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 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]. 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 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 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 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 M. Vasilescu and D.Terzopoulos, “Multilinear Analysis of Image Ensembles: TensorFaces”, in European Conference on Computer Vision 2002, LNCS 2350(1): , A. Elgammal and C. Lee, “Separating Style and Content on a Nonlinear Manifold”, in Proc. of Computer Vision and Pattern Recognition, B. Scholkopf, A. Smola and K.R. Muller, "Nonlinear component analysis as a kernel eigenvalue problem", Neural Computation, Vol. 10, pp , 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 , Contact information Richard J. Radke, Assistant Professor Dept. of Electrical, Computer, and Systems Engineering Rensselaer Polytechnic Institute 110 8th Street, Troy, NY phone: (518) , 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 ) 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. 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 1. Original shape (blue) and Reconstructed shape (green) from KPCA principal components (pre- image). 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 2. New prostate shapes generated from KPCA modeling. Horizontal axis: first mode of variation, Vertical axis: second mode of variation Figure 4. Prostate/bladder joint model. Red: Bladder Cyan: Prostate