Sheet Case Medial Surface Detection

We assume that the direction of the surface normal is given by e1 at the voxel around the medial surface. The 1-D intensity function, c(v), which is the profile of f (X; af) along e3, should have its peak on the medial surface. The second-order approximation of c(v) is given by c(v) = f (X0; a f) + vc0 + 1 v2cl (10.36)

where ve3 = x — e, c'0 = Vf • e3, and c^ = X3. c(v) should have its peak on the medial surface of the sheet. The peak is located at the position satisfying

By solving Eq. (10.37), we have the offset vector, p, of the peak position from X given by p = te3, (10.38)

where t = — vf ^e3. The medial surface is detected only if \px\ < 1, \py\ < |,and

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