Adjusting Atlas Plates
The "Atlas of the Human Brain" is a drawing of a coronal sliced brain of a human being. On the one hand some deformation occures while slicing and on the other hand there are inaccuracies in drawing the structures. So the atlas suffers of the fact that coronal plates do not fit on each other exactly. On this page a technique of non-linear transformation on the plates to adjust neighbours to each other to a high level of accuracy is described.
To adjust the coronal plates, each plate is matched to the previous and following plate in a nonlinear but quite stiff manner. To avoid our atlas to converge into a cones shape, the transformation is executed simultaneously on all plates. This is achieved by computing a direction of increase in congruence on each plate. Then the optimal stepsize for all layers in common is determined via a collective line-search. This is exactly the same procedure as in matching a pair of two dimensional images by monomodal measure.
- e142_02, sagittal, horizontal view. rwa=sin, r=2
- e142_03, sagittal, horizontal view. rwa=sin, r=3
- e142_04, sagittal, horizontal view. rwa=sin, r=4
- e142_12, sagittal, horizontal view. rwa=cos, r=2, s=1
- e142_13, sagittal, horizontal view. rwa=cos, r=3, s=1
- e142_14, sagittal, horizontal view. rwa=cos, r=4, s=1
- e142_42, sagittal, horizontal view.. rwa=fft, r=2, β=2
- e142_45, sagittal, horizontal view.. rwa=fft, r=2.5, β=2
- e142_46, sagittal, horizontal view.. rwa=fft, r=2.5, β=2, gray tone by averaged RGB channels of colored atlas.
- e144_02, sagittal, horizontal view.. rwa=fft, r=2.5, β=2, gray tone by averaged RGB channels of colored atlas, bicubic interpolation. matching adjusted atlas on MR.
- e149_01, sagittal, horizontal view. rwa=fft, r=2.5, β=2, gray tone by averaged RGB channels of colored atlas, global histogram equalisation, shape preserving bicubic interpolation.
- e149_02, sagittal, horizontal view. rwa=fft, r=2.5, β=2, gray tone by averaged RGB channels of colored atlas, local histogram equalisation, shape preserving bicubic interpolation.
- e154_01, sagittal, horizontal view. rwa=fft, r=2.5, β=2, gray tone by averaged RGB channels of colored atlas, local histogram equalisation, shape preserving bicubic interpolation. (improved visualisation of displacement)
- e142_43, sagittal, horizontal view.. rwa=fft, r=3, β=2
- e142_44, sagittal, horizontal view.. rwa=fft, r=4, β=2
Explanation of Parameters
- boundary condition (rwa) on regularisation of forces: Dirichlet (sin); Neumann (cos); periodic (fft); solely affin-linear transformation (lin).
- regularisation strength (r): frequencies f are weighted by 1/fr. E.g. stiffnes increases with r. r = ∞ is affin-linear transform only.
- regualisation of defective eigenvalue in cosine transform by adding s before inversion.
- Weighting β of mixed derivative term in periodic boundary condition (fft). β = 2 has a strong tendency to volume conservation.