We present a novel statistical texture descriptor employing level-crossing statistics. Images are first mapped into 1D signals using space-filling curves, such as Peano or Hilbert curves, and texture features are extracted via signal-dependent sampling. Texture parameters are based on the level-crossing statistics of the 1D signal, i.e. crossing rate, crossing slope and sojourn time. Despite the simplicity of texture features used, our approach offers state-of-the art performance in the texture classification and texture segmentation tasks, outperforming other tested algorithms.