Finding the edge of a Poisson forest

B. D. Ripley; J.-P. Rasson

doi:10.2307/3213451

Abstract

The points of a homogeneous Poisson process within a compact convex set are observed. We consider how to reconstruct this domain from the observations.

References

Matheron, G. (1975) Random Sets and Integral Geometry. Wiley, New York.Google Scholar

Renyi, A. and Sulanke, R. (1964) Über die konvexe Hülle von n zufällig gewählten Punkten II. Z. Wahrscheinlichkeitsth. 3, 138–147.Google Scholar

Crossref Citations

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Kendall, David G. and Kendall, Wilfrid S. 1980. Alignments in two-dimensional random sets of points. Advances in Applied Probability, Vol. 12, Issue. 2, p. 380.

Eddy, William F. and Gale, James D. 1981. The convex hull of a spherically symmetric sample. Advances in Applied Probability, Vol. 13, Issue. 4, p. 751.

Orton, C.R. 1982. Stochastic process and archaeological mechanism in spatial analysis. Journal of Archaeological Science, Vol. 9, Issue. 1, p. 1.

Small, Christopher 1982. Random uniform triangles and the alignment problem. Mathematical Proceedings of the Cambridge Philosophical Society, Vol. 91, Issue. 2, p. 315.

Hoffman, Richard and Jain, Anil K 1983. A test of randomness based on the minimal spanning tree. Pattern Recognition Letters, Vol. 1, Issue. 3, p. 175.

Moore, Marc and Laniel, Normand 1983. Reconstruction échantillonnale d'une forme convexe. Canadian Journal of Statistics, Vol. 11, Issue. 3, p. 181.

DeGroot, Morris H. and Eddy, William F. 1983. Recent Advances in Statistics. p. 175.

Buchta, Christian 1984. Stochastische Approximation konvexer Polygone. Zeitschrift f�r Wahrscheinlichkeitstheorie und Verwandte Gebiete, Vol. 67, Issue. 3, p. 283.

Smith, Stephen P. and Jain, Anil K. 1984. Testing for Uniformity in Multidimensional Data. IEEE Transactions on Pattern Analysis and Machine Intelligence, Vol. PAMI-6, Issue. 1, p. 73.

Davis, R. Mulrow, E. and Resnick, S. 1987. The convex hull of a random sample in. Communications in Statistics. Stochastic Models, Vol. 3, Issue. 1, p. 1.

Schneider, Rolf 1988. Random approximation of convex sets*. Journal of Microscopy, Vol. 151, Issue. 3, p. 211.

Davis, Richard A. Mulrow, Edward and Resnick, Sidney I. 1988. Almost sure limit sets of random samples in ℝd. Advances in Applied Probability, Vol. 20, Issue. 3, p. 573.

Small, Christopher G. 1989. On functionals of random convex hulls. Canadian Journal of Statistics, Vol. 17, Issue. 1, p. 41.

Carlstein, E. and Krishnamoorthy, C. 1992. Boundary Estimation. Journal of the American Statistical Association, Vol. 87, Issue. 418, p. 430.

1993. Statistics for Spatial Data. p. 803.

Mcbeth, Douglas and Resnick, Sidney 1994. Stability of random sets generated by multivariate samples. Communications in Statistics. Stochastic Models, Vol. 10, Issue. 3, p. 549.

Hardy, André 1994. New Approaches in Classification and Data Analysis. p. 178.

Rasson, Jean-Paul and Kubushishi, Tite 1994. New Approaches in Classification and Data Analysis. p. 186.

Gordon, A.D. 1994. Identifying genuine clusters in a classification. Computational Statistics & Data Analysis, Vol. 18, Issue. 5, p. 561.

Jacob, Pierre and Suquet, Charles 1995. Estimating the edge of a Poisson process by orthogonal series. Journal of Statistical Planning and Inference, Vol. 46, Issue. 2, p. 215.

Download full list

Article contents

Finding the edge of a Poisson forest

Abstract

Keywords

Access options

References

This article has been cited by the following publications. This list is generated based on data provided by Crossref.

Article contents

Finding the edge of a Poisson forest

Abstract

Keywords

Access options

References

Save article to Kindle

Save article to Dropbox

Save article to Google Drive

Reply to: Submit a response

Your details

You have entered the maximum number of contributors

Conflicting interests