Instead of adjusting the intensities of , the second algorithm synthesizes a new volume from a convex combination of the source volumes and . The relative levels of contribution from and are determined by how much deviates from , where is defined by Eq. 1 and is the intensity of the gray background in . Specifically, we form
Here, in terms of the framework in Fig. 3, the upper branch's extraction of high-frequency components from and scaling depicted are contained in the term . Similarly, the lower branch's extraction of low-frequency components from and scaling are contained in the term .
When combining the slices from Fig. 1, we obtained the synthesized result shown in Fig. 5. The advantage of the second algorithm is that it synthesizes the local structures from in the new volume more accurately than does the first algorithm, but this is done at the expense of sacrificing a small amount of textural smoothness inherited from . Again, the local means from are well preserved.