@inproceedings{3e6fba19c2594d5ca3746a28d660b254,

title = "Minimum partial-matching and hausdorff RMS-distance under translation: Combinatorics and algorithms",

abstract = "We consider the RMS-distance (sum of squared distances between pairs of points) under translation between two point sets in the plane. In the Hausdorff setup, each point is paired to its nearest neighbor in the other set. We develop algorithms for finding a local minimum in near-linear time on the line, and in nearly quadratic time in the plane. These improve substantially the worst-case behavior of the popular ICP heuristics for solving this problem. In the partial-matching setup, each point in the smaller set is matched to a distinct point in the bigger set. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision of the plane and derive improved bounds on its complexity. In addition, we show how to compute a local minimum of the partial-matching RMS-distance under translation, in polynomial time.",

keywords = "Hausdorff RMS-distance, local minimum, partial matching, polyhedral subdivision",

author = "Rinat Ben-Avraham and Matthias Henze and Rafel Jaume and Bal{\'a}zs Keszegh and Raz, {Orit E.} and Micha Sharir and Igor Tubis",

year = "2014",

doi = "10.1007/978-3-662-44777-2_9",

language = "American English",

isbn = "9783662447765",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer Verlag",

pages = "100--111",

booktitle = "Algorithms, ESA 2014 - 22nd Annual European Symposium, Proceedings",

address = "Germany",

note = "22nd Annual European Symposium on Algorithms, ESA 2014 ; Conference date: 08-09-2014 Through 10-09-2014",

}