Two-dimensional polar harmonic transforms for invariant image representation
Related Experiment Video
Updated: Jun 12, 2026

Detection of Architectural Distortion in Prior Mammograms via Analysis of Oriented Patterns
Published on: August 30, 2013
Pew-Thian Yap1, Xudong Jiang, Alex Chichung Kot
1School of Electrical and Electronic Engineering,Nanyang Technological University, Singapore 639798, Singapore. ptyap@med.unc.edu
Abstract:
This paper introduces a set of 2D transforms, based on a set of orthogonal projection bases, to generate a set of features which are invariant to rotation. We call these transforms Polar Harmonic Transforms (PHTs). Unlike the well-known Zernike and pseudo-Zernike moments, the kernel computation of PHTs is extremely simple and has no numerical stability issue whatsoever. This implies that PHTs encompass the orthogonality and invariance advantages of Zernike and pseudo-Zernike moments, but are free from their inherent limitations. This also means that PHTs are well suited for application where maximal discriminant information is needed. Furthermore, PHTs make available a large set of features for further feature selection in the process of seeking for the best discriminative or representative features for a particular application.
Related Concept Videos
Polar Coordinates
Polar and Cylindrical Coordinates
Transformations of Functions III
Polar Coordinate System
Curvilinear Motion: Polar Coordinates
The particle's location is described using a unit vector along the radial direction. Deriving the particle's position with respect to time...
Graphs of Polar Equations
