@techreport{TR-IC-01-04,
  number = {IC-01-04},
  author = {Helena Cristina da Gama Leitão and Jorge Stolfi},
  title = {A Multi-Scale Technique for Computer Assisted Re-Assembly of Fragmented Objects},
  month = {March},
  year = {2001}, 
  institution = {Institute of Computing, University of Campinas},
  note = {In English, 23 pages.
    \par\selectlanguage{english}\textbf{Abstract}
      We describe here an efficient algorithm for reassembling one or more
      unknown objects that have been broken or torn into a large number $N$
      of irregular fragments.  The algorithm works by comparing the
      curvature-encoded fragment outlines, using a modified dynamic
      programming sequence-matching algorithm.  By comparing the outlines at
      progressively increasing scales of resolution, we manage to reduce the
      cost of the search from $\theta(N^2 L^2)$ (where $L$ is the mean number of
      samples per fragment) to about $O(N^2 L)$; which, in
      principle, allows the method to be used for problems of practical size
      ($N = 10^3$ to $10^5$ fragments, $L = 10^3$ to $10^4$ samples).  The
      performance of the algorithm is illustrated with an artificial but
      realistic example.
      \par
      {\em A shorter version of this report was presented at the British
      Machine Vision Confrence (BMVC) in Bristol, UK (September 2000).}
  }
}