Surface extraction method and device for X-ray CT volumes

Abstract

Surface extraction method for X-ray CT volumes, comprising: Extracting voxels or grid points with a specific CT value f(p) from volume data obtained by X-ray CT to generate an isosurface mesh or grid (M); and Correcting each vertex (p) of the isosurface grid (M) using gradient information about a CT value f(p) at the vertex (p) of the isosurface grid (M); where the vertex (p) of the isosurface grid (M) is corrected by: • Calculating a gradient vector g(p) of the CT value f(p) at the vertex (p), • Generating a plurality of sampling points (S) in the positive and negative directions of the calculated gradient vector g(p), • Calculating gradient norms (N) of CT values ​​f(p) at the respectively generated sampling points (S) and • Moving the vertex (p) to a sample point (Sm) with a calculated maximum gradient norm (Nm).

Description

Technical area

[0001] The present invention relates to a surface extraction method and apparatus for an X-ray CT volume. More particularly, the present invention relates to a surface extraction method and apparatus for an X-ray CT volume that can perform high-precision surface extraction that is robust to CT value fluctuations. State of the art

[0002] Medical X-ray CT scanners were put into practice in the 1970s. Based on this technology, X-ray CT scanners for industrial products appeared in the early 1980s. Since then, industrial X-ray CT scanners have been used to observe and examine cavities in castings, welding defects in welded parts, and defects in the circuit patterns of electronic circuit components that are difficult to identify from their external appearance. Meanwhile, the widespread use of 3D printers in recent years has increased the demand for observation and inspection of workpieces produced by 3D printers, as well as for 3D dimensional measurements of internal structures and their precision improvement.

[0003] In light of the above technological trends, measuring X-ray CT devices are gaining ground, particularly in Germany (see Japanese Patent Application Laid-Open Nos. JP 2002-71345 A and JP 2004-12407 A). In such measuring X-ray CT devices, an object to be measured is placed in the center of a rotating table, and X-ray irradiation is performed while the object to be measured is rotated.

[0004] Furthermore, US 2019 / 0000564 A1 discloses a system and method for generating medical images. The method uses an algorithm for jointly registering cone beam computed tomography (CBCT) volumes and additional imaging techniques such as optical or RGB-D images.

[0005] Fig. 1 shows a configuration of a typical X-ray CT apparatus 1 used for measurement. An X-ray source 12, an X-ray detector 14, a rotary table 16, and an XYZ movement mechanism unit 18 are housed in a casing 10 for blocking X-rays. The X-ray source 12 is configured to emit X-rays 13 in the form of a cone beam. The X-ray detector 14 is configured to detect the X-rays 13. An object to be measured (for example, a workpiece) W is placed on the rotary table 16. The rotary table 16 is configured to rotate the workpiece W for CT imaging. The XYZ movement mechanism unit 18 is to adjust the position and magnification of the workpiece W projected onto the X-ray detector 14. The X-ray CT apparatus 1 further includes a controller 20 for controlling orControl of such devices, and a control PC 22 configured to give instructions to the controller 20 based on user operations.

[0006] Apart from various device controls, the control PC 22 has a function of displaying a projection image of the workpiece W projected onto the X-ray detector 14 and a function of reconstructing a tomographic image from a plurality of projection images of the workpiece W.

[0007] As in Fig. As shown in Figure 2, the X-rays 13 emitted from the X-ray source 12 are transmitted through the workpiece W on the rotary table 16 and reach the X-ray detector 14. The X-ray detector 14 obtains transmission images (projection images) of the workpiece W in all directions while the workpiece W is rotated. A tomographic image of the workpiece W is generated by reconstructing the projection images using a CT reconstruction algorithm such as backprojection and iterative reconstruction.

[0008] The position of the workpiece W can be moved by controlling the X, Y, and Z axes of the XYZ movement mechanism unit 18 and a θ axis of the rotary table 16. The imaging range (position and magnification) and the imaging angle of the workpiece W can thus be adjusted.

[0009] In order to obtain a tomographic image or volume data of the workpiece W (stereoscopic image or a set of tomographic images of the workpiece W in the Z-axis direction), which is the final goal of the X-ray CT apparatus 1, a CT scan is performed on the workpiece W.

[0010] The CT scan includes two processes, namely the acquisition of transmission images (projection images) of the workpiece W and CT reconstruction. In the transmission image acquisition process, the rotary table 16 carrying the workpiece W is rotated continuously at a constant speed or intermittently at constant pitches during X-ray irradiation, thereby obtaining transmission images of the workpiece W in all directions (constant intervals). CT reconstruction is performed on the obtained transmission images in all directions (constant intervals) using a CT reconstruction algorithm such as backprojection and iterative reconstruction. As a result, a tomographic image or volume data of the workpiece (in Fig. 3 the main sphere B) is generated, as shown in Fig. 3 is shown.

[0011] From the generated volume data, a mesh or grid with a desired surface shape can be created for evaluation and analysis (see Japanese Patent Application Laid-Open No. 2018-40790). SUMMARY OF THE INVENTIONTechnical Problem

[0012] The basic methods for generating a mesh with a surface shape from volume data include a method for extracting voxels or grid points with a specific CT value to generate a mesh (isosurface mesh generation). A surface shape in volume data typically contains fluctuations in CT values ​​due to artifacts (noise). Since the method is directly affected by CT value fluctuations due to artifacts and the like, there is a problem that the surface shape cannot be accurately extracted only from an isosurface that defines a surface with a specific CT value.

[0013] The present invention has been created to solve the above conventional problem, and an object thereof is to perform high-precision surface extraction robust to CT value fluctuations. Solution to the problem

[0014] The present invention solves the above problem by extracting voxels having a certain CT value from volume data obtained by X-ray CT during surface extraction of the X-ray CT volume 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.

[0015] The vertex of the isosurface grid is corrected by calculating a gradient vector of the CT value at the vertex, generating a plurality of sampling points in the positive and negative directions of the calculated gradient vector, calculating gradient norms of CT values ​​at the respectively generated sampling points, and moving the vertex to a sampling point having the calculated maximum gradient norm.

[0016] The CT value at the vertex can be calculated using the following equation according to a Feldkamp method. f(p)=12∫02πα(θ,p)2Sfiltered(θ,p)dθ where the coefficient α(θ, p) is equal to d sod / (d sod + d z ) is, θ is a rotation angle, d sod is a distance from light source to center of rotation, and S filtered (θ, p) is a filter-corrected projection value (using a Shepp-Logan filter).

[0017] The present invention provides a surface extraction device for an X-ray CT volume for performing surface extraction on an X-ray CT volume, the surface extraction device for an X-ray CT volume including: a unit configured to extract voxels having a specific CT value from volume data obtained by X-ray CT to generate an isosurface mesh; and a unit configured to correct each vertex of the isosurface mesh using gradient information about a CT value at the vertex of the isosurface mesh.

[0018] The unit configured to correct the vertex of the isosurface mesh includes: a unit configured to calculate a gradient vector of the CT value at the vertex; a unit configured to generate a plurality of sampling points in positive and negative directions of the calculated gradient vector; a unit configured to calculate gradient norms of CT values ​​at the respective generated sampling points; and a unit configured to move the vertex to a sampling point having the calculated maximum gradient norm. Advantageous effects of the invention

[0019] According to the present invention, high-precision surface extraction can be performed by correcting the isosurface grid using the gradient information about the CT values.

[0020] These and other novel features and advantages of the present invention will become apparent from the following detailed description of preferred embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] The preferred embodiments will be described with reference to the drawings, wherein like elements are designated by the same reference numerals throughout the figures, and wherein: Fig. 1 is a sectional view showing an overall configuration of a typical X-ray CT apparatus used for measurement; Fig. 2 is a perspective view showing an arrangement of essential parts thereof; Fig. Figure 3 is a diagram outlining the CT reconstruction of the same; Fig. 4 is a flowchart showing a processing procedure according to an embodiment of the present invention; Fig. 5 is a perspective view for describing an example of a method for analytically calculating a CT value gradient according to the embodiment; Fig. 6 is a diagram showing an example of a plurality of sample points extracted in the directions of the gradient vectors ±g according to the embodiment; Fig. 7 is a diagram showing how a vertex is moved to a sampling point according to the embodiment; and Fig. 8 is a perspective view showing a stepped cylinder which is an example of an object to be measured. Description of embodiments

[0022] An embodiment of the present invention will be described in detail below with reference to the drawings. The present invention is not limited to the following description of the embodiment and examples. The components of the embodiment and examples described below include what is easily conceived by those skilled in the art, what is substantially the same, and what falls within a so-called range of equivalence. The components disclosed in the following embodiment and examples can be combined as needed or selectively used as needed.

[0023] An algorithm according to the present invention handles volume data generated by X-ray CT as input and surface-extracted mesh data as output.

[0024] Fig. 4 outlines a processing procedure according to the embodiment of the present invention.

[0025] In step 100, an isosurface mesh or grid M is first created from the volume data.

[0026] Each voxel of the volume data has a CT value. An isosurface mesh can be generated by extracting voxels with a specific CT value. The CT value can be selected by examining a histogram of CT values ​​of the volume data for selection. The histogram typically contains peaks representing respective work materials and air. For example, to extract the outer surface of the workpiece (interface between air and workpiece), an intermediate value (CT value) between the peaks representing air and the outer surface material of the workpiece is selected in the histogram. An isosurface mesh is generated using the selected appropriate CT value corresponding to a desired surface shape in the volume data.

[0027] In step 110, a vertex p is extracted, which forms the mesh M.

[0028] In step 120, a gradient vector g is calculated at the extracted grid vertex p. The gradient vector g can be calculated in the following way.

[0029] First, using the Feldkamp method (FDK method), which is one of the commonly used backprojection methods, a CT value f (p) at the vertex p (x, y, z) is calculated by the following equation (see Fig. 5): f(p)=12∫02πα(θ,p)2Sfiltered(θ,p)dθ where the coefficient α(θ, p) is equal to d sod / (d sod + d z ) is, θ is a rotation angle, d sod is a distance from light source to center of rotation, and S filtered (θ, p) is a filter-corrected projection value (using a Shepp-Logan filter).

[0030] In Fig. 5, reference numeral 30 denotes a computer that performs the calculation.

[0031] In addition to the Shepp-Logan filter, the filter-corrected projection value can be determined using the Ram-Lak filter or the Kak-Slaney filter.

[0032] Next, the gradient vector g (p) of the CT value at point p (x, y, z) is generated by the following equation: g(p)=12∫02πα(θ,p)3R−0(∂∂(u,p)Sfitlered(θ,p),0)τdθ where R -θ is a three-dimensional rotation matrix for the angle -θ, and ∂ / ∂(u, v) is a derivative in the detector coordinate system (calculation of the center difference between filter-corrected projection values).

[0033] An assumption of α(θ, p) = α(θ) (α is independent of p) can be used to simplify the calculation.

[0034] Points p are treated as continuous values. Interpolation processing is performed when calculating the projection values ​​if necessary.

[0035] In step 130, as in Fig. As shown in Figure 6, a plurality of sampling points S are extracted from the gradient vectors ±g passing through the grid vertex p. The extraction range and extraction intervals can be freely set, for example, with respect 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 approximately 0.1 to 0.2 times the voxel size.

[0036] In step 140, as in Fig. 7, gradient norms N at all extracted sample points S are calculated from the absolute values ​​of the gradient vectors g by the following equation: N=|g(S)|

[0037] In step 150, a sample point Sm having the maximum value Nm among the gradient norms N at the sample points S is derived.

[0038] In step 160, the vertex p is moved to the sampling point Sm. This is because the sampling points S vary greatly at the interface between the workpiece and air or at the interface between different work materials.

[0039] After step 160, processing proceeds to step 170. In step 170, it is checked whether all vertices p have been corrected.

[0040] If not all vertices p have been corrected, processing returns to step 110 to correct the next vertex p.

[0041] On the other hand, if it is determined in step 170 that all vertices p have been corrected, the processing ends.

[0042] The inventors have carried out a simulation to obtain measured values ​​of a stepped cylinder as used 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.

[0043] The main ball B or ruby ​​ball, which is in Fig. 3 was also evaluated. According to the conventional method, a difference between the actual measurement of the ball diameter 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 trend was observed for all the balls.

[0044] In the present embodiment, using the FDK method makes it easier to obtain the derivative of the equation for determining the CT value, thereby making it easy to obtain gradient information about the CT value. The method for obtaining gradient information about the CT value is not limited to the FDK method.

[0045] In the above embodiment, the gradient information is gradient standards. However, the gradient information is not limited to this. The object to be measured is also not limited to a workpiece.

[0046] Those skilled in the art will appreciate that the exemplary embodiments described above are merely illustrative, illustrating 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 scope of the invention.

Claims

[1] Surface extraction method for X-ray CT volumes, comprising: Extracting voxels or grid points with a specific CT value f(p) from volume data obtained by X-ray CT to generate an isosurface mesh or grid (M); and Correcting each vertex (p) of the isosurface grid (M) using gradient information about a CT value f(p) at the vertex (p) of the isosurface grid (M); where the vertex (p) of the isosurface grid (M) is corrected by: • Calculating a gradient vector g(p) of the CT value f(p) at the vertex (p), • Generating a plurality of sampling points (S) in the positive and negative directions of the calculated gradient vector g(p), • Calculating gradient norms (N) of CT values ​​f(p) at the respectively generated sampling points (S) and • Moving the vertex (p) to a sample point (Sm) with a calculated maximum gradient norm (Nm). [2] An X-ray CT volume surface extraction device for performing a surface extraction on an X-ray CT volume, the X-ray CT volume surface extraction device comprising: a unit configured to extract voxels with a specific CT value f(p) from volume data obtained by X-ray CT to generate an isosurface mesh (M); and a unit configured to correct each vertex (p) of the isosurface grid (M) using gradient information about a CT value f(p) at the vertex (p) of the isosurface grid (M); wherein the unit configured to correct the vertex (p) of the isosurface grid (M) comprises: • a unit configured to calculate a gradient vector g(p) of the CT value f(p) at the vertex (p); • a unit configured to generate a plurality of sampling points (S) in positive and negative directions of the calculated gradient vector g(p); • a unit configured to calculate gradient norms (N) of CT values ​​f(p) at the respective generated sample points (S); and • a unit configured to move the vertex (p) to a sampling point (Sm) with the calculated maximum gradient norm (Nm).

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