Extraction of principal component shapes from grids

Abstract

The country?s increasing collection of data sets and increasing resolution of instruments creates an opportunity to put the redundant data to work. The shape of the grid on fine scales may not be evident to the eye. However if a vector of shape components at each point is available, images and quantities may be extracted. This paper shows how to extract such a multiband dataset using shape filters in the locality of each point in the original grid, and then characterise it by constructing the principal component shapes. The basis components are obtained by running basis filters composed of orthonormal functions across the grid. The functions are on the scale of the locality of interest, so that each characterisation is on the scale selected. Consequently the shapes associated with each of the principal components for an area can readily be extracted. Apart from mapping, the principal component shapes are expected to be of value for numerical modeling and for automated searching in GIS.