Volume will have a global mean, which we take to be the sample mean

(1) | ||

(2) |

Since volume maps to , with *V*(*S*) defined by Eq. 2, the DC component of corresponding to the gray background is mostly removed. Then, . The algorithm adds the primarily low-frequency to the almost DC-less to synthesize .

In practice, a scaled is added to to avoid significant alteration of local means when going from to . The exact value of alpha depends on the relative signal levels in and . Relating back to the framework in Fig. 3, the upper branch's extraction of high-frequency components from and scaling are contained in the term . The lower branch's behavior is simpler: all frequency components are extracted from and the scaling factor is unity.

The synthesized result of the slices from Fig. 1 is shown in Fig. 4. It can be seen that the first algorithm performs well in presenting the fine details of . Because we avoided significant alteration of the local means of through the scaling factor , the textural smoothness and regional boundaries of are well preserved.

Figure 4

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