## The Algorithm

8.4.2.2.1 Definition. Even though many algorithms have been invented to minimize MRF's energy function as discussed in section 8.2.2.3, for mMRF model, only few algorithms have been proposed. The most recent solution published in literature was by Chang et al. [46], which is based on adaptive ICM method [84].

Since it has been shown in section 8.2 that the QHCF outperforms other algorithms, in this study, we extend it to multidimensional scenario. Its processing diagram is shown in Fig. 8.16. After having the images from all channels partitioned

Merging

Merging

Energy Function E Update

Energy Function E Update

with a Quad-Tree procedure, a "initial region merging" process is applied, in which a new region map is created as an initial segmentation result for the QHCF algorithm by combining all the regions found in different channels. The "merging" basically means the integration of region maps from all channels.

Under this presegmentation map, the definition of confidence for each pixel is the same as Eq. (8.29). However, the energy calculation is based on Eq. (8.47).

8.4.2.2.2 Dynamic Weighting. In multichannel data/image processing, different channels usually convey different amount of information. For example, in the soft tissue type identification with MR imaging [81], subjects are generally scanned with the multiple contrast weightings, such as T1-weighted (T1W), T2-weighted (T2W), proton density-weighted (PDW), and 3D time-of-flight (3D TOF). Since each contrast weighting imaging technique is sensitive only to certain tissue types, therefore, they usually contribute differently to the final decision when different tissue type is analyzed.

However, since there is no prior knowledge about the tissue type sensitivity layout in each channel, it is very impractical for human interaction involved in the segmentation process. In this study, a dynamic weighting system is proposed as a simulation of human's decision process, which automatically decides the weighting coefficient for the energy calculation among channels. In our implementation, two factors are significant in managing the dynamic weighting:

1. Complexity factor (CF): It measures the amount of details that each channel provides at a certain location. In the surrounding region of each location, we assume the complexity is proportional to the number of edges. The more edge points can be detected, the more details this channel can provide. Since Canny Edge detector [15] has been used successfully in the energy calculation, it is utilized in our implementation to generate edge map. Based on the requirements of segmentation performance, two ways are proposed to evaluate the complexity factor.

(i) Local CF: The number of edge points within a local neighboring region in each channel.

(ii) Global CF: The number of edge points in the whole image in each channel (it is equivalent to local CF with neighboring range as the whole image).

Obviously, global CF is simple in terms of computation and represents the importance of each channel in a general sense. It is very efficient when one of channels plays a critical role in the segmentation process. On the other hand local CF is more complicated because it estimates the complexity of each channel at every location. However, it is very effective in preserving the segmentation details from each channel. Local CF is also very suitable to the situation where no prior knowledge of each channel's potential contribution to segmentation results.

2. Weighting factor (WF): It is used to calculate the exact weighting of each channel based on the measurement of complexity factor. Assume the complexity factor from each channel is represented as: CFi_, i = 1, 2,...,d, the weighting factor is denoted as

and the clique energy at each locataion Vs (x) in Eq. (8.9) can be computed as d

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