Comparing and classifying one-dimensional spatial patterns: an application to laser altimeter profiles

Numerical analyses of remotely sensed data may valuably contribute to an understanding of the vegetation/land surface interface by pointing out at which scales a given variable displays a high level of spatial variability. Thus, there is a need of methods aimed at classifying many one-dimensional signals, such as airborne laser profiles, on the basis of their spatial structure. The present paper proposes a theoretical framework ensuring a consistent combination of a multi-scale pattern characterization, based on the Haar wavelet variance (also called in ecology Two Terms Local Variance, TTLV), with two multivariate techniques such as principal components analysis (PCA) and hierarchical cluster analysis. We illustrate our approach by comparing and classifying 257 laser profiles, with a length of 64 measurements (448 m), that were collected by the BRGM in French Guiana over three main landscape units with distinct geomorphological and ecological characteristics. We calculate for each profile a scalogram that summarized the multi-scale pattern and analyze the structural variability of profiles via a typology and a classification of one-dimensional patterns. More than 80% of the variability between spatial patterns of laser profiles has been summarized by two PCA axes, while four classes of spatial patterns were identified by cluster analysis. Each landscape unit was associated with one or two dominant classes of spatial patterns. These results confirmed the ability of the method to extract landscape scaling properties from complex and large sets of remotely sensed data. D 2003 Elsevier Science Inc. All rights reserved.