2014 資訊管理實務研討會 Image Reconstruction from Legendre Moments Amy Chiang and Simon Liao Applied Computer Science, University of Winnipeg Winnipeg, Manitoba, Canada achiang0602@gmail.com, s.liao@uwinnipeg.ca Abstract In this research, the issue of Legendre moment computing is addressed and a numerical integration method is proposed. To clarify the improved computation scheme, image reconstructions from higher Legendre moments orders, up to 120, are performed. 1. Introduction Moment methods have been the subject of intensive research since the concept of image moments was introduced by Hu in 1962[1]. Since then, different types of conventional continuous orthogonal moments have been well studied as the unique image shape features for applications in fields of pattern recognition and image analysis. For a general background study of the moment methods, please refer to [5][6][7]. Legendre moment is one of the important continuous orthogonal moments defined in the rectangular region and has been well investigated since the earlier years of moment-based descriptors studies[2][3][4]. However, some computational issues have bottlenecked the further development of efficient applications driven by Legendre moment-based techniques. These computational issues will be addressed and some solutions will be proposed in this research. 2. Legendre Moments The (m,n)-th order of Legendre moment of an image function (, ) f xy is defined on the square [-1, 1]×[-1,1] 1 1 1 1 (2 1)(2 1) ( , ) ( ) ( ) , 4 mn m n m n f x yP xP y dxdy           (1)