Differential Morphological Profiles (DMPs) and their generalized Differential Attribute Profiles (DAPs) are spatial signatures used in the classification of earth observation data. The Characteristic-Salience-Leveling (CSL) is a model allowing the compression and storage of the multi-scale information contained in the DMPs and DAPs into raster data layers, used for further analytic purposes. Computing DMPs or DAPs is often constrained by the size of the input data and scene complexity. Addressing very high resolution remote sensing gigascale images, this paper presents a new concurrent algorithm based on the Max-Tree structure that allows the efficient computation of CSL. The algorithm extends the "one-pass" method for computation of DAPs, and delivers an attribute zone segmentation of the underlying trees. The DAP vector field and the set of multi-scale characteristics are computed separately and in a similar fashion to concurrent attribute filters. Experiments on test images of 3.48 to 3.96 Gpixel showed an average computational speed of 59.85 Mpixel per second, or 3.59 Gpixel per minute on a single 2U rack server with 64 opteron cores. The new algorithms could be extended to morphological keypoint detectors capable of handling gigascale images.