TY - JOUR

T1 - Rolling-Ball method for estimating the boundary of the support of a point-process intensity

AU - Hall, Peter

AU - Park, B

AU - Turlach, B

PY - 2002

Y1 - 2002

N2 - We suggest a generalisation of the convex-hull method, or 'DEA' approach, for estimating the boundary or frontier of the support of a point cloud. Figuratively, our method involves rolling a ball around the cloud, and using the equilibrium positions of the ball to define an estimator of the envelope of the point cloud. Constructively, we use these ideas to remove lines from a triangulation of the points, and thereby compute a generalised form of a convex hull. The radius of the ball acts as a smoothing parameter, with the convex-hull estimator being obtained by taking the radius to be infinite. Unlike the convex-hull approach, however, our method applies to quite general frontiers, which may be neither convex nor concave. It brings to these contexts the attractive features of the convex hull: simplicity of concept, rotation-invariance, and ready extension to higher dimensions. It admits bias corrections, which we describe and illustrate through implementation.

AB - We suggest a generalisation of the convex-hull method, or 'DEA' approach, for estimating the boundary or frontier of the support of a point cloud. Figuratively, our method involves rolling a ball around the cloud, and using the equilibrium positions of the ball to define an estimator of the envelope of the point cloud. Constructively, we use these ideas to remove lines from a triangulation of the points, and thereby compute a generalised form of a convex hull. The radius of the ball acts as a smoothing parameter, with the convex-hull estimator being obtained by taking the radius to be infinite. Unlike the convex-hull approach, however, our method applies to quite general frontiers, which may be neither convex nor concave. It brings to these contexts the attractive features of the convex hull: simplicity of concept, rotation-invariance, and ready extension to higher dimensions. It admits bias corrections, which we describe and illustrate through implementation.

U2 - 10.1016/S0246-0203(02)01132-9

DO - 10.1016/S0246-0203(02)01132-9

M3 - Article

VL - 38

SP - 959

EP - 971

JO - Annales de l Institut Henri Poincare B: Probability and Statistics

JF - Annales de l Institut Henri Poincare B: Probability and Statistics

IS - 6

ER -