Both the double tree and the dual double tree provide an asymmetric treatment of space and frequency. As a result, neither tree attains the full joint decomposition in space and frequency. In order to produce the full joint decomposition, all nodes in the trees need both a frequency and segmentation branch. In other words, the outputs at each stage must be split by frequency and by segmentation. This creates the much larger tree structure which is illustrated in Figure 9(a). This full space and frequency tree combines both the double tree and the dual double tree into a single structure.
Figure 9: (a) full space and frequency decomposition tree, (b) Image joint space and frequency expansion.