Transcript Document

Evaluation of an Automatic Algorithm Based on Kernel
Principal Component Analysis for Segmentation of the Bladder
and Prostate in CT Scans
Siqi Chen and Richard J. Radke
Rensselaer Polytechnic Institute
D. Michael Lovelock and Ping Wang
Memorial Sloan-Kettering Cancer Center
Abstract
We evaluate the performance of non-linear kernel principle
component analysis (KPCA) based shape modeling
algorithm and the automatic segmentation of prostate and
bladder during radiotherapy. If the shape deforms in a
nonlinear way, then traditional linear method like PCA will
not truly express the shape variation. We apply our KPCA
model to 9 patient's full treatment CT scans, each patient
has 10 to 18 scans. The performance of segmentation on 3
previously unseen data sets of each patient at the beginning,
middle and end of the treatment are compared with the
contours drawn by a physician. We also compare the result
of segmentation using prostate-only model, bladder-only
model and prostate-bladder joint model.
State-of-the-art
ASM (Active Shape Model) – Captures variation in
training data using PCA. T. Cootes et al. (1995)
Bilinear model – Models two independent variations.
Y.Jeong and R.J.Radke (2006)
Multilinear model – Models more than two independent
variations. M. Vasilescu & D. Terzopoulos (2002)
Nonlinear multifactor models – Decouples multivariations on a manifold. A. Elgammal & C. Lee (2004)
1.2 Shape modeling
A library of approximately 300 CT scans of 25 prostate
patients, acquired in an IRB approved protocol, has been
manually segmented by physicians. Each patient had about 13
CT scans acquired during their course of treatment.
As part of a preliminary analysis, the performance of the method
was first evaluated intra-fractionally, that is, the system was
trained using contours from CT scans from the same patient taken
on different days throughout their treatment course. Three
different models have been studied: a prostate-only model, a
bladder-only model, and a joint prostate-bladder model. As the
bladder fills and expands, it presses against the prostate. These
complex bladder surfaces were simplified by constructing a
convex hull; the models were trained using these convex hulls.
Each organ was represented by 400 points uniformly distributed
around its surface, and the KPCA models were built using a
Gaussian kernel with s=3 mm and 10 modes.

Challenges and significance
• Shape modeling of anatomical objects is important to
diagnosis/treatment planning.
• The shape of soft tissue structures often deform in a nonlinear fashion.
Figure 4. Prostate/bladder
joint model. Red: Bladder
Cyan: Prostate
This work was supported in part by Gordon-CenSSIS,
the Bernard M. Gordon Center for Subsurface Sensing
and Imaging Systems, under the Engineering Research
Centers Program of the National Science Foundation
(Award Number EEC-9986821)
Table 1. Average Ratios of the Overlap Volume to the Volume of the Physician Drawn
Structure. Each number is the average of the three ratios from the beginning, middle,
and end of treatment
3. Conclusion
The overlap ratios averaged over the three test cases for each of the first
seven patients for all three models are listed in the above table. No
significant differences were found in any model between segmentations of
the prostate or bladder from the beginning, middle, and end of treatment.
The results from the joint model are not significantly different for
individual organ models. In regions of the prostate in which the edge can
be detected, an excellent match between models and the physician’s
contour were found.
Opportunities for technology transfer
• A successful system can be used as a reliable reference for manual
contouring, if not actually substituting for it.
Publications acknowledging NSF support
Technical approach
1. Shape modeling using a KPCA model
1.1 Background
• KPCA: Kernel PCA (KPCA) [4] is a non-linear modeling
technique in which input vector is mapped into a high
dimensional feature space and a linear model is built using
PCA. The advantage of KPCA is that PCA computation in
high dimensional feature space can be circumvented by
doing only inner product operations in feature space, and
this computation can be represented by a kernel function
k(x,y). A typical kernel is Gaussian radial basis function.
• Pre-image problem: While the mapping
from input

space to feature space is of primary importance,
the
reverse-mapping from feature space back to input space is
also useful, since we need to reconstruct the shape from
principal components. Pre-image can be estimated via
numerical optimization [5].
Figure 1. Original shape
(blue) and Reconstructed
shape (green) from KPCA
principal components (preimage).
Figure 2. New prostate shapes generated from KPCA modeling. Horizontal
axis: first mode of variation, Vertical axis: second mode of variation
2. Segmentation results
The segmentation algorithm is based on our previous method
[Freedman 2005]. The Result was evaluated by comparing the
bladder and prostate contours generated on three CT studies for
each patient that had been excluded from the training set. For
each patient, the evaluation scans were from the beginning,
middle, and end of the treatment course. The generated contours
were used to construct surfaces for the prostate and bladder.
Performance was evaluated by comparing the ratio of the overlap
volume of the generated shape with the physician-drawn contours’
volume. Shape change was evaluated by first aligning the centers
of gravity of the model-generated prostate and drawn prostates,
then constructing a 2D map of the distance between the surfaces
as a function of the azimuthal and polar angles.
Figure 4. Segmentation
result of one patient
data (Top left: prostate
only. Top right:
Bladder and Prostate.
Bottom left: Bladder
and Prostate. Bottom
Right: Bladder Only ) .
Blue contours are the
actual contour drawn
by physician, while the
red contours are the
segmentation results
1.Y. Jeong and R.J. Radke, “Modeling inter- and intra-patient anatomical
variation using a bilinear model,” IEEE Computer Society Workshop on
Mathematical Methods in Biomedical Image Analysis, June 2006.
2. D. Freedman, R.J.Radke et al, “Model-based Segmentation pf medical
imagery by matching distributions”, IEEE Transactions on Medical Imaging,
vol 24, No.3 March 2005.
References
1. T. Cootes, C. Taylor, D. Cooper, and J. Graham, “Active Shape Models –
Their Training and Application”, in Computer Vision and Image
Understanding, 61(1):38-59, January 1995.
2. M. Vasilescu and D.Terzopoulos, “Multilinear Analysis of Image
Ensembles: TensorFaces”, in European Conference on Computer Vision
2002, LNCS 2350(1):447-460, 2002.
3. A. Elgammal and C. Lee, “Separating Style and Content on a Nonlinear
Manifold”, in Proc. of Computer Vision and Pattern Recognition, 2004.
4. B. Scholkopf, A. Smola and K.R. Muller, "Nonlinear component analysis as a
kernel eigenvalue problem", Neural Computation, Vol. 10, pp. 1299-1319, 1998.
5. B. Scholkopf , S. Mika , A. Smola, G. Ratsch and K.R. Muller, "Kernel PCA
pattern reconstruction via approximate preimages, Proc. 8th Int. Conf. on Artificial
Neural Networks, pp. 147-152, 1998.
Contact information
Richard J. Radke, Assistant Professor
Dept. of Electrical, Computer, and Systems Engineering
Rensselaer Polytechnic Institute
110 8th Street, Troy, NY 12180
phone: (518) 276-6483, e-mail: [email protected]