## Shape Fitting on Point Sets with Probability Distributions

Citations: | 6 - 4 self |

### BibTeX

@MISC{Löffler_shapefitting,

author = {Maarten Löffler and Jeff M. Phillips},

title = {Shape Fitting on Point Sets with Probability Distributions},

year = {}

}

### OpenURL

### Abstract

Abstract. We consider problems on data sets where each data point has uncertainty described by an individual probability distribution. We develop several frameworks and algorithms for calculating statistics on these uncertain data sets. Our examples focus on geometric shape fitting problems. We prove approximation guarantees for the algorithms with respect to the full probability distributions. We then empirically demonstrate that our algorithms are simple and practical, solving for a constant hidden by asymptotic analysis so that a user can reliably trade speed and size for accuracy. 1