This section deals with kidney segmentation algorithms followed by computer-aided detection or diagnosis of kidney pathologies.
Overview of Kidney Segmentation Algorithms Several kidney segmentation algorithms have been proposed for a non-contrast or a contrast-enhanced CT volume, such as a region-growing-based algorithm [176, 230], an algorithm based on knowledge of organs’ location and CT values . Three-dimensional deformable model-based approaches have been proposed [137, 289] to achieve more sophisticated boundaries. This section presents a 3D deformable model-based segmentation algorithm with CA, or statistical shape feature .
A NURBS-based surface was employed to represent the surface of the kidney because of its high flexibility in shape representation (see Fig. 3.80).
The following energy function was used for the segmentation:
where Vd represents a gradient operator of gray values with difference distance d, G0 is a Gaussian function with standard deviation о, I denotes an original image, and * is a convolution operator. Function Dir defines the similarity between direction of a gradient vector and that of a normal vector of the NURBS-based surface. The second term is an internal energy which is the sum of Mahalanobis distances from the shape feature vectors to its average. Shape feature vector x is defined at each sampling point on the surface marked by black dots in Fig. 3.81,
Fig. 3.79 Examples of segmentation results by ShapeBoost and AdaBoost (a) case 5, (b) case 14
Fig. 3.80 Kidney surface represented by a NURBS function with control points (white dots) and sampling points used for measuring shape features (black dots) (Figure 3 of Ref. )
Fig. 3.81 An example of kidney segmentation; initial boundary (left) and final boundary extracted by the proposed algorithm (right)
and components of the shape feature vector are principal curvatures, or minimum and maximum curvatures, at the sampling points. Statistical information about the shape variation is incorporated into the deformable model via an internal energy whose average vector x and covariance matrix Euv were computed from training dataset of kidneys.
Thirty-three upper abdominal CT volumes were used to evaluate the performance of the algorithm. The size of the volume was 512 x 512 x 18-24, the resolution was 0.625 or 0.630 mm, and the section thickness was 10 mm. Figure 3.81 shows an example of initial boundaries of the deformable model and its segmentation results after minimizing Eq. 3.21, in which the final state of the deformable model succeeded in capturing the true boundaries of the kidney. When we used the internal energy, the JI between an extracted kidney region and a true one increased by 0.028 on average from 33 cases compared with the results of the same cases without the internal energy, resulting in a mean of 0.865.
Computer-Aided Diagnosis of the Kidneys The number of kidney cancers in Japan is increasing every year . It is desirable to detect the disease at the earliest possible stage using state-of-the-art imaging modalities, such as MDCT, to increase the likelihood of successful diagnosis and treatment.
Some studies described algorithms to measure clinically useful information, e.g., volume of a kidney tumor, in which region-growing- and thresholding-based segmentation algorithms were used to segment tumors [155,270]. A semiautomated tumor segmentation algorithm from multiphase CT volumes was proposed  where a level set-based segmentation algorithm was presented followed by experimental results using 12 tumors from ten cases. The Dice coefficient between a true tumor and an extracted one was 0.80 on average. Figure 3.82 shows an example of extracted tumors . In the segmented lesions, the histograms of curvature- related features were computed to quantify and classify the lesion types [177, 178].