A simple and effective clustering algorithm for multispectral images using space-filling curves

With the wide usage of multispectral images, a fast efficient multidimensional clustering method becomes not only meaningful but also necessary. In general, to speed up the multidimensional images' analysis, a multidimensional feature vector should be transformed into a lower dimensional space. The Hilbert curve is a continuous one-to-one mapping from N-dimensional space to one-dimensional space, and can preserves neighborhood as much as possible. However, because the Hilbert curve is generated by a recurve division process, 'Boundary Effects' will happen, which means data that are close in N-dimensional space may not be close in one-dimensional Hilbert order. In this paper, a new efficient approach based on the space-filling curves is proposed for classifying multispectral satellite images. In order to remove 'Boundary Effects' of the Hilbert curve, multiple Hilbert curves, z curves, and the Pseudo-Hilbert curve are used jointly. The proposed method extracts category clusters from one-dimensional data without computing any distance in N-dimensional space. Furthermore, multispectral images can be analyzed hierarchically from coarse data distribution to fine data distribution in accordance with different application. The experimental results performed on LANDSAT data have demonstrated that the proposed method is efficient to manage the multispectral images and can be applied easily.