Spatial Segmentation - Clustering for Scattered Observations

Description

This function performs segmentation of scattered 2D data based on sampling density and location.

Usage

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Arguments

object

An Intamap type object containing the element (list) observations, which includes the coordinates of the observation locations

Details

This function performs segmentation of scattered 2D data based on sampling density and location. Let us assume that No is the number of observation locations. If No< 200, then a single cluster is returned.

(1) The segmentation algorithm first removes isolated distant points, if there are any, from the observation locations. Points $(xi,yi)$ are characterized as 'isolated' and 'distant' if they satisfy the following conditions : $abs(xi-mean(x)) > 4 *std(x) or abs(yi-mean(y)) > 4 *std(y)$ and distance from closest neighbor $> sqrt((std(x)/2)^2+(std(y)/2)^2)$. After the first step the size of the original dataset is reduced to N (N= No - isolated points) points.

(2) A sampling density matrix (lattice) consisting of N cells that cover the study area is constructed. Each cell is assigned a density value equal to the number of observation points inside the cell. In addition, each observation point is assigned the sampling density value of the containing cell.

(3) Unsupervised clustering edge detection is used to determine potential cluster perimeters.

(4) Each closed region's perimeter is labeled with a different cluster (segment) number.

(5) All observation points internal to a cluster perimeter are assigned to the specific cluster.

(6) Each cluster that contains fewer than 50 observation points is rejected.

(7) The observation points that have not initially been assigned to a cluster and those belonging to rejected (small) clusters are assigned at this stage. The assignment takes into account both the distance of the points from the centroids of the accepted clusters as well as the mean sampling density of the clusters.

Note: The No< 200 empirical constraint is used to avoid extreme situations in which the sampling density is concentrated inside a few cells of the background lattice, thereby inhibiting the edge detection algorithm.

Value

A modified Intamap object which additionally includes the list element clusters. This element is a list that contains (i) the indices of removed points from observations; (ii) the indices of the clusters to which the remaining observation points are assigned and (iii) the number of clusters detected.

clusters

list element added to the original object containing the segmentation results.

  • rmdistIndices of removed points.

  • indexIndex array identifying the cluster in which each observation point belongs.

  • clusterNumberNumber of clusters detected.

Author(s)

A. Chorti, Spiliopoulos Giannis, Hristopulos Dionisis

References

[1] D. T. Hristopulos, M. P. Petrakis, G. Spiliopoulos, A. Chorti (2009). Non-parametric estimation of geometric anisotropy from environmental sensor network measurements, StatGIS 2009: Geoinformatics for Environmental Surveillance Proceedings (ed. G. Dubois).

Examples

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library(gstat)

data(walker)
# coordinates(walker)=~X+Y
object=createIntamapObject(observations=walker)
object=doSegmentation(object)

print(summary(object$clusters$index))