154
K. Miller et al.
distance values for different percentiles. A plot of the Hausdorff distance values
at different percentiles immediately reveals the percentage of edges that have
misalignments below an acceptable error.
6.3.6.3 Results
Qualitative Evaluation of Registration Results
Deformation Field
The deformation fields predicted by the biomechanical model are compared to these
obtained from the BSpline transform (available in 3D Slicer [116]) used to register
pre- to intra-operative neuroimages. These deformation fields are three dimensional.
However, for clarity, only arrows representing 2D vectors (x and y components of
displacement) are shown overlaid on undeformed pre-operative slices. Each of these
arrows represents the displacement of a voxel of the pre-operative image domain.
In general the displacement fields calculated by the BSpline registration algorithm
are similar to the predicted displacements by the biomechanical model at the outer
surface of the brain, but in the interior of the brain volume, the displacement vectors
differ in both magnitude and direction (Fig. 6.10).
Overlap of Canny Edges
From Fig. 6.11 we can see that misalignment between the edges detected from
the intra-operative images and the edges from the pre-operative images updated
to the intra-operative brain geometry is much lower for the biomechanics-based
warping than for BSpline registration. This is an indication that the biomechanicsbased prediction of brain deformations may perform more reliably than the BSpline
registration algorithm if large deformations are involved.
Quantitative Evaluation of Registration Results
The plot of percentile edge-based Hausdorff distance (HD) versus the corresponding
percentile provides an estimation of the percentage of edges whose displacements
have been computed with sufficient accuracy. As the accuracy of edge detection
is limited by the image resolution, an alignment error smaller than two times the
original in-plane resolution of the intra-operative image (which is 0.86 mm for the
13 cases considered) is difficult to avoid [117]. Hence, for the clinical cases analysed
here, we considered any edge pair having an HD value less than 1.7 mm to be
successfully registered. This choice is consistent with the fact that it is generally
considered that manual neurosurgery has an accuracy of no better than 1 mm
[117, 118]. It is obvious from Fig. 6.12 that biomechanical warping was able to
successfully register more edges than the BSpline registration.
K. Miller et al.
distance values for different percentiles. A plot of the Hausdorff distance values
at different percentiles immediately reveals the percentage of edges that have
misalignments below an acceptable error.
6.3.6.3 Results
Qualitative Evaluation of Registration Results
Deformation Field
The deformation fields predicted by the biomechanical model are compared to these
obtained from the BSpline transform (available in 3D Slicer [116]) used to register
pre- to intra-operative neuroimages. These deformation fields are three dimensional.
However, for clarity, only arrows representing 2D vectors (x and y components of
displacement) are shown overlaid on undeformed pre-operative slices. Each of these
arrows represents the displacement of a voxel of the pre-operative image domain.
In general the displacement fields calculated by the BSpline registration algorithm
are similar to the predicted displacements by the biomechanical model at the outer
surface of the brain, but in the interior of the brain volume, the displacement vectors
differ in both magnitude and direction (Fig. 6.10).
Overlap of Canny Edges
From Fig. 6.11 we can see that misalignment between the edges detected from
the intra-operative images and the edges from the pre-operative images updated
to the intra-operative brain geometry is much lower for the biomechanics-based
warping than for BSpline registration. This is an indication that the biomechanicsbased prediction of brain deformations may perform more reliably than the BSpline
registration algorithm if large deformations are involved.
Quantitative Evaluation of Registration Results
The plot of percentile edge-based Hausdorff distance (HD) versus the corresponding
percentile provides an estimation of the percentage of edges whose displacements
have been computed with sufficient accuracy. As the accuracy of edge detection
is limited by the image resolution, an alignment error smaller than two times the
original in-plane resolution of the intra-operative image (which is 0.86 mm for the
13 cases considered) is difficult to avoid [117]. Hence, for the clinical cases analysed
here, we considered any edge pair having an HD value less than 1.7 mm to be
successfully registered. This choice is consistent with the fact that it is generally
considered that manual neurosurgery has an accuracy of no better than 1 mm
[117, 118]. It is obvious from Fig. 6.12 that biomechanical warping was able to
successfully register more edges than the BSpline registration.