Surface extraction method and apparatus for X-ray CT volume

Abstract

An isosurface mesh M is generated by extracting voxels having a certain CT value from volume data obtained by X-ray CT. A gradient vector g of a CT value is calculated at each vertex p of the isosurface mesh M. A plurality of sample points S are generated in positive and negative directions of the calculated gradient vector g. Gradient norms N of CT values at the respective generated sample points S are calculated. The vertex p of the isosurface mesh is moved and corrected to a sample point Sm having the maximum norm Nm calculated.

Claims

1. A surface extraction method for X-ray Computed Tomography (CT) volume, comprising: extracting voxels having a certain CT value from volume data obtained by X-ray CT to generate an isosurface mesh; and correcting each vertex of the isosurface mesh using gradient information about a CT value at the vertex of the isosurface mesh to remove artifacts from a resultant CT image, wherein the vertex of the isosurface mesh is corrected by calculating a gradient vector of the CT value at the vertex, generating a plurality of sample points in a positive direction and a plurality of sample points in a negative direction of the calculated gradient vector, calculating gradient norms of CT values at the respective generated sample points, and moving the vertex to a sample point having a maximum gradient norm calculated, and wherein the plurality of sample points in the positive direction and the plurality of sample points generated in the negative direction are generated at predetermined intervals.

2. The surface extraction method for X-ray Computed Tomography (CT) volume according to claim 1, wherein the CT value at the vertex is calculated by using following equation according to a Feldkamp method,
f(p)=½∫.sub.0.sup.2πα(θ,p).sup.2S.sup.filtered(θ,p)dθ  (1), where the coefficient α(θ, p) equals to d.sub.sod/(d.sub.sod+d.sub.z), θ is a rotation angle, d.sub.sod is a light-source-to-rotation-center distance, and S.sup.filtered(θ, p) is a filter-corrected projection value (using Shepp-Logan filter).

3. A surface extraction apparatus for X-ray Computed Tomography (CT) volume for performing surface extraction on X-ray CT volume, the surface extraction apparatus for X-ray CT volume comprising: a processor; and a memory that stores a program therein, which when the program is executed by the processor, causes the processor to perform CT operations, including extracting voxels having a certain CT value from volume data obtained by X-ray CT to generate an isosurface mesh, and correcting each vertex of the isosurface mesh by using gradient information about a CT value at the vertex of the isosurface mesh to remove artifacts from a resultant CT image, wherein the correcting each vertex of the isosurface mesh includes calculating a gradient vector of the CT value at the vertex, generating a plurality of sample points in a positive direction and a plurality of sample points in a negative direction of the calculated gradient vector, calculating gradient norms of CT values at the respective generated sample points, and moving the vertex to a sample point having the maximum gradient norm calculated, and wherein the plurality of sample points in the positive direction and the plurality of sample points generated in the negative direction are generated at predetermined intervals.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

(1) The preferred embodiments will be described with reference to the drawings, wherein like elements have been denoted throughout the figures with like reference numerals, and wherein;

(2) FIG. 1 is a sectional view showing an overall configuration of a typical X-ray CT apparatus used for measurement;

(3) FIG. 2 is a perspective view showing an arrangement of essential parts of the same;

(4) FIG. 3 is a diagram outlining CT reconstruction of the same;

(5) FIG. 4 is a flowchart showing a processing procedure according to an embodiment of the present invention;

(6) FIG. 5 is a perspective view for describing an example of a method for analytically calculating a CT value gradient according to the embodiment;

(7) FIG. 6 is a diagram showing an example of a plurality of sample points extracted in the directions of gradient vectors ±g according to the embodiment;

(8) FIG. 7 is a diagram showing how a vertex is moved to a sample point according to the embodiment; and

(9) FIG. 8 is a perspective view showing a step cylinder that is an example of an object to be measured.

DESCRIPTION OF EMBODIMENTS

(10) An embodiment of the present invention will be described in detail below with reference to the drawings. The present invention is not limited by the following description of the embodiment and examples. The components of the embodiment and examples described below include what are easily conceivable by those skilled in the art, what are substantially the same, and what fall within a so-called range of equivalence. The components disclosed in the following embodiment and examples may be combined as appropriate or selectively used as appropriate.

(11) An algorithm according to the present invention handles volume data generated by X-ray CT as an input, and surface-extracted mesh data as an output.

(12) FIG. 4 outlines a processing procedure according to the embodiment of the present invention.

(13) In step 100, an isosurface mesh M is initially generated from the volume data.

(14) Each voxel of the volume data has a CT value. An isosurface mesh can be generated by extracting voxels having a certain CT value. The CT value can be selected by a method of checking a histogram of CT values of the volume data for selection. The histogram typically includes peaks representing respective work materials and air. For example, to extract the external surface of the work (interface between air and the work), an intermediate value (CT values) between the peaks representing air and the material of the external surface of the work in the histogram is selected. An isosurface mesh is generated by using the selected appropriate CT value corresponding to a desired surface shape in the volume data.

(15) In step 110, a vertex p constituting the mesh M is extracted.

(16) In step 120, a gradient vector g at the extracted mesh vertex p is calculated. The gradient vector g can be calculated in the following manner.

(17) Initially, using the Feldkamp method (FDK method) which is one of the commonly used back projection methods, a CT value f(p) at the vertex p(x, y, z) is calculated by the following equation (see FIG. 5):
f(p)=½∫.sub.0.sup.2πα(θ,p).sup.2S.sup.filtered(θ,p)dθ  (1),

(18) where the coefficient α(θ, p) equals to d.sub.sod/(d.sub.sod+d.sub.z),

(19) θ is a rotation angle,

(20) d.sub.sod is a light-source-to-rotation-center distance, and

(21) S.sup.filtered(θ, p) is a filter-corrected projection value (using Shepp-Logan filter).

(22) In FIG. 5, the reference numeral 30 represents a computer that performs the calculation.

(23) Aside from the Shepp-Logan filter, the filter-corrected projection value can be determined by using the Ram-Lak filter or the Kak-Slaney filter.

(24) Next, the gradient vector g(p) of the CT value at the point p(x, y, z) is generated by the following equation:

(25) $\begin{array}{cc}g\left(p\right)\simeq \frac{1}{2}{\int }_0^{2\pi }{\alpha \left(\theta ,p\right)}^3{R_{-\theta }\left(\frac{\theta }{\partial \left(u,v\right)}{S}^{\mathrm{filtered}}\left(\theta ,p\right),0\right)}^{r}d\theta ,& \left(2\right)\end{array}$

(26) where R.sub.−θ is a three-dimensional rotation matrix for angle −θ, and

(27) ∂/∂(u, v) is derivative in the detector coordinate system (calculation of center difference between filter-corrected projection values).

(28) Here, an assumption of α(θ, p)=α(θ) (α is independent of p) can be employed for simplification of calculation.

(29) Points p are treated as continuous values. In calculating projection values, interpolation processing is performed as appropriate.

(30) In step 130, as shown in FIG. 6, a plurality of sample points S are extracted on the gradient vectors ±g passing through the mesh vertex p. The extraction range and extraction intervals may be freely set, for example, with reference to the voxel size. For example, the sampling range (extraction range) can be set to ±4 voxels or so. The sampling intervals (extraction intervals) can be set to around 0.1 to 0.2 times the voxel size.

(31) In step 140, as shown in FIG. 7, gradient norms N at all the extracted sample points S are calculated from the absolute values of the gradient vectors g by the following equation:
N=|g(S)|  (3)

(32) In step 150, a sample point Sm having the maximum value Nm among the gradient norms N at the sample points S is derived.

(33) In step 160, the vertex p is moved to the sample point Sm. The reason is that the sample points S deviate greatly at the interface between the work and air or at the interface between different work materials.

(34) After step 160, the processing proceeds to step 170. In step 170, whether all the vertices p have been corrected is checked.

(35) If all the vertices p have not been corrected, the processing returns to step 110 to correct the next vertex p.

(36) On the other hand, if, in step 170, all the vertices p are determined to have been corrected, the processing ends.

(37) The inventors made a simulation to evaluate measurement values of a step cylinder such as illustrated in FIG. 8, with an outer diameter of 20 mm at the first stage and an outer diameter of 60 mm at the fifth stage. A conventional isosurface mesh method produced particularly large errors at the first and second stages. According to the present invention, the errors at the first and second stages were successfully reduced by half.

(38) The master ball B, or ruby ball, illustrated in FIG. 3 was also evaluated. By the conventional method, a difference between the actual measurement of the diameter of the ball and the diameter obtained by fitting was 8 to 9 μm. According to the method of the present invention, the difference was successfully reduced to 0 to 2 μm. A similar tendency was observed for all the balls.

(39) In the present embodiment, the use of the FDK method facilitates obtaining the derivative of the equation for determining the CT value, whereby gradient information about the CT value can be easily obtained. The method for obtaining the gradient information about the CT value is not limited to the FDK method.

(40) In the foregoing embodiment, the gradient information is gradient norms. However, the gradient information is not limited thereto. The object to be measured is not limited to a work, either.

(41) It should be apparent to those skilled in the art that the above-described exemplary embodiments are merely illustrative which represent the application of the principles of the present invention. Numerous and varied other arrangements can be readily devised by those skilled in the art without departing from the spirit and the scope of the invention.