Thus the fewer the range blocks, the fewer bits will be consumed by the compressed image file. A careful selection of the domain pool may reduced the number of range blocks needed to construct the global contractive mapping, thus reduced the total number of bits encoded in the compressed image. We modified Fisher's quadtree code by adding more domains to his domain pool. Fisher's code uses horizontally and vertically oriented domains that are twice as large as the ranges. This works extremely well for images that has horizontal and vertical block structure.
Many images also possess block structures oriented in other directions.
Since each diamond domain has more points than its square counterpart, a different sub-sampling and averaging process must be used to compare the domain with the range. Each sub-diamond has 5 points on and within its boundary. The average value of these 5 points is assigned to pixel at the center of the sub-diamond. The following figure demonstrates the averaging and sub-sampling process. The performance of our modified code is shown in the next section .