Expected complexity in hierarchical representations for random fields

The soft-linked quadtree is proposed as a hierarchical representation paradigm for random fields. It is shown that, through the use of such a model, a priori information can be obtained on the complexity of a quadtree. Because of this property, a parametric analysis can be substituted for simulation. However, this capability is only one of the many such features of a soft-linked model. Almost all the concepts defined over a conventional quadtree, e.g., neighbor and neighbor finding, perimeter and area, etc., can be revisited. Since the notions of state probability and link strength are means of expressing confidence in assigned labels, the soft-linked model can be further developed into a hierarchical representation paradigm for uncertainty