New invariant moments for non-uniformly scaled images

Ramaswamy Palaniappan, Paramesran Raveendran, Sigeru Omatu

Research output: Contribution to journalArticleResearchpeer-review

19 Citations (Scopus)


The usual regular moment functions are only invariant to image translation, rotation and uniform scaling. These moment invariants are not invariant when an image is scaled non-uniformly in the x- and y-axes directions. This paper addresses this problem by presenting a new technique to obtain moments that are invariant to non-uniform scaling. However, this technique produces a set of features that arc only invariant to translation and uniform/non-uniform scaling. To obtain invariance to rotation, moments are calculated with respect to the x-y-axis of the image. To perform this, a neural network is used to estimate the angle of rotation from the x-y-axis and the image is unrotated to the x-y-axis. Consequently, we are able to obtain features that are invariant to translation, rotation and uniform/non-uniform scaling. The mathematical background behind the development and invariance of the new moments are presented. The results of experimental studies using English alphabets and Arabic numerals scaled uniformly/non-uniformly, rotated and translated are discussed to further verify the validity of the new moments.

Original languageEnglish
Pages (from-to)78-87
Number of pages10
JournalPattern Analysis and Applications
Issue number2
Publication statusPublished - 2000
Externally publishedYes


  • Neural network
  • Non-uniform scaling
  • Principal axis
  • Regular moments
  • Rotation
  • Tilt angle

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