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Magnetic Resonance Image Segmentation with
Thin Plate Spline Thresholding
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Xianhong Xie1,2,
Moo K. Chung1,2,3, Grace Wahba1,2
1Department of
Statistics, University of Wisconsin-Madison, 2Department
of Biostatistics and Medical Informatics, University of
Wisconsin-Madison, 3W.M. Keck
Laboratory for Functional Brain Imaging and Behavior, University of
Wisconsin-Madison
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Objective:
To
develop a new method for segmenting T1-Weighted magnetic resonance image into gray
matter
(GM), white matter (WM), cerebrospinal fluid (CSF), and other types of
tissues.
Methods:
Our method has 4 steps. First, we divide each slice into overlapping
blocks. Second, we fit thin plate splines to each block with different
number of knots, and search for the knots configuration that gives us
the smallest GCV score with a fudge factor [1].
Third, we fit the thin plate spline with the knots configuration found,
and predict on a really fine grid. We also find the thresholds on the
block with the K-means algorithm. Finally, we blend the predicted block
images and the thresholds with some smooth weighting functions. The
averages of the corresponding thresholds on all the blocks and the
thresholds on the blended smooth image are calculated as well. We can
apply all 3 thresholding scheme to the blended image, and pick the one
that suits our needs best. Our empirical results show that images from
different sources might need different thresholding.
The TPS method was tested on 5 subjects from the IBSR 20 normal data.
We selected the 2nd, 6th, 10th, 14th, 18th subject after we sorted the
20 subjects based on their id's. One slice near the middle of the brain
for each subject was used with our method. SPM segmentation was applied
to the whole volumes of the 5 subjects. Note that the 20 normal data is
provided with human segmentation results.
Results & Discussion:
The comparison between TPS method, SPM, and manual segmentation on one
subject is given in Figure 1 and 2.
They show that TPS method matches manual segmentation reasonably well.
And the TPS is doing really close to SPM. The correlation coefficients
and kappa indices [2] between each 2 of the 3 methods
for all the subjects were calculated (Table 1). The
numbers confirm our conclusions. Note that the TPS method gives
subpixel segmentation (Figure 3).
Conclusions:
Our method is an intensity based method. It uses thin plate splines to
reconstruct the image. Our results show that the new method is
comparable to the SPM segmentation, as well as the human segmentation.
The TPS method has the advantage of giving subpixel level results and
generating smoother boundaries. The partial volume effects are
addressed by the subpixel segmentation. Also, it offers the potential
for more accurate estimate of distances and curvatures on the cortical
surfaces. Our method tackles the image non-uniformity through local
thresholding and blending. It depends less heavily on correction for
non-uniformity.
References & Acknowledgements:
[1] Luo, Z. and Wahba, G. (1997). Journal
of the American Statistical Association, 92:107-116.
[2] Zijdenbos, A.P. et al
(1994). IEEE Transactions on Medical Imaging, 13:716-724.
Figure 1: Comparison of TPS
Segmentation vs Manual Segmentation
Figure 2: Pairwise Comparison of
TPS, SPM, and Manual Segmentation
Figure 3: Zoomed View of the TPS
Segmentation Boundaries
| Table 1:
Coefficients for all the Comparisons with Mean and SD Summary |
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subject
no. |
corr. coef. |
kappa index |
| GM |
WM |
GM |
WM |
| tps vs manual |
1 |
0.660 |
0.827 |
0.836 |
0.872 |
| 2 |
0.702 |
0.757 |
0.841 |
0.827 |
| 3 |
0.654 |
0.787 |
0.811 |
0.850 |
| 4 |
0.410 |
0.678 |
0.723 |
0.770 |
| 5 |
0.612 |
0.791 |
0.776 |
0.838 |
| mean(sd) |
|
0.608(0.115) |
0.768(0.056) |
0.798(0.049) |
0.831(0.038) |
| spm vs manual |
1 |
0.675 |
0.846 |
0.883 |
0.866 |
| 2 |
0.686 |
0.839 |
0.887 |
0.880 |
| 3 |
0.637 |
0.810 |
0.863 |
0.842 |
| 4 |
0.091 |
0.672 |
0.679 |
0.753 |
| 5 |
0.450 |
0.803 |
0.825 |
0.824 |
| mean(sd) |
|
0.518(0.250) |
0.794(0.071) |
0.827(0.087) |
0.833(0.050) |
| tps vs spm |
1 |
0.806 |
0.883 |
0.848 |
0.900 |
| 2 |
0.626 |
0.759 |
0.794 |
0.824 |
| 3 |
0.734 |
0.822 |
0.808 |
0.861 |
| 4 |
0.426 |
0.767 |
0.730 |
0.793 |
| 5 |
0.645 |
0.800 |
0.785 |
0.836 |
| mean(sd) |
|
0.647(0.143) |
0.806(0.050) |
0.793(0.043) |
0.843(0.040) |
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