Projective Invariants of D-moments of 2D Grayscale Images

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• 作者：YuanBin Wang (1)
  XingWei Wang (1)
  Bin Zhang (1)
  Ying Wang (2)
  
  1. College of Information Science and Engineering ; Northeastern University ; ShenYang聽 ; 110004 ; China
  2. Department of Computer Science ; Worcester Polytechnic Institute ; Worcester ; MA ; USA
  
• 关键词：Derivative image ; Invariant ; Moment ; Projective transformation
• 刊名：Journal of Mathematical Imaging and Vision
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：51
• 期：2
• 页码：248-259
• 全文大小：939 KB
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• 刊物类别：Computer Science
• 刊物主题：Computer Imaging, Vision, Pattern Recognition and Graphics
  Image Processing and Computer Vision
  Artificial Intelligence and Robotics
  Automation and Robotics
  
• 出版者：Springer Netherlands
• ISSN：1573-7683

文摘

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.