Automatic 3D Segmentation of Liver Tissue from CT Datasets Alun Evans*, Tryphon Lambrou, Alf Linney and Andrew Todd-Pokropek Department of Medical Physics and Bioengineering, University College London, WC1E 6BT Abstract. Manual segmentation of liver tissue from computerised tomography (CT) datasets can provide useful information to clinicians, such as an estimation of the volume of the liver and the quantification of abnormalities. However, manual segmentation is a slow, laborious process, and an automatic segmentation method has potential to assist in both the diagnosis of disease and in treatment planning. This paper presents initial results from work that extends on previous 2D segmentation methods by implenting full 3D liver segmentation, using a selfreparameterising active contour model. 3D liver segmentation has the advantage over 2D techiques, as the whole liver dataset is analysed at once, rather than as a series of individual slices. Initial results are presented showing volumetric analysis of four liver datasets, assembled from over 500 CT image slices. Further work on improving the segmentation technique, and methods to validate the results, are then discussed in detail.
1 Introduction As part of the diagnosis of liver disease, a Computerised Tomography (CT) scan is taken of the patient, which the clinician then uses to assist in determining the presence and extent of the disease. Frequently the clinician is required to hand segment the liver tissue, in order to obtain further information such as liver volume, or to quantify the extent of diseased tissue. As hand-segmentation is slow and time-consuming, an automatic segmentation tool for the liver could greatly reduce the workload for the clinician. The automatic detection of the liver from CT scans is considered one of the harder segmentation challenges in medical image processing. The difficulties arise due to large variations of liver geometry between patients, the limited contrast between the liver and the surrounding organs, and image noise [1]. All previous efforts at liver segmentation have been based upon 2D segmentation in each CT image slice. Bae et al. [2] used simple thresholding and logic functions to obtain the outline of the liver before smoothing the boundary using B-splines. Gao et al. [1] extended this work by using mathematical morphology on the thresholded image to separate the liver from other organs, before refining the obtained contour with a Fourier-based deformable contour model. Qatarneh et al. [3] introduced active contour models (or snakes) as a stand-alone liver segmentation tool, as part of their work to construct a radiation therapy planning atlas. The main problem encountered in these works is that low-level segmentation techniques are not robust enough to consistantly provide an accurate starting point for any higher level contour refinement. Our previous work on segmenting the liver in 2D [4] solves this problem by inflating an active contour model from a single point inside the liver. As the contour expands, it is reparameterised according to a grid overlaying the image, whereby a new control point is created at the intersection of the contour and the lines of the grid. The segmentation is improved by estimating the local curvature of the contour at each control point, and reparameterising the contour to a smaller resolution grid at areas of higher curvature. This method attempts to facilitate the contour’s movement into sharp corners within the liver, and through narrow contrictions between the lobes of the liver that are present in certain slices. The segmentation results are very promising, though occasionally errors in segmentation were caused in individual slices due to the presence of noise in those slices (which is not present in slices preceeding it or following it), or the structure of the liver’s vascular tree. One significant drawback to all these methods is that they each involve segmentation in 2D only. Each instance of any technique can only respond to information present in one image slice - data on preceeding and following slices are not considered. In this paper, we present preliminary results from an active surface technique that segments the liver in true 3D. While 3D active surface models and 3D level sets have been used for other purposes [5], we are not aware of other published results regarding 3D segmentation of the liver. Our active surface differs from many others in that, in an analogy to our 2D technique, it expands from a single point and reparameterises at certain iterations to enable correct segmentation. Volumetric results are presented from four separate datasets, comprised of over 500 slices. The implications of these results are discussed along with plans for future work, and other techniques that could be used to validate the data.
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Author' s email:
[email protected]
2 Methodology Our 2D segmentation technique is conceptually extended into 3D; instead of an active contour inflating to segment liver tissue in individual slices, the set of image slices is amalgamated into a 3D dataset and an active surface is inflated from a point within the liver tissue. The surface is described as a mesh consisting of both a set V = {v1, v2, v3…vm-1} of vertices, and a set F = {f1, f2, f3…fn-1} of faces, where fn = {va , vb , vc}. The surface moves iteratively according to a set of movement equations derived from the energy minimising equations developed by Kass et al.[6]. Each vertex moves according to the sum of energies that can be expressed as:
E move = αEelastic + β Ecurv + γE Normal
(1)
where , and are constants that allow the forces to be balanced. If Emove is greater than an external energy Eext, then a vertex will move along the direction vector predicted during the calculation of Emove. Eelastic and Ecurv attempt to minimise the distance between each vertex and minimise the local curvature of the surface respectively, and are both calculated using the location of the vertices surrounding the control vertex. Let Sj,d = {Sj,d,m}, m = 1, …, M, be the set of M vertices on a distance d steps from a control vertex vj (e.g. if d = 1, S is the set of M vertices directly adjacent to the control vertex; if d = 2, S is the set of M vertices two places away from the control vertex). Let cj,d be the average location of the set of vertices at distance d:
Pj , d , m
c j ,d = m
Pj , d
(2)
where j represents the central vertex v in the data structure, Pj,d,m is coordinates of vertex m in Sj,d, and |Pj,d| is the total number of vertices in S; then the elasticity and curvature energies at the point vj can be expressed as:
Eelast (v j ) = c j ,1 − v j
(3)
Ecurv (v j ) = 4c j ,1 − c j , 2 − 3v j
(4)
Eext is calculated using a Kirsch filter applied in 3D to each voxel in the dataset. The Kirsch filter is an edge detector that utilises several convolutions to approximate the gradient of voxel intensity along multiple axes through a central voxel, and outputs the maximal gradient value. Further external influence is used to control the movement of the surface in the form of direct use of the voxel intensity values at each vertex location. If the voxel intensity value is outside certain threshold values, the normal force is reversed and the surface begins to deflate.This property is useful if Eext in an area of the liver boundary is weak and the surface ‘leaks’ into tissue other than the liver. As the surface inflates the average distance between each vertex increases, until the distance results in Eelastic and Ecurv energies that are greater than or equal to Enormal, at which point the expansion of the surface is halted. In addition, the increased spacing of the vertices greatly reduces the resolution of the surface, which affects the accuracy of the segmentation. As the final size of the segmented liver is not known, creating a surface with an initial fixed set of vertices is impractical; thus to ensure continual movement of the surface and accurate representation of the segmented liver, the surface needs to be regularly reparameterised. The reparameterisation scheme developed is very different to that implemented in 2D, as calculating the intersection lines between the faces of the surface and planes of a 3D grid, then reconstructing the surface from those lines, would be needlessly slow. Instead, the surface is reparameterised based on the size, measured in voxel area, of the faces of F. If the area of a face fi is greater than a certain value (AK) a new vertex is inserted into the mesh at the coordinates of the centre of gravity of fi. Three new faces are generated using the vertices of fi and the new vertex; while fi is deleted.
To ensure mesh quality, a 3D surface version of Lawson’s edge flipping algorithm is used, in a similar manner to that employed by Chew[7]. The algorithm ensures that no new vertices are located within the smallest circumsphere that can be created from two neighbouring vertices. The results of applying the reparameterisation algorithm to a simple shape are shown in Figure 1.
Figure 1. Three images demonstrating reparameterisation of a surface. The surface at left is the original, unreparameterised surface; the surface at center is reparameterised so the minimum area for all faces (AK) is 500 voxel units; and the surface at right is reparameterised so that AK = 100 voxel units. As the surface expands, the liver' s complex topology causes it to crease and fold, which results in the selfintersection of the surface. A collision detection system based on Möller' s intersection algorithm [8] is employed to detect such collisions. To avoid O(N2) face-pair tests, an octree is used to divide the surface space and only carry out an intersection test for those faces that are in close proximity to each other. Once a collision is detected, the vertices of colliding faces are locked; this prevents further movement for those vertices, but allows their locations to be used in determining the movement of other vertices.
Results Four complete liver datasets, with an average of 125 images per dataset, were used to test the active surface. At present the only validation method used is to measure the volume of the segmented structure and compare it with the volume of manually segmented results from the same dataset, which are treated as the gold standard. Future work on validation is discussed below. Table 1 shows the results of the segmentation for each dataset. Each automatic segmentation volume is in the region of 5% less than the equivalent manual segmentation volume, with the exception of dataset three, which is ~6.5% above the manual segmentation result. Figure 2 shows a wireframe mesh diagramatic example of the automatic segmentation.
Dataset # 1 2 3 4
Slices in Dataset 180 149 122 50
Manual segmentation
Automatic segmentation
Percentage
3269385 3560413 1962612 1416370
3157572 3407085 2090305 1357732
96.58% 95.69% 106.51% 95.86%
Table 1. Volume, in voxels, of manually segmented liver regions compared to automatically segmented liver regions. The final column expresses the automatic result as a percentage of the manual result.
Figure 2. A wireframe mesh showing an example of the result of the automatic segmentation.
Discussion and Future Work The results show that, for three datasets, the automatic segmentation had ~5% lower volume than the manual segmentation. One likely reason for this is that in these three datasets, a contrast agent was used during the scan, which has the effect of the vascular structure being displayed as bright white voxels within the dataset. As the active surface expands, it wraps around the liver' s vascular structure, thus excluding it from the segmented volume of the liver. Visual analysis of the manual segmentation shows that, if the hepatic portal vein is wholly surrounded by liver tissue in an image slice, the operator includes it within the manual segmentation of that liver slice. The inclusion of the portal vein in the manual segmentation, and its exclusion by the automatic segmentation, could account for the differences in segmented volumes. In dataset three, no contrast was injected into the bloodstream during the scan, as a result the vascular structure appears at a similar intensity to the liver. Thus, in this situation, the portal vein and vascular structure were included in the automatic segmentation. Visual analysis of the automatic segmentation result showed that the lack of contrast allowed the surface to ' leak'outside the boundary of the liver and along the portal vein. Furthermore the lack of contrast between heart tissue and liver tissue allowed the surface again to leak and cross the boundary between the liver and the heart. From this result it can be concluded that, to facilitate accurate segmentation, scans taken while the patient is injected with contrast agent are preferable. The hypothesis for the differences between segmented volumes highlights a key problem when dealing with any segmentation results (especially regarding 3D segmentation), that of validation. To improve upon the work presented in this paper, several different techniques are in development in an attempt to obtain a more accurate estimation of the success of the automatic segmentation. Firstly, to obtain significant results a much higher number of datasets must be used, which should be manually segmented by two separate operators. Secondly, more tests for the accuracy of segmentation must be used, such as volumetric overlap, probabilistic distances between segmentations, and measurements of surface distance[9]. There are also improvements planned for the segmentation technique itself. The immediate improvement is to fully implement a surface merging algorithm at locations where the surface selfintersects. A novel surface merging algorithm is currently development and it is expected that it will enable the active surface model to provide more accurate results in a shorter time period. It is anticipated that, once the technique is refined, it could be applied to the segmentation of other abdominal organs with complex topologies, such as the aorta. In addition, a comparison with other 3D segmentation techniques, such as level set methods, could be studied. In conclusion, this paper presents initial results of true 3D segmentation of the liver. These results show that the algorithm has great potential, and that further development and validation work should be carried out. It is hoped that eventually the segmentation methods can be extended to analyse abnormal livers, and assist in the diagnosis and quantification of disease such as cirrhosis and cancer.
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