Efficient anisotropic scaling and translation invariants of Tchebichef moments using image normalization

Chih-Yang Pee, S. H. Ong, P. Raveendran, L. K. Wong

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1 Citation (Scopus)


Anisotropic scaling and translation invariants of Tchebichef moments are commonly used in image analysis to address issues arising from patterns distorted by non-uniform scaling and translation. In this paper, we formulate a new fast computational algorithm and a new normalization scheme based on the properties of Tchebichef moments. The proposed model can correctly resolve the mirror reflection ambiguities caused by the scaling transformations and gives smaller size deviations for various patterns so that the canonical form can easily fit within the normalized space. An empirical study shows that the proposed method significantly improves numerical computation and classification accuracy under non-noisy and noisy conditions when compared with existing methods. The main contribution of this paper is a novel fast computational algorithm for anisotropic scaling and translation invariants of Tchebichef moments and a new normalization scheme that produces features with higher discriminative power. The proposed algorithm is useful for recognizing objects with non-uniform size and displacement deformations. It is also a key component in formulating a better affine invariant algorithm for the image analysis community.

Original languageEnglish
Pages (from-to)8-16
Number of pages9
JournalPattern Recognition Letters
Publication statusPublished - May 2023


  • Anisotropic scaling and translation invariant
  • Discrete orthogonal moment
  • Image normalization
  • Moment invariant
  • Pattern classification
  • Tchebichef moment

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