Thus, the fuzzy tesselation of the feature space is transformed into an exhaustive and mutually exclusive “hard” tesselation that assigns each feature vector x, i.e., each voxel of the 3D dataset to the nearest-neighbor codebook vector w j. (7.47) w ( x ) = w j, with ‖ x - w j ‖ = min i ‖ x - w i ‖. As a result, each of the m tissue classes λ is represented by a set of codebook vectors w j λ. If a clear decision for a codebook vector cannot be made, additional images with highlighted pixels belonging to the specific codebook vector can be viewed in order to perform a proper tissue class assignment. Step-by-step, you get to see how your favorite. Thus, it is usually sufficient to analyze N images for assigning each codebook vector to a tissue class. One of the coolest things about drawing books is that you get an insiders view into the artists process. Interactive visual inspection of the images of the 3D data set that contain the maximal number of pixels belonging to a specific codebook vector w j usually enables a decision on which tissue class λ is represented by this codebook vector. For this reason, for each of the N codebook vectors w j, all the voxels of the 3D data set belonging to this codebook vector according to Eq. In a second step, each codebook vector w j is assigned to a tissue class λ ∈ (e.g., 1 = ^ gray matter, 2 = ^ white matter, 3 = ^ CSF) that is represented by the codebook vector. Thus, the fuzzy tesselation of the feature space is transformed into an exhaustive and mutually exclusive “hard” tesselation that assigns each feature vector x, i.e., each voxel of the 3D data set to the nearest-neighbor codebook vector w j. (47) w ( x ) = w j, with ‖ x − w j ‖ = min i ‖ x − w i ‖.
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