Radial Thickness Calculation and Visualization for Volumetric Layers

Defeng WangThe Chinese University of Hong Kong

Overview

Motivation Algorithm User’s Guide Results Conclusion

Motivation (1)

Volumetric layers are often encountered in medical image analysis E.g., skull vault; myocardium of the left

ventricle, etc. Automatic landmarking method for

structures with coupled surfaces [1] Consider thickness in landmarking

volumetric layers Higher quality compared with landmark

optimization on two surfaces separately.[1] L. Shi, D. Wang, et al. Landmark Correspondence Optimization for Coupled Surfaces, MICCAI 2007, Brisbane, Australia

Motivation (2)

Definitions for layer thickness Closest thickness (Tclose) Normal thickness (Tnormal)

We propose to use radial thickness (Tradial) Distance between each pair of corresponding

points on two surfaces with the same polar coordinates

In comparison Tclose and Tnormal depend on the starting surface Tradial is unique and landmarks are grouped in pairs

Motivation (3)

Thickness definitions illustration

Figure 1: Different thickness definitions illustrated on a part of one axial plane of the skull boundary: (a) the coupled surfaces; (b) the closest thickness measure; (c) the normal thickness measure; (d) the radial thickness

Algorithm description (1)

Two coupled triangle meshes are treated as A master mesh A supplementary mesh

Each ray is generated from the center to each vertex in the master mesh

Radial thickness calculation is to determine the distance between Each vertex on the master mesh The intersection point of the compatible ray

with the supplementary surface

Algorithm description (2)

Specifically, the radial thickness calculation is reduced to Checking if there is any intersection of a

ray and a triangle in the supplementary mesh

Determine the coordinates if the intersection exists

We adopt the fast and minimum-storage algorithm of ray/triangle intersection examining [2]

[2] T. Moller and B. Trumbore. Fast, minimum storage ray/triangle intersection. Journal of Graphics Tools, 2(1):21–28, 1997.

Algorithm description (3)

A ray emitted from center C0 to one vertex V in the master mesh

A point T(u,v), on a triangle defined by 3 verticesV0, V1, V2,

(u,v) are the barycentric coordinates The intersection is equivalent to

Algorithm description (4)

By using the Cramer’s rule and defining A B C

The final speeded-up computations are in the following form

User’s guide (1)

The vtkRadialThicknessCalculate class take VTK meshes as inputs One master mesh One supplementary mesh

Output can be radial thickness values, or the normalized ones in [0,1]

Ray directions can be Calculated from the master mesh, Specified in a text file containing each

direction as 3 real number in a row

User’s guide (2)

Include the header file

Declare an instance

Set master and supplementary meshes

User’s guide (3) Specify the file name to save radial

thickness values Two output files, one is “thicknessFile.txt”

containing radial thickness values The other is “thicknessFile_normalize.txt” saving

the normalized ones Start calculation

The directions can also be set with a direction file

Results (1) In order to reproduce the results, require

packages CMake 2.4.6 Visualization Toolkit VTK 5.0.3 KWMeshvisu [3], is adopted to visualize the

calculated radial distances on the master mesh Neurolib [4], the VTK2Meta tool in the

MetaMeshTools project from the Neurolib package is adopted to convert the mesh data from VTK to the Meta format, which can be loaded in KWMeshvisu for visualization[3] Ipek Oguz, et al. KWMeshvisu: A mesh visualization tool

for shape analysis. In IJ - 2006 MICCAI Open Science Workshop, Kopenhagen, 2006.[4] http://www.ia.unc.edu/dev/

Results (2)

Results on human skull vaults Skull vault is defined as the upper part of

the skull Skull vault is an open coupled-surface

structure The skull volume was segmented from the

head CT data, Acquired at the Prince of Wales Hospital, Hong

Kong Field of view of the CT data is 512 * 512 Voxel size is 0.49mm * 0.49mm * 0.63mm

Results (3)

Figure 2: Coupled surfaces of the skull vault: (a) the back view; (b) the top view.

Results (4)

Figure 3: The color-coded thickness values plotted on the surface of the inner skull: (a) the back view; (b) the top view; (c) the color bar used to code the normalized thickness values.

Inner surface is taken as the master surface

Results (5)

Figure 4: The color-coded thickness values plotted on the surface of the outer skull: (a) the back view; (b) the top view; (c) the color bar used to code the normalized thickness values.

Outer surface is taken as the master surface

Results (6)

Note that, if there is no intersection between the ray and the supplementary surface, we artificially set the thickness value 0

This explains Figure 3 shows a ribbon of zero values in the inner surface of the skull vault

From the results, the radial thickness values represent the layer thickness reasonably

No matter whether the master surface is inner surface, or outer surface, the resultant thickness value will not be altered, except marginal regions

Conclusion

We implement a new thickness definition for volume layer structures, radial thickness

This implementation is encapsulated in the vtkRadialThicknesscalculate class

This class contains a realization of the fast ray/triangle intersection algorithm

Experimental results demonstrate that radial thickness is a suitable thickness measurement for the structures with a near-spherical morphology.

Acknowledgment

The work described in this paper was supported by a grant from the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CUHK4453/06M) and CUHK Shun Hing Institute of Advanced Engineering.