Multi-scale self-similarity features of terrain surface

Self-similarity features of natural surface play a key role in region segmentation and recognition. Due to long period of natural evolution, real terrain surface is composed of many self-similar structures. Consequently, the Self-similarity is not always so perfect that remains invariable in whole scale space and the traditional single self-similarity parameter can not represent such abundant self-similarity. In this view, the self-similarity is not a constant parameter over all scales, but multi-scale parameters. In order to describe such multi-scale self-similarities of real surface, firstly we adopt the Fractional Brownian Motion (FBM) model to estimate the self-similarity curve of terrain surface. Then the curve is divided into several linear regions to represent relevant self-similarities. Based on such regions, we introduce a parameter called Self-similar Degree (SSD) in the similitude of information entropy. Moreover, the small value of SSD indicates the more consistent self-similarity. We adopt fifty samples of terrain images and evaluate SSD that represents the multi-scale self-similarity features for each sample. The samples are clustered by unsupervised fuzzy c mean clustering into various classes according to SSD and traditional monotone Hurst feature respectively. The measurement for separability of features shows that the new parameter SSD is an effective feature for terrain classification. Therefore the similarity feature set that is made up of the monotone Hurst parameter and SSD provides more information than traditional monotone feature. Consequently, the performance of terrain classification is improved.