Matching with matrix norm minimization

  • Shouwen Tang
  • Kaizhong Zhang
  • Xiaolin Wu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 807)


Given (r1,r2,...r n ) ∈ R n , for any I=(I1,I2,...I n ) ∈ Z n , let E I =(e ij ), where e ij =(r i r j )−(I i I i ), find I ∈ Z n such that ∥E I ∥ is minimized, where ∥·∥ is a matrix norm. This is a matching problem where, given a real-valued pattern, the goal is to find the best discrete pattern that matches the real-valued pattern. The criterion of the matching is based on the matrix norm minimization instead of simple pairwise distance minimization. This matching problem arises in optimal curve rasterization in computer graphics and in vector quantization of data compression. Until now, there has been no polynomial-time solution to this problem. We present a very simple O(nlgn) time algorithm to solve this problem under various matrix norms.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Shouwen Tang
    • 1
  • Kaizhong Zhang
    • 2
  • Xiaolin Wu
    • 2
  1. 1.Department of Computer ScienceBeijing Computer InstituteBeijingChina
  2. 2.Department of Computer ScienceUniversity of Western OntarioLondonCanada

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