An interactive analysis method for multidimensional images using a Hilbert curve

Abstract

AbstractTo analyze multidimensional images we need a mapping of feature vectors from a multidimensional space to a lower dimensional space. In general, these are performed using linear transformation methods, such as principal component analysis, etc. Linear transformation requires many rotations of data from several points of view because the mapping is not one‐to‐one. Here, a new interactive method for classifying multispectral images using a Hilbert curve is presented. The Hilbert curve is a one‐to‐one mapping from N‐dimensional space to one‐dimensional space and preserves the neighborhood as much as possible. Hilbert curve is a kind of space filling curves, and provides a continuous scan. The merit of the system presented is that the user can extract category clusters without computing any distance in N‐dimensional space easily. The method presented here is explained in brief. Clusters are extracted from 1‐D data mapped by a Hilbert curve interactively, i.e., a pixel is classified as a category. The user can analyze multidimensional images hierarchically from gross data distribution to fine data distribution. To realize the real time response from the system, data tables storing the addresses and the occurrences of data are used. Here, the address is defined by using the coordinates in N‐dimensional space, and a part of mapping which cannot preserve the neighborhood is utilized. In the experiments ex‐extracting categories from LANDSAT data, it is confirmed that the user can obtain the real time response from the system after once making the data tables.