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Adaptive Mesh Expansion Model (AMEM) for liver segmentation from CT image.

Wang X, Yang J, Ai D, Zheng Y, Tang S, Wang Y - PLoS ONE (2015)

Bottom Line: The triangular facet of the DSM is adaptively decomposed into smaller triangular components, which can significantly improve the segmentation accuracy of the irregularly sharp corners of the liver.Experiments demonstrate that the proposed AMEM algorithm is effective and robust and thus outperforms six other up-to-date algorithms.Moreover, AMEM can achieve a mean overlap error of 6.8% and a mean volume difference of 2.7%, whereas the average symmetric surface distance and the root mean square symmetric surface distance can reach 1.3 mm and 2.7 mm, respectively.

View Article: PubMed Central - PubMed

Affiliation: Beijing Engineering Research Center of Mixed Reality and Advanced Display, School of Optics and Electronics, Beijing Institute of Technology, Beijing 100081, China.

ABSTRACT
This study proposes a novel adaptive mesh expansion model (AMEM) for liver segmentation from computed tomography images. The virtual deformable simplex model (DSM) is introduced to represent the mesh, in which the motion of each vertex can be easily manipulated. The balloon, edge, and gradient forces are combined with the binary image to construct the external force of the deformable model, which can rapidly drive the DSM to approach the target liver boundaries. Moreover, tangential and normal forces are combined with the gradient image to control the internal force, such that the DSM degree of smoothness can be precisely controlled. The triangular facet of the DSM is adaptively decomposed into smaller triangular components, which can significantly improve the segmentation accuracy of the irregularly sharp corners of the liver. The proposed method is evaluated on the basis of different criteria applied to 10 clinical data sets. Experiments demonstrate that the proposed AMEM algorithm is effective and robust and thus outperforms six other up-to-date algorithms. Moreover, AMEM can achieve a mean overlap error of 6.8% and a mean volume difference of 2.7%, whereas the average symmetric surface distance and the root mean square symmetric surface distance can reach 1.3 mm and 2.7 mm, respectively.

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Adaptive triangular facet decomposition.
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pone.0118064.g005: Adaptive triangular facet decomposition.

Mentions: Adaptive Mesh Decomposition. During mesh expansion under the constraints of external and internal forces, the facet size of the mesh gradually increases for the model to reach the boundary of the liver. However, if the facet size is extremely large, the mesh cannot deform to several long and narrow regions. To segment the liver accurately, the adaptive mesh decomposition methods [30–32] reported by several studies are adapted. Most current methods drive the deformation of the triangular mesh by controlling the simplex angle θi. Although such methods can effectively navigate the deforming degree of the mesh, the size of the triangular facet may become increasingly large with mesh expansion in space. Hence, the mesh can hardly deform into some long and narrow regions. The shape of the liver is irregular and has some sharp corners. Thus, previous methods cannot achieve high accuracy. In this study, a novel mesh decomposition method was proposed for the accurate segmentation of the long and narrow boundaries of the liver. The new vertex is adaptively inserted into the gravity center of the facet with size larger than a predefined threshold, which guarantees that the long and large facets will decomposed into smaller facets. At each step of the deformation, the triangular mesh is calculated from the simplex mesh, and then, the size of the enclosing area of the triangular facet is determined. If the area is larger than a predefined threshold, a vertex will be inserted at the center of gravity. At this point, the triangles will be broken into three smaller triangles, as shown in Fig. 5. The criterion is then iteratively applied on all the triangular meshes. The implementing flow of the algorithm can be found in Table 1. The proposed method certifies that a large and smoothed boundary comprises large facets, whereas long and narrow boundaries comprise small facets. This method is effectively balanced between calculation efficiency and accuracy.


Adaptive Mesh Expansion Model (AMEM) for liver segmentation from CT image.

Wang X, Yang J, Ai D, Zheng Y, Tang S, Wang Y - PLoS ONE (2015)

Adaptive triangular facet decomposition.
© Copyright Policy
Related In: Results  -  Collection

License
Show All Figures
getmorefigures.php?uid=PMC4358832&req=5

pone.0118064.g005: Adaptive triangular facet decomposition.
Mentions: Adaptive Mesh Decomposition. During mesh expansion under the constraints of external and internal forces, the facet size of the mesh gradually increases for the model to reach the boundary of the liver. However, if the facet size is extremely large, the mesh cannot deform to several long and narrow regions. To segment the liver accurately, the adaptive mesh decomposition methods [30–32] reported by several studies are adapted. Most current methods drive the deformation of the triangular mesh by controlling the simplex angle θi. Although such methods can effectively navigate the deforming degree of the mesh, the size of the triangular facet may become increasingly large with mesh expansion in space. Hence, the mesh can hardly deform into some long and narrow regions. The shape of the liver is irregular and has some sharp corners. Thus, previous methods cannot achieve high accuracy. In this study, a novel mesh decomposition method was proposed for the accurate segmentation of the long and narrow boundaries of the liver. The new vertex is adaptively inserted into the gravity center of the facet with size larger than a predefined threshold, which guarantees that the long and large facets will decomposed into smaller facets. At each step of the deformation, the triangular mesh is calculated from the simplex mesh, and then, the size of the enclosing area of the triangular facet is determined. If the area is larger than a predefined threshold, a vertex will be inserted at the center of gravity. At this point, the triangles will be broken into three smaller triangles, as shown in Fig. 5. The criterion is then iteratively applied on all the triangular meshes. The implementing flow of the algorithm can be found in Table 1. The proposed method certifies that a large and smoothed boundary comprises large facets, whereas long and narrow boundaries comprise small facets. This method is effectively balanced between calculation efficiency and accuracy.

Bottom Line: The triangular facet of the DSM is adaptively decomposed into smaller triangular components, which can significantly improve the segmentation accuracy of the irregularly sharp corners of the liver.Experiments demonstrate that the proposed AMEM algorithm is effective and robust and thus outperforms six other up-to-date algorithms.Moreover, AMEM can achieve a mean overlap error of 6.8% and a mean volume difference of 2.7%, whereas the average symmetric surface distance and the root mean square symmetric surface distance can reach 1.3 mm and 2.7 mm, respectively.

View Article: PubMed Central - PubMed

Affiliation: Beijing Engineering Research Center of Mixed Reality and Advanced Display, School of Optics and Electronics, Beijing Institute of Technology, Beijing 100081, China.

ABSTRACT
This study proposes a novel adaptive mesh expansion model (AMEM) for liver segmentation from computed tomography images. The virtual deformable simplex model (DSM) is introduced to represent the mesh, in which the motion of each vertex can be easily manipulated. The balloon, edge, and gradient forces are combined with the binary image to construct the external force of the deformable model, which can rapidly drive the DSM to approach the target liver boundaries. Moreover, tangential and normal forces are combined with the gradient image to control the internal force, such that the DSM degree of smoothness can be precisely controlled. The triangular facet of the DSM is adaptively decomposed into smaller triangular components, which can significantly improve the segmentation accuracy of the irregularly sharp corners of the liver. The proposed method is evaluated on the basis of different criteria applied to 10 clinical data sets. Experiments demonstrate that the proposed AMEM algorithm is effective and robust and thus outperforms six other up-to-date algorithms. Moreover, AMEM can achieve a mean overlap error of 6.8% and a mean volume difference of 2.7%, whereas the average symmetric surface distance and the root mean square symmetric surface distance can reach 1.3 mm and 2.7 mm, respectively.

Show MeSH