In this paper, we present a novel approach for the extraction of the Level-crossing Statistics (LCS) texture descriptor and the application of this descriptor to the processing of remote sensing data. The LCS is a recently presented statistical texture descriptor that first maps the images into 1D signals using space-filling curves, then applies a signal-dependent sampling and finally extracts texture parameters (such as crossing rate, crossing slope and sojourn time) from the 1D signal. In the new extraction approach introduced in this paper, a pyramidal decomposition is employed to extract texture features of different spatial resolution. Despite the simplicity of the texture features used, our approach offers state-of-the art performance in the texture classification and texture segmentation tasks, outperforming other tested algorithms. In the remote sensing field, the LCS descriptor has been tested in segmentation and classification scenarios. A land-use/land-cover analysis system has been designed and the new texture descriptor has shown very good results in the supervised segmentation of satellite images, even when very few training samples are provided to the system.