80	A. Alfiansyah

Fig. 4.12 Role of the regional energy term in bone surface segmentation. The model on the left evolves without a regional term, while such a term is applied on the right hand figure

computation time, Gradient Vector Flow and other image energy computations are confined within a thin narrow band around the evolved curve.

For the purpose of bone surface reconstruction from ultrasound imagery, other enhancements have been proposed [37] following the presented model. A set of bone contours is first extracted from a series of free-hand 2D B-Mode localized images, using an automatic segmentation method based on snakes with region-based energy as previously described. This data point-set is then post-processed to obtain a homogeneous re-sampling point-grid form. For each ultrasound slice, the algorithm first computes an approximation of the bone slice center. Using these central points, it approximates a line corresponding to the central axis of the bone. Then, for each slice, it: (a) updates the value of the central point as the intersection point of the line and the corresponding slice plane; (b) casts rays from the center towards the surface at regular intervals (spaced by a specific angle); (c) computes the new vertex as the intersection between rays and segments connecting the original points.

Three-dimensional B-Spline is applied to approximate the surface departing from these points. The method ensures a smooth surface and helps to overcome the problem of false positives in segmentation. Model reconstructions from localized ultrasound images using the proposed method are shown in Figure 4.13 and 4.14.

4.4.2 Spinal Cord Segmentation

4.4.2.1 Spinal Cord Measurements

This study has been conducted for quantitative assessment of disease progression in multiple sclerosis using MRI. For this study we use IR-FSPGR volume data as

4 Deformable Models and Level Sets in Image Segmentation

81

Fig. 4.13 Reconstructed surface of a real radius. Results for different numbers of control points c

Fig. 4.14 Reconstructed radius and ulna. Data scanned from a real subject

shown in Fig. 4.15, in which the spinal cord under analysis can be characterized by a bright structure against a dark background (representing CFS), normally with a cylindrical topology. Segmentation difficulties can arise due to artifacts, noise, and proximity to other structures such as vertebrae.

82	A. Alfiansyah

Fig. 4.15 MRI Image in which the spinal cords need to be segmented

Atrophy is generally assessed by measuring the cross-sectional areas at specific levels (typically C2–C5) along the cervical cord. This protocol introduces several uncertainties, including the choice of the level at which the measurements should be performed, the cord orientation, as well as the cord segmentation process itself. To provide non-biased area measurements, an MRI image, or part of the image, often needs to be re-formatted or acquired with slices perpendicular to the cord.

Moreover, the spinal cord cross-sectional area has often been measured either manually or using intensity-based 2D processing techniques. The limitations of such methods are various: measurements are restricted to a predefined level at which cords and slices are orthogonal; intensity-based segmentation is hindered by intensity variations caused by surface coils typically used during acquisition; 2D measurements are more prone to being biased by partial volume effects than 3D measurements; manual analysis is more time-consuming and more sensitive to intraand inter-operator variability.

4 Deformable Models and Level Sets in Image Segmentation

83

Fig. 4.16 Segmentation of an MRI Image using a naive geodesic active contour

4.4.2.2 Segmentation Using Geodesic Active Contour

We propose to apply a geometric deformable model to perform the segmentation without any image preprocessing of the data image. The model is initialized by placing a sphere in the spinal cord and letting this sphere evolve until the process reaches the convergence. Figure 4.16 shows that the segmentation method encounters difficulties in extracting the spinal cord at lower levels of vertebrae, due to the proximity of these organs in the image. Using a surface evolution-based segmentation method, such as geodesic active contour, the evolved surface passes over the vertebrae border.

We propose an intensity integration approach to solve this organ concurrence problem in a specific area, by applying a contrast-based selection to the surface of the organ in order to drive the curve evolution bi-directionally according to that contrast. Figure 4.17 illustrates the idea of contrast-based selection: suppose that the gray box in the middle is the spinal cord, the two black boxes represent the vertebrae and the red contour is the evolved curve. When the contour is placed in the spinal cord then g and φ have different signs and the contour should be evolved towards the spinal cord border. But, when the contour placed in the vertebrae then g andφ have the same sign and the contour should be evolved inversely.

Such an approach can be integrated directly into the geodesic active contour’s evolution as:

∂ φ	= g · div	φ		| φ | + sign( g φ )( g φ ) + ν g φ .
∂ t		| φ |

84	A. Alfiansyah

Fig. 4.17 Selective contrast

Fig. 4.18 User interface places the spheres in the spinal cord area (a) and the initialization begins (b and c)

We also enhanced the interactivity of the method, such that the user is allowed to initialize the method using various spheres in the spinal cord. These spheres can be provided interactively by means of a user interface in order to browse through axial slices and then locate the center of the sphere in that slice. It is not necessary to place the spheres in the middle of the spinal cord, but they should be situated entirely inside the spinal cord region in the MRI image.

The curve evolution process of the proposed deformable model for spinal cord segmentation purposes, deviating from the initial curve in Fig. 4.18, prior to reaching the convergence, is visualized in Fig. 4.19.

Applying this type of geometric deformable model, we find that the spinal cord can be obtained with better quality in a shorter computation time.