Analysis and Machine Intelligence.

[10]  Kin-Man Lam,et al.  Generation of moment invariants and their uses for character recognition , 1995, Pattern Recognit. Lett..

[11]  Raveendran Paramesran,et al.  Image analysis by Krawtchouk moments , 2003, IEEE Trans. Image Process..

[12]  Jan Flusser,et al.  On the inverse problem of rotation moment invariants , 2002, Pattern Recognit..

[13]  P. Davis.  Plane regions determined by complex moments , 1977 .

[14]  Sim Heng Ong,et al.  Image Analysis by Tchebichef Moments , 2001, IEEE Trans. Image Process..

[15]  R. Mukundan.  A New Class of Rotational Invariants Using Discrete Orthogonal Moments , 2004 .

[16]  Jin Liu,et al.  Recognition of the blurred image by complex moment invariants , 2005, Pattern Recognit. Lett..

[17]  Alireza Khotanzad,et al.  Invariant Image Recognition by Zernike Moments , 1990, IEEE Trans. Pattern Anal. Mach. Intell..

[18]  Ivar Balslev.  Noise tolerance of moment invariants in pattern recognition , 1998, Pattern Recognit. Lett..

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

[20]  Demetri Psaltis,et al.  Recognitive Aspects of Moment Invariants , 1984, IEEE Transactions on Pattern Analysis and Machine Intelligence.

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

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

[23]  Thomas R. Crimmins.  A Complete Set of Fourier Descriptors for Two-Dimensional Shapes , 1982, IEEE Transactions on Systems, Man, and Cybernetics.

[24]  Faouzi Ghorbel,et al.  Robust and efficient Fourier-Mellin transform approximations for invariant grey-level image description and reconstruction , 2001 .

[25]  Jan Flusser,et al.  Graph method for generating affine moment invariants , 2004, Proceedings of the 17th International Conference on Pattern Recognition, 2004. ICPR 2004..

[26]  Ziliang Ping,et al.  Multidistortion-invariant image recognition with radial harmonic Fourier moments. , 2003, Journal of the Optical Society of America. A, Optics, image science, and vision.

[27]  Faouzi Ghorbel,et al.  Comparaison de deux familles complètes de descripteurs de formes pour l’indexation de bases d’objets 2D à niveaux de gris , 2000, Ann. des Télécommunications.