  We study the convex-hull problem in a probabilistic setting, motivated by the
need to handle data uncertainty inherent in many applications, including sensor
databases, location-based services and computer vision. In our framework, the
uncertainty of each input site is described by a probability distribution over
a finite number of possible locations including a \emph{null} location to
account for non-existence of the point. Our results include both exact and
approximation algorithms for computing the probability of a query point lying
inside the convex hull of the input, time-space tradeoffs for the membership
queries, a connection between Tukey depth and membership queries, as well as a
new notion of $\some$-hull that may be a useful representation of uncertain
hulls.

Computational Geometry