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Journal of Mathematical Imaging and Vision

, Volume 51, Issue 2, pp 248–259 | Cite as

Projective Invariants of D-moments of 2D Grayscale Images

  • YuanBin WangEmail author
  • XingWei Wang
  • Bin Zhang
  • Ying Wang
Article

Abstract

This paper presents a novel method to derive invariants of 2D grayscale images under projective transformation. Invariants of images are good features for object recognition and have attracted extensive attention. Although geometric invariants of point locations such as cross ratios are well known for centuries, we have found no reported invariants for grayscale images that remain the same under projective transformation. It has even been proven that projective invariants of images cannot be derived from the standard geometric moments of images. However, this does not mean that there is no projective invariant of images in other forms. We will prove in this paper that projective invariants of images do exist as functions of the generalized moments of images. We first derive some projective invariant relations between an image function and its derivative functions. Next, we extend the traditional definition of moments by considering both the image function and its derivative functions. Then we derive a set of functions of the generalized moments that are projective invariant. Experimental results indicate that the proposed invariants have certain discriminating power for object recognition.

Keywords

Derivative image Invariant Moment Projective transformation 

Notes

Acknowledgments

The authors wish to thank the editor and the reviewers for their comments which helped to improve the quality of our manuscript. This work is supported by the National Science Foundation for Distinguished Young Scholars of China under Grant no. 61225012 and No. 71325002; the National Natural Science Foundation of China under Grant No. 61073062; the Specialized Research Fund of the Doctoral Program of Higher Education for the Priority Development Areas under Grant No. 20120042130003; the Specialized Research Fund for the Doctoral Program of Higher Education under Grant No. 20110042110024; the Fundamental Research Funds for the Central Universities under Grant No. N110204003, No. N120804001 and No. N120104001

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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  • YuanBin Wang
    • 1
    Email author
  • XingWei Wang
    • 1
  • Bin Zhang
    • 1
  • Ying Wang
    • 2
  1. 1.College of Information Science and EngineeringNortheastern UniversityShenYang China
  2. 2.Department of Computer ScienceWorcester Polytechnic InstituteWorcesterUSA

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