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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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Force determination on the circumscribed sphere of the defined triangular mesh.(a) shows the construction of internal force for one triangle facet on the deformable model; (b) shows the cross-section between plane  and the sphere Si.
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pone.0118064.g004: Force determination on the circumscribed sphere of the defined triangular mesh.(a) shows the construction of internal force for one triangle facet on the deformable model; (b) shows the cross-section between plane and the sphere Si.

Mentions: Internal Forces of AMEM. The internal force of the proposed AMEM is constructed by combining the tangential and normal forces of the triangle facet on the deformable model, as shown in Fig. 4(A). Suppose that Pi1, Pi2 and Pi3 are the three closest neighboring points of vertex Pi on the model surface. Let represent the circle composed of points Pi1, Pi2, and Pi3. Moreover, let represent the normal vector of and Si represent the circumscribed sphere of a tetrahedron. Let Oi represent the center of the sphere and Si. Ci represent the center of the circular section between plane and sphere Si. Furthermore, let represent the projection of Pi on the plane, whereas Fnormal and Ftan gent represent the normal and tangential forces at point Pi, respectively. Fig. 4(B) shows the cross-section between plane and the sphere Si. Let θi represent the simplex angle and Ri represent the center of the sphere Si. Suppose that the internal force of the model is composed of normal and tangential forces, such that we haveFinternal=αtangentFtangent+αnormalFnormal(3)


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)

Force determination on the circumscribed sphere of the defined triangular mesh.(a) shows the construction of internal force for one triangle facet on the deformable model; (b) shows the cross-section between plane  and the sphere Si.
© Copyright Policy
Related In: Results  -  Collection

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

pone.0118064.g004: Force determination on the circumscribed sphere of the defined triangular mesh.(a) shows the construction of internal force for one triangle facet on the deformable model; (b) shows the cross-section between plane and the sphere Si.
Mentions: Internal Forces of AMEM. The internal force of the proposed AMEM is constructed by combining the tangential and normal forces of the triangle facet on the deformable model, as shown in Fig. 4(A). Suppose that Pi1, Pi2 and Pi3 are the three closest neighboring points of vertex Pi on the model surface. Let represent the circle composed of points Pi1, Pi2, and Pi3. Moreover, let represent the normal vector of and Si represent the circumscribed sphere of a tetrahedron. Let Oi represent the center of the sphere and Si. Ci represent the center of the circular section between plane and sphere Si. Furthermore, let represent the projection of Pi on the plane, whereas Fnormal and Ftan gent represent the normal and tangential forces at point Pi, respectively. Fig. 4(B) shows the cross-section between plane and the sphere Si. Let θi represent the simplex angle and Ri represent the center of the sphere Si. Suppose that the internal force of the model is composed of normal and tangential forces, such that we haveFinternal=αtangentFtangent+αnormalFnormal(3)

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