Evaluation of an Automatic Algorithm Based on Kernel Principal Component Analysis for Segmentation o

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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 D. Michael Lovelock
and Ping Wang Rensselaer
Polytechnic Institute Memorial
Sloan-Kettering Cancer Center
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)
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 multi-variations
on a manifold. A. Elgammal C. Lee
(2004) Challenges and significance Shape
modeling of anatomical objects is important to
diagnosis/treatment planning. The shape of soft
tissue structures often deform in a non-linear
fashion. 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.
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 s3 mm and 10 modes.
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.
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
Figure 4. Prostate/bladder joint model. Red
Bladder Cyan Prostate
Figure 2. New prostate shapes generated from
KPCA modeling. Horizontal axis first mode of
variation, Vertical axis second mode of variation
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
Figure 1. Original shape (blue) and
Reconstructed shape (green) from KPCA principal
components (pre-image).