Introduction The spleen is located in the left upper quadrant of the abdomen (see Fig. 3.76) and is an important part of the reticuloendothelial system. Most of the spleen segmentation algorithms from a CT volume have been reported as part of the multi-organ segmentation scenario (Sect. 3.9.6). This subsection focuses on a segmentation algorithm with a CA model, or an SSM, customized to the spleen .
Machine learning is a popular technique in the field of medical image segmentation. In principle, an arbitrary machine learning algorithm, such as a support vector machine and the AdaBoost algorithm [38, 84], can be applied to organ segmentation where each voxel in a 3D image is classified by the algorithm as organ or background. Because of the powerful classification performance of state-of-the-art machine learning algorithms, this algorithm achieves higher segmentation accuracy than conventional algorithms. The inherent weakness of machine learning-based segmentation is, however, that voxel classification is carried out voxel by voxel, independently, producing unnatural shapes from the point of view of anatomy. To solve this problem, shape information has been incorporated in a machine learning- based segmentation algorithm.
This section focuses on ensemble learning as a promising machine learning technique, in particular a boosting algorithm, such as AdaBoost, whose performance has been proved to be favorable in terms of not only classification accuracy but also computational cost [38, 84]. Combining MRF with AdaBoost decreased false isolated connected components and holes in an extracted target region . Several papers have presented algorithms that consider shape features of a target region, such as SpatialBoost  and Spatial AdaBoost . Shape features used in these algorithms are local features which do not capture global shape features. Global shape features were introduced in the literature [4, 201]. There is, however, no boosting algorithm that can take into account statistical shape variations of an organ. This section presents ShapeBoost , which minimizes not only error loss but also shape loss, and evaluates the accuracy of an extracted shape based on a subspace of an SSM of the spleen.
Proposed Shape Loss Function Given a sample x, and its class label y;, the conventional boosting algorithm AdaBoost [38, 84] generates a strong classification function F(x), which consists of a series of weak classifiers by minimizing the following loss function of F(x):
where a set ?2 represents the entire area of the image to be processed. Because the algorithm focuses on the error in each voxel, a surface extracted by a constructed classifier often includes undesirable irregularity. We propose a new loss function, given in Eq. (3.20), to make an extracted surface reasonable from the point of view of CA:
where H is a Heaviside function and ф denotes a signed distance function. U is a matrix which consists of eigenvectors of an SSM of an organ, or a level set distribution model of the spleen in this study. W is a vector of signed distance function of a training spleen label which includes w*. O; is an operator that extracts the /th element of a vector. The coefficient A represents the weighting between error loss and shape loss. Intuitively speaking, shape loss G in Eq. 3.20 represents distance between an extracted shape and a subspace of SSM, and its minimization causes the segmentation results to be closer to the subspace, or the natural shape, in terms of anatomy. Eventually, GradientBoost  was employed to minimize the loss of function that is not a convex function, and a strong classifier for spleen segmentation was obtained after minimization using a set of training labels.
Materials for validation were three-phase contrast-enhanced CT volumes, or early/arterial, portal, and venous phases (see Fig. 3.77) scanned from 80 cases. The size of the CT volume was 512 x 512 x 253-675 (voxels). A registration algorithm based on a radial basis function with normalized mutual information was used to align the different phase CT volumes. Spatial standardization based on the abdominal cavity was employed to reduce variation in location of the spleen . Forty-two features were measured for weak classifiers of the ShapeBoost.
Cross validation tests using 80 cases were carried out to validate the performance, in which 40 cases were used for training a level set distribution model and a strong classifier, and the constructed classifier was tested on the remaining 40 cases. The same procedure was repeated after switching the roles of training and test.
Figure 3.79 shows examples of segmentation results where the resultant shape, in particular, the shape of the splenic hilum (denoted by arrows), by the ShapeBoost was more natural than that of AdaBoost, resulting in a higher JI between an extracted spleen and a true one. The error rate decreased from 3.09 to 2.66% on average (p < 0.01; Wilcoxon signed-rank test). After extracting a connected component with maximum volume, average JI by ShapeBoost reached 0.764, which was significantly higher than that by AdaBoost (p < 0.01; Wilcoxon signed-rank test). Note that this process is a rough segmentation process which can be refined by a graph cut-based algorithm as is done in lung and liver segmentation [210, 288].