TY - JOUR
T1 - Numerically efficient algorithms for anisotropic scale and translation Tchebichef moment invariants
AU - Pee, Chih Yang
AU - Ong, S. H.
AU - Raveendran, P.
N1 - Publisher Copyright:
© 2017 Elsevier B.V.
PY - 2017/6/1
Y1 - 2017/6/1
N2 - Anisotropic scale and translation invariants (ASTI) for Tchebichef moments have been proposed by Zhu et al. [27]. Since these invariants are derived via the decomposition of Tchebichef polynomials, it is unavoidable that the invariant algorithms inherit the complexities from the Tchebichef polynomials defined in terms of hypergeometric functions. Furthermore, in order to achieve anisotropic scale and translation invariance, the computation of translation invariants and scale invariants need to be performed sequentially. These have turned out to be the bottleneck for the invariant algorithms. Experimental results show that some of the computed ASTI features from symmetric patterns are less accurate. Thus, we would like to extend the work of Zhu et al. [27] to simplify the complexity of the algorithms and further improve the accuracy of the computed features. The three terms recurrence relation of the Tchebichef polynomials has been used to simplify and improve the computational efficiency of the invariant algorithms. Skew transformations are deployed to enhance the numerical accuracy of ASTI for Tchebhcief moments. Our studies show that the skewed features are less sensitive to noise and significantly enhance the accuracy of pattern recognition systems. This has been verified by the experiments on recognition of printed English letters and leaf patterns corrupted by noise and scaled and translated deformations. The simplification of the algorithms using the orthogonal property of basis functions also can be used to simplify more complex invariants like affine invariants of discrete Tchebichief moments. It can also be extended to derive invariants for other orthogonal based moments like Legendre moments, Krawtchouk moments, Hahn moments, etc.
AB - Anisotropic scale and translation invariants (ASTI) for Tchebichef moments have been proposed by Zhu et al. [27]. Since these invariants are derived via the decomposition of Tchebichef polynomials, it is unavoidable that the invariant algorithms inherit the complexities from the Tchebichef polynomials defined in terms of hypergeometric functions. Furthermore, in order to achieve anisotropic scale and translation invariance, the computation of translation invariants and scale invariants need to be performed sequentially. These have turned out to be the bottleneck for the invariant algorithms. Experimental results show that some of the computed ASTI features from symmetric patterns are less accurate. Thus, we would like to extend the work of Zhu et al. [27] to simplify the complexity of the algorithms and further improve the accuracy of the computed features. The three terms recurrence relation of the Tchebichef polynomials has been used to simplify and improve the computational efficiency of the invariant algorithms. Skew transformations are deployed to enhance the numerical accuracy of ASTI for Tchebhcief moments. Our studies show that the skewed features are less sensitive to noise and significantly enhance the accuracy of pattern recognition systems. This has been verified by the experiments on recognition of printed English letters and leaf patterns corrupted by noise and scaled and translated deformations. The simplification of the algorithms using the orthogonal property of basis functions also can be used to simplify more complex invariants like affine invariants of discrete Tchebichief moments. It can also be extended to derive invariants for other orthogonal based moments like Legendre moments, Krawtchouk moments, Hahn moments, etc.
KW - Discrete orthogonal moment
KW - Moment invariant
KW - Pattern classification
KW - Tchebichef polynomial
UR - http://www.scopus.com/inward/record.url?scp=85018327952&partnerID=8YFLogxK
U2 - 10.1016/j.patrec.2017.04.008
DO - 10.1016/j.patrec.2017.04.008
M3 - Article
AN - SCOPUS:85018327952
SN - 0167-8655
VL - 92
SP - 68
EP - 74
JO - Pattern Recognition Letters
JF - Pattern Recognition Letters
ER -