We have examined the problem of the number of quad-tree blocks that an n-dimensional rectangle will be decomposed into on the average. the contribution of this paper are both practical and theoretical. In this paper, we develops the overlapping multi-scale models and the region quad-tree models which is useful in computer graphics animation, image processing, pattern recognition and also for modeling three dimensional objects. These models, which represent something of a conceptual departure from other models developed for multi-scale framework were developed with the specific interest of producing smooth estimates.