Image Segmentation and Nonuniformity Correction Methods

Region-Based Segmentation

In region-based segmentation, the algorithms are based on the intensity homogeneity within the target object and/or the background. The simplest example of a region-based algorithm is intensity thresholding, where the input 3D image is divided into foreground (i.e., target object) and background, by comparing the intensity of each voxel to a constant value (threshold). The output of thresholding is usually a binary image of the same dimension as the input image, called a mask. Let I(x , y , z) be the voxel intensity at coordinate (x , y , z) , then the voxel intensity of mask M is defined as

where T is a constant. In some cases, the constant threshold T is set manually based on prior knowledge. Automated algorithms have also been developed to identify a threshold, such as Otsu's method.

Another commonly used region-based algorithm is region growing. First, a seed region containing one or more voxels is defined on the 3D image, either manually or by automated computational tools. The seed region is then extended to its neighboring voxels, until it reaches certain preset constraints, such as the similarity of all neighbors. The final form of the region is used as the target object. A common example of region growing is the watershed algorithm. Consider a simple case of a 2D image. The image is treated as an elevation map, with voxel intensity representing the voxel’s altitude. The watershed method uses one of two strategies to decompose the image into subregions, or watersheds: 1) flooding or immersion and 2) rainfall. For both strategies, the process begins with identifying and tagging all local minima. In watershed by flooding, water sources are placed in each local minimum. The water level is systematically increased, creating a set of barriers. The process terminates when different water regions merge. In watershed by rainfall, for each voxel, the algorithm finds the direction in which a raindrop would flow if it fell on this voxel. The neighboring voxel is found at the flow direction. The voxel and its neighbor are then merged, and the process continues until the local minimum is reached.

Instead of region growing, sometimes region peeling is necessary in order to reduce the size of the segmented region, or separate two target regions touching each other. The mathematical morphology provides an elegant framework for both region growing and region peeling. For binary morphology, a binary mask (named a structuring element) B is set, which defines the connected components (or neighborhood) for any voxel z in the image. Common 2D examples of B are illustrated in Fig. 3.2 . Note that the radius of B is conventionally an odd number. The 3D version of B can be obtained by extending the 5 × 5 matrices in Fig. 3.2 to 5 × 5 × 5 matrices, while maintaining the same binary profiles.

Let A be the input image. Then for any given voxel z in A, a set of connected voxels (denoted B _z ) can be obtained by shifting the center of the structuring element B to the coordinates of z and including all the voxels covered by B. The four basic morphological operations —erosion E(A , B) , dilation D(A , B) , opening O(A , B) , and closing C(A , B) — can then be defined as

In other words, the erosion of image A by element B is the set of all voxels z such that B _z is contained in A , while the dilation of A by B is the set of all voxels z such that B _z overlaps with A by at least one voxel. The closing operation, which consists of dilation followed by erosion, is particularly useful for 3D printing, as it can fill small holes in the segmented regions before 3D reconstruction and printing.

In practice, different region-based algorithms can be combined to achieve more accurate segmentation. For example, in orthopedic imaging, thresholding and morphological operations can be jointly applied to separate gypsum cast from the bone on CT scans ( Fig. 3.3 ).

Boundary-Based Segmentation

In boundary-based segmentation, the algorithms locate the tissue boundary (i.e., the edge) by evaluating local changes (known as gradients) of voxel intensity. For example, the Canny edge detector measures the intensity gradient within a moving window called a kernel. The active contours algorithm converts intensity change into the energy functions, and locates the boundary via optimization searches.

A boundary-based algorithm can also be combined with other algorithm types to achieve a more sophisticated segmentation. One such example is the EdgeWave algorithm in FireVoxel , which combines boundary detection with thresholding and morphology, or the shape characteristics of an image ( Fig. 3.4 ). In FireVoxel, the EdgeWave algorithm is used for several key processing workflows, such as measuring body fat composition on abdominal CT images. The EdgeWave algorithm contains the following main steps:

• 1.

  The original image is resampled, as needed.

• 2.

  Thresholding by image intensity is applied to roughly delineate the region that needs to be segmented, called the Core Set. The Core Set must enclose the segmentation target, otherwise the segmentation will fail.

• 3.

  Edges detection is performed and the locations of the Core Set where image intensity changes abruptly are defined.

• 4.

  The boundary of the Core Set is eroded, or peeled. The Peel operation removes all voxels within a certain distance from the boundary using rules applied to each voxel and its neighbors. Peeling enlarges the gaps between different regions of the image, removes small details, and breaks “bridges” between weakly connected areas. The thickness of the region to be removed is controlled by the peel distance , measured in voxels or millimeters.

• 5.

  The algorithm breaks up the peeled Core Set into blobs, or connected components. It then determines which connected components are to be retained and which ones should be discarded.

• 6.

  The selected connected components are subjected to constrained growth, or dilation. The Grow operation adds voxels within a given distance of the region of interest (ROI) boundary. Any recovered voxels must still belong to the Core Set. The thickness of the recovered region is controlled by the grow distance , which should be larger than the peel distance .

Atlas-Based Segmentation

In atlas-based segmentation, ROIs are first segmented (usually manually) on a reference image called a template. This reference segmentation is commonly known as the atlas. To perform segmentation on a new image, the template image is first warped to the target image through image registration. The same transformation computed during the registration step is then applied to the preexisting atlas to propagate the ROIs on the target image. Fig. 3.5 illustrates this procedure with brain image samples. To reduce the impact of intersubject variability, multiple reference images can be registered to the same target image, with different reference segmentations propagated and merged into a final segmentation. This approach is called multi-atlas segmentation.