HOME HELP FEEDBACK SUBSCRIPTIONS ARCHIVE SEARCH TABLE OF CONTENTS		QUICK SEARCH:   [advanced] Author: Keyword(s): Year:  Vol:  Page:

This Article Abstract Full Text Submit a response Services Email this article to a friend Alert me to new issues of the journal

© RSNA, 2008

Appendix E1

Methodologic Details

The method consists of five steps: 1) definition of regions of interest, 2) masking of nonarterial structures, 3) automatic seed-point selection in the ICAs and the basilar artery (BA), 4) segmentation of the ICAs followed by a rough segmentation of the intracranial vasculature, 5) a final and accurate segmentation of the complete vasculature.

Regions of Interest Definitions

Some steps of the method are applied only to specific regions in the data set. These regions of interests are indicated by labels in Figure E1. The most important regions are defined, and the method to automatically determine them is described.

E1a.	E1b.

Figure E1. (a) Sagittal view of a volume-rendered cerebral CT angiography data set. (b) Coronal view of an isosurface-rendered ICA segmentation. The arrows in a indicate the superior sagittal sinus, a large vein that lies just below the skull midline. The arrow in b points to the middle cerebral artery.

z0	The first section in the data set at the caudal side of the head.
zmax	This is based on the classical Shannon entropy measure (1):                 (Eq E1) With pi the probability of occurrence of an intensity value in the image, an entropy profile is determined as a function of the z-axis. The section with maximum entropy zmax is used as the anchor point for the definition of other regions, as it is consistently located in the skull base (2).
zsb	A region selected so that the skull base (sb) and a small part above the skull base are included. This is achieved by adding an empirically defined offset to zmax to obtain zsb. The region between z0 and zsb is called the lower region.
zseed	A cross section selected by subtracting a fixed offset from zmax. This value is empirically defined. The section will be used to select seed points in the carotid and basilar arteries.
zica	In the lower region, each ICA is first segmented separately. The segmentation of an ICA generally extends to the upper section, zsb. Normally, the ICA branches into the middle cerebral artery (MCA) and anterior cerebral artery. For some segmentations, this transition occurs before zsb has been reached; therefore, an additional label zica is defined at the minimum of both ICA segmentations (Fig E1b). The label zica is used for the initialization of rough intracranial vessel segmentation by region growing. This label is required to achieve a complete segmentation of the vasculature connected to both ICAs.
yvein	To suppress the superior sagittal sinus (Fig E1a), which runs midsagittally below the skull, and the left and right transverse sinuses (Fig E2, arrows 3 and 5), which are large veins close to the skull, an offset yvein (25 mm) is empirically defined to select a region containing these veins.

   
   E2.

Figure E2. Axial section from CT angiography data and masks that have been obtained by means of segmentations based on image intensity information combined with morphologic operations. The final mask is obtained by merging all four masks. Regions 1 and 2 are part of the sphenoid sinus, an air-filled cavity near the ICAs. Arrows 3 and 5 denote the transverse sinus (left and right portions), and arrow 4 indicates the superior sagittal sinus. The arrows in the masked image point to parts of the skull base that are not covered.

Masking

The next step is to suppress all nonarterial structures as much as possible without affecting the arterial vasculature. The nonarterial structures include background, air, bone, and veins, and are segmented on the basis of intensity information combined with morphologic operations. All morphologic operations are performed by using a spherical structure element. We use the notation , where n represents the number of iterations and k the kernel size. The values mentioned in this section have been obtained in pilot experiments, and most of them are not critical.

Background	Denotes the area outside the scanned head and inside the field of view of the scanner. The image is thresholded at −1000 HU, followed by an erosion to remove all areas inside the head containing air. Seeded region growing (3) is then applied with an upper bound of −950 HU, followed by an opening for cleaning and a dilation . An opening is defined as an erosion followed by a dilation .
Air	Denotes the air-filled cavities inside the scanned head, such as the sphenoid sinus and mastoid air cells (Fig E2). A threshold T ≤ 0 HU is applied followed by an opening and a dilation .
Bone	The image is thresholded at T ≥ T1 = 500 HU, and the largest connected component is selected. Selecting the largest connected component ensures that only the outer skull is included and clips, stents, and calcifications are discarded. Seeded region growing with T ≥ 480 HU is then applied followed by a dilation .
Veins	Denote the large veins close to the skull (Figure E1a). These veins are suppressed by first selecting the skull with use of thresholding, largest-component selection, and region growing. The skull is then dilated to suppress nearby veins. Since the skull is sometimes partially outside the field of view of the reconstructed image, both bone and background are selected as a mask dilated with .

The final mask is obtained by merging all four masks with use of the Boolean logical OR operator. An example of an axial section with its corresponding mask is shown in Figure E2.

Seed Selection

The segmentation process is initialized by placing seed points in the feeding arteries of the circle of Willis (ie, the ICAs and the BA). This is achieved automatically as follows. In the masked data set, the image intensity gradient is calculated and thresholded; high values correspond to partially masked bone structures, noise, and the vessel boundaries of the ICA. The Hough transform (4) is then applied in the cross section z_seed to search for circular shapes within a fixed range of diameters. The center points of these circles define the seed points in the ICAs and BA.

Rough Segmentation

In this step, a rough segmentation of the arterial vasculature is obtained for initialization of the final segmentation. The ICAs are segmented by a topology-constrained level set, and the remaining vessels are segmented by region growing.

Consider the standard partial differential equation for level set evolution (5): Φ_t + F |∇Φ| = 0, with Φ the level set function (Φ < 0) denotes the inside of the surface) and F the image-based speed function steering the level set. In our implementation, the level set is initialized by the center points of the ICAs found in the previous step, and evolves with a gradient-based speed function:

                    (Eq E2)

where σ denotes the gradient scale of the Gaussian and c a tuning parameter that determines the weighting of this gradient. The speed function is set at −1 for the main mask. To increase the robustness of the method, the level set is constrained so that it follows the shape of a tubular segment (6). When the level set reaches the first section, z₀, the current segmentation is used to construct an additional mask to prevent leaking. Two masks are used: First, a mask is created to freeze the vessel segmentation between z₀ and z_seed; second, the current vessel mean intensity is determined to define a vessel intensity window. That is,

                    (Eq E3)

where ρ₁ is a tuning factor. The speed function is set at −1 for M in Equation 3. The process of segmentation and reinitialization is stopped if either z_sb has been reached (which is generally the case) or if a maximum number of reinitializations has occurred. This number is set at an arbitrarily large value. An example of ICA segmentation is shown in Figure E1b.

After a rough segmentation of the ICAs has been obtained, the remaining vessels are segmented by seeded region growing. Seeded region growing is initialized by the current ICA segmentations above z_ica (Fig E1b) and the BA seed point. The vessel mean intensity of the ICA segmentation is used to determine two successive and decreasing intensity lower bounds for the region-growing process. First, region growing is applied to the complete image. Then a second region growing is applied to the image above z_sb to capture the small intracranial vessels. The main mask does not completely cover the skull base and therefore region growing would leak into the structures close to the ICAs if no additional masking were applied. We use the current ICA segmentation and dilation progressively below z_ica to cover these structures.

The complete rough segmentation is obtained by merging the region-growing results with ICA segmentation by the OR operator.

Final Segmentation

In the final step, a level set is evolved for accurate boundary determination. The rough segmentation of the previous step is used for initialization, and the level set evolves by the following equation:

                   (E4)

where F_I is the intensity-based speed function, κ_min is the minimal principal curvature component of the 3D curvature measure to achieve a preferred smoothing along the vessel axis (7), and ε is the weighting of κ_min.

The speed function F_I is defined on the basis of vessel and background statistics, assuming Gaussian distributions for both. In previous work (8), it was shown that this model provides accurate diameter measurements in phantom and patient data. The histogram of the original image, [−500,500] HU, determines the background statistics (μ_b, σ_b); the current rough segmentation determines the vessel statistics (μ_v, σ_v). The vessel mean intensity μ_v is multiplied by a factor ρ to control the vessel diameter. F_I is then defined as

                   (E5)

where g_vb are Gaussian functions and g_v + g_b is a normalization factor. F_I is zero where the Gaussian curves intersect and corresponds to the point of minimal classification error. To prevent leaking, the speed function is set at −1 for the main mask and for the surrounding volume of the rough segmentation. Parameters ρ and ε are used for fine-tuning the boundary positions.

Parameter Optimization

Region-of-interest selection required optimization of the lower bound of intensity (290 HU) in the histogram for entropy calculation and of the offset values added to z_max for z_sb (25 mm) and for z_seed (−23 mm for ICA and −8.5 mm for BA). Seed selection required optimization of the radii of the expected circles (7–12 mm for ICA and 0.5–7.5 mm for BA). The rough segmentation required optimization of the gradient tuning factor (c = 6.5), the number of level set iterations (N = 180) and the ρ tuning factors (ρ₁ = 0.45, ρ₂ = 0.5, ρ₃ = 0.4). In practice, most of the time was spent optimizing the c and N of the shape-constrained level set segmentation, as the sensitivity of the segmentation results compared to the other parameters was not large.

Diameter optimization required optimization of ρ and curvature ε of the level-set evolution of the final segmentation. A minimum diameter was found for ρ = 0.97, which was used as a fixed value in the optimization of ε, for which a minimum diameter was found at ε = 0.30.

Rotating View

Movie. A rotating view of a 3D surface rendering of cerebral arteries from one of the data sets obtained by our CT angiography segmentation method.

References

1. Shannon CE. A mathematical theory of communication. Bell System Technical Journal 1948;27:379-423,623-656.

2. Suryanarayanan S, Mullick R, Mallya Y, Kamath V, Nagaraj N. Automatic partitioning of head CTA for enabling segmentation. In: Fitzpatrick JM, Sonka M, eds. Proceedings of SPIE: medical imaging 2004—image processing; Vol 5370. Bellingham, Wash: International Society for Optical Engineering, 2004;410-419.

3. Adams R, Bischof L. Seeded region growing. IEEE Transactions on Pattern Analysis and Machine Intelligence 1994;16:641-647.

4. Hough PVC. Methods and means for recognizing complex patterns. U.S. patent 3,069,654, 1962.

5. Sethian JA. Level set methods and fast marching methods. 2nd ed. Cambridge University Press, 1999.

6. Manniesing R, Viergever MA, Niessen WJ. Vessel axis tracking using topology constrained surface evolution. IEEE Transactions on Medical Imaging 2007;26:309-316.

7. Lorigo LM, Faugeras OD, Grimson WEL, et al. CURVES: curve evolution for vessel segmentation. Medical Image Analysis 2001;5:95-206.

8. Manniesing R, Velthuis BK, van Leeuwen MS, van der Schaaf IC, van Laar PJ, Niessen WJ. Level set based cerebral vasculature segmentation and diameter quantification in CT angiography. Medical Image Analysis 2006;10:200-214.

This Article Abstract Full Text Submit a response Services Email this article to a friend Alert me to new issues of the journal