@techreport{ChoiSeidel2001,
TITLE = {Linear one-sided stability of {MAT} for weakly injective domain},
AUTHOR = {Choi, Sung Woo and Seidel, Hans-Peter},
LANGUAGE = {eng},
URL = {http://domino.mpi-inf.mpg.de/internet/reports.nsf/NumberView/2001-4-004},
NUMBER = {MPI-I-2001-4-004},
INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
ADDRESS = {Saarbr{\"u}cken},
YEAR = {2001},
DATE = {2001},
ABSTRACT = {Medial axis transform (MAT) is very sensitive to the noise,<br>in the sense that, even if a shape is perturbed only slightly,<br>the Hausdorff distance between the MATs of the original shape and<br>the perturbed one may be large. But it turns out that MAT is stable,<br>if we view this phenomenon with the one-sided Hausdorff distance,<br>rather than with the two-sided Hausdorff distance. In this paper, <br>we show that, if the original domain is weakly injective,<br>which means that the MAT of the domain has no end point which<br>is the center of an inscribed circle osculating the boundary at<br>only one point, the one-sided Hausdorff distance of the original <br>domain's MAT with respect to that of the perturbed one is bounded <br>linearly with the Hausdorff distance of the perturbation.<br>We also show by example that the linearity of this bound cannot be <br>achieved for the domains which are not weakly injective. In particular, <br>these results apply to the domains with the sharp corners, which <br>were excluded in the past. One consequence of these results is that<br>we can clarify theoretically the notion of extracting ``the essential <br>part of the MAT'', which is the heart of the existing pruning methods.},
TYPE = {Research Report / Max-Planck-Institut für Informatik},
}