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Differential area profiles (DAPs) are point-based multiscale descriptors used in pattern analysis and image segmentation. They are defined through sets of size-based connected morphological filters that constitute a joint area opening top-hat and area closing bottom-hat scale-space of the input image. The work presented in this paper explores the properties of this image decomposition through sets of area zones. An area zone defines a single plane of the DAP vector field and contains all the peak components of the input image, whose size is between the zone's attribute extrema. Area zones can be computed efficiently from hierarchical image representation structures, in a way similar to regular attribute filters. Operations on the DAP vector field can then be computed without the need for exporting it first, and an example with the leveling-like convex/concave segmentation scheme is given. This is referred to as the one-pass method and it is demonstrated on the Max-Tree structure. Its computational performance is tested and compared against conventional means for computing differential profiles, relying on iterative application of area openings and closings. Applications making use of the area zone decomposition are demonstrated in problems related to remote sensing and medical image analysis.