@techreport{lei-sto-01-reltec, author = {Helena C. G. {Leit{\~a}o} and Jorge Stolfi}, title = {A Multiscale Technique for Computer Assisted Re-Assembly of Fragmented Objects}, institution = {Institute of Computing, Univ. of Campinas}, number = {IC-01-04}, pages = {23}, year = 2001, month = mar, 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.} }