CN110956618A - CT image small defect quantification method based on coefficient of variation method - Google Patents
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Abstract
A CT image small defect quantification method based on a coefficient of variation method comprises the following steps: acquiring CT images of a contrast test piece and a tested piece; selecting a plurality of regions which have the same size and contain a small defect or do not contain a defect from the CT image of the comparison test piece, performing wavelet decomposition on the selected region image for t times, and calculating the variation coefficient of the low-frequency component wavelet coefficient of each selected region image after each wavelet decomposition; establishing the relation between the variation coefficient of the low-frequency component wavelet coefficient after each wavelet decomposition and the defect area; calculating the correlation coefficient and the slope between the variation coefficient of the low-frequency component wavelet coefficient and the defect area after wavelet decomposition in different size areas; further selecting the best wavelet decomposition times; finally, fitting a mathematical relation between the defect sizes in the regions with different sizes and the low-frequency component wavelet coefficient variation coefficient decomposed by the optimal wavelet decomposition times; the quantification can be carried out. The method has better efficiency and practicability.
Description
Technical Field
The invention relates to the field of defect quantification, in particular to a CT image small defect quantification method based on a coefficient of variation method.
Background
The industrial CT imaging technology is not limited by the material, shape, surface condition and the like of the detected object, can give a two-dimensional image and a three-dimensional image of the detected object, has the advantages of visual imaging and high resolution, and is widely used for detecting welding seams of various electron beam welding parts such as an electromagnetic valve, a self-locking valve, an injector, a pressure reducing valve and the like in a space satellite propulsion system. Due to the uncertainty of the welding process, the defects of air holes with different degrees and quantities are most easily generated in the welding joint, so that the structural strength of the joint of the welding joint is reduced, and explosion or explosion caused by the 'wall penetration' condition is seriously caused. The air hole defects formed by electron beam welding are mostly close to the conventional focus size (small defects) of an X-ray source of an industrial CT system. The small defects occupy less pixels in the image, and the imaging gray level is close to the background gray level value, so that the defects are difficult to extract. In the traditional small defect detection, a professional distinguishes the small defect according to the characteristics of defect distribution, size, form and the like, the workload is huge, and the quantitative accuracy is easily influenced by the state of a detector, so that the efficiency and the reliability of industrial CT detection are seriously restricted. Therefore, it is necessary to research a small defect quantification method suitable for industrial CT images.
According to the general technical route of image processing, threshold segmentation and area statistics are carried out on the small defects. The linear array industrial CT image has the following 4 gray characteristics, so that the traditional image processing method is difficult to apply, and the following problems exist:
(1) the brightness of the same density material region in the linear array industrial CT image is not consistent, the material background brightness difference is related to the shape and relative position of a scanning section, when a reconstruction region contains more than two products, one product can affect the gray level of the other product in the same projection region, although the gray level difference of the region is optimized and corrected in the CT image reconstruction algorithm, the weak difference still exists, and the interference is caused to the identification of small defects;
(2) the industrial CT image contains ring artifacts and noise, the noise is derived from electronic noise of an X-ray detection system and a data detection and acquisition system, and Gaussian noise and particle noise are represented on the image. The reasons for the formation of the ring artifacts can be attributed to the correction deviation of the detector, the inconsistent response of array elements, the defects of the scintillator and even dust adsorption, and the like;
(3) the weak and small defects occupy less pixels in the image, and the imaging gray level is close to the background gray level value, so that the defects are difficult to extract;
(4) and the influence of the X-ray source focus of the CT system causes the edge degradation of an object in an image, and the gray level distribution of the edge of a small defect is nonlinear. The adoption of a fixed threshold value easily causes over (under) segmentation, and finally influences the measurement precision of the defect size. The characteristics are the basis for designing the small defect segmentation algorithm in the linear array industrial CT image.
In recent years, in terms of the proposal of CT image defects (objects), a great deal of highly effective research has been carried out by domestic and foreign researchers, and the study is mainly applied to the medical field. The method is less related to the aspect of industrial small defect quantification, and a learner provides a compression cycle boundary condition method and combines a recursion acceleration algorithm on the basis of performing threshold segmentation on an image by using the characteristics of a low-contrast image in a two-dimensional entropy theory, so that the calculation efficiency is improved, and the image target recognition rate under low contrast is enhanced; the learner also uses a method of converting the low-contrast segmentation problem in the whole image into a higher-contrast segmentation problem in a local topological structure, judges whether each topological structure is a defect part or not and extracts low-contrast defect information in the image; in addition, the scholars also provide an image boundary detection method based on the region gray scale change rate, filtering is carried out according to a neighborhood weighted average filtering method based on the region gray scale change rate, and the boundary is refined, tracked and connected to obtain the boundary.
Firstly, a learner estimates a Point Spread Function (PSF) of a CT image, performs convolution operation on the PSF and an ideal defect to form defect degradation gray distribution, compares the defect degradation gray distribution with a real defect to be measured, and determines an optimal solution by adopting loop iteration, but the method has large operation amount, and a measurement result depends on the accuracy of PSF estimation and is easily interfered by noise; the learners also calculate the gray characteristic value by respectively selecting the defect and non-defect areas, calculate the circumferential equivalent steel coefficient by taking the edge of the workpiece as a boundary, establish the noise parameter of the defect area, divide the defect based on the noise parameter and carry out statistical quantification on the defect area, but the method needs manual intervention and has a more complex process. Further improvements are therefore desirable.
Disclosure of Invention
The invention aims to solve the technical problem of the prior art and provides a method for quantifying the small defects of a CT image based on a variation coefficient method, which is simple in measurement method and free of influence of the position of the defects on the quantification result.
The technical scheme adopted by the invention for solving the technical problems is as follows: a CT image small defect quantification method based on a coefficient of variation method is characterized in that: the method comprises the following steps:
wherein t is the wavelet decomposition times, t is a positive integer, stIs the standard deviation of the wavelet coefficients of the low frequency components after the t-th wavelet decomposition, mu is the mean value of the wavelet coefficients of the low frequency components after the t-th wavelet decomposition, ft(i, j) is the value of the coordinate position in the low-frequency component wavelet coefficient after the tth wavelet decomposition as the position (i, j); mtAnd NtRespectively obtaining the length and the width of the region obtained after the t-th wavelet decomposition of the M-N region;
step 6, comparing according to the correlation coefficient and the slope in the step 5, selecting the optimal wavelet decomposition times, recording as k times, and respectively fitting a mathematical relation between the defect size under the regions with different sizes and the variation coefficient of the wavelet coefficient of the low-frequency component after the wavelet decomposition for k times; wherein k is a positive integer;
and 7, randomly setting the size m x n of the selected region, randomly selecting an m x n region containing a small defect in the CT image of the tested piece, calculating the variation coefficient of the low-frequency component wavelet coefficient obtained after the m x n region is subjected to k times of wavelet decomposition, and substituting the variation coefficient into the mathematical relation between the defect size of the m x n region and the variation coefficient of the low-frequency component wavelet coefficient obtained after the k times of wavelet decomposition in the step 6 to obtain the small defect size in the m x n region selected by the tested piece, namely completing the small defect quantification.
In order to reduce the interference of noise and improve the detection accuracy, the specific steps in step 2 are: and attaching the un-punched piece to the back of the punched piece to form an internal artificial hole of the punched piece, and respectively performing linear array CT scanning on the front of the punched piece and the tested piece.
As an improvement, the specific step of selecting the optimal wavelet decomposition times in step 6 is as follows:
step 6-1, comparing the correlation coefficient between the variation coefficient of the low-frequency component wavelet coefficient after wavelet decomposition and the defect area in different size areas, and turning to step 6-2 when the correlation coefficient between the variation coefficient of the low-frequency component wavelet coefficient after wavelet decomposition and the defect area is basically larger than a set value in different size areas;
and 6-2, comparing the slopes of the wavelet coefficients of the low-frequency components after wavelet decomposition and the defect areas which meet the condition of the correlation coefficients in the step 6-1 for all times, selecting the corresponding wavelet decomposition times when the slope between the wavelet coefficients of the low-frequency components after certain wavelet decomposition and the defect areas is basically the maximum value, and taking the wavelet decomposition times as the optimal wavelet decomposition times.
Preferably, the value range of the set value of the correlation coefficient in the step 6-1 is 0.99-0.995.
Compared with the prior art, the invention has the advantages that: wavelet decomposition is introduced, the influence rule of the defect size on the variation coefficient is further analyzed through the variation coefficient of the low-frequency component wavelet coefficient after each wavelet decomposition, and a linear array industrial CT image small defect size quantitative method is established according to the influence rule, so that the effectiveness of nondestructive detection is improved.
Drawings
FIG. 1 is a CT image of a comparative test piece in an example of the present invention;
FIG. 2 is a graph of the relationship between defect size and the coefficient of variation of each sub-wavelet decomposition for a 140 pixel by 140 pixel region;
FIG. 3 is a graph of correlation coefficients between the variation coefficients of wavelet coefficients of low frequency components and defect areas after wavelet decomposition for each time in regions of different sizes;
FIG. 4 is a slope curve between the variation coefficient of the wavelet coefficient of the low frequency component and the defect area after each wavelet decomposition in regions of different sizes;
FIG. 5 is a comparison graph of the small defect size quantification results of the 4 algorithms in the example of the present invention.
Detailed Description
The invention is described in further detail below with reference to the accompanying examples.
A CT image small defect quantification method based on a coefficient of variation method comprises the following steps:
in this example, the comparative test piece is a wafer made of 304 stainless steel material and having a diameter of 30 mm, a diameter of 40 mm, a diameter of 50mm, and a thickness of 1.2 mm; polishing the surface of the manufactured wafer to enable the roughness to be about Ra1.6; machining through holes with diameters of 0.1 mm, 0.3mm, 0.5mm, 0.7 mm, 0.9 mm and 1.1mm on a polished wafer by adopting an electric spark (EDM) micropore machining technology, observing the micropore appearance by adopting a ZEISS imager, Z2m laser scanning Confocal microscope (CLSM for short) in order to ensure the accuracy of an experiment, measuring the upper and lower pore diameters of each through hole, and ensuring the consistency of artificial small defects;
in this embodiment, a linear array high-energy industrial CT system of the beijing gehong IPT 61106 MeV is used for the experiment, the accelerator energy is 6MeV, the focal size is fixed to be 2mm, the detector 608 channel has a vertical collimator opening of 0.3mm, and the horizontal collimator is adjustable between 0.3mm and 5.0 mm. The main process parameters of the industrial CT system of the high-energy accelerator are slice thickness, micro-motion times and trigger times, wherein the micro-motion times and the trigger times are in a monotonically increasing relation with small defect finding capability, namely the defect finding capability is stronger when the set value is larger, but the scanning and reconstruction time is greatly increased. Considering the test efficiency, on the premise of finding most defects of the through holes, the third-generation CT micro-motion times are selected for 5 times and the triggering times are selected for 4096 times;
in addition, in order to ensure the detection precision, an unpunched contrast test block with the same specification as the punched contrast test block is attached to the back of the punched contrast test block to form an internal artificial hole during detection, the front of the punched contrast test block is subjected to linear array industrial CT scanning by respectively adopting the slice thicknesses of 0.3mm, 0.5mm and 1.0mm, and the ray penetration direction is parallel to the punching plane of the wafer; obtaining a CT image of the contrast test piece shown in FIG. 1; the natural defect shape of the tested block is not limited, but the tested block is also circular in the CT image;
wherein t is the wavelet decomposition times, t is a positive integer, stIs the standard deviation of the wavelet coefficients of the low frequency components after the t-th wavelet decomposition, mu is the mean value of the wavelet coefficients of the low frequency components after the t-th wavelet decomposition, ft(i, j) is the value of the coordinate position in the low-frequency component wavelet coefficient after the tth wavelet decomposition as the position (i, j); mtAnd NtRespectively obtaining the length and the width of the region obtained after the t-th wavelet decomposition of the M-N region;
as shown in fig. 1, the selected M × N region is a rectangular frame marked in the figure, and the rectangular frame contains a circular through hole;
the calculation method of the correlation coefficient is an existing conventional calculation method, and is not described here. As shown in fig. 2, the relationship curve between the defect size in the 140 pixel region and the variation coefficient of each Wavelet decomposition is 140 pixels by 140 pixels, in this embodiment, four Wavelet decompositions are performed, in fig. 2, Wavelet1, Wavelet2, Wavelet3, and Wavelet4 correspond to the corresponding curves of 1-time Wavelet decomposition, 2-time Wavelet decomposition, 3-time Wavelet decomposition, and 4-time Wavelet decomposition, and the correlation coefficients of the low-frequency component Wavelet coefficient variation coefficient after the Wavelet decomposition of 1, 2, 3, and 4-time Wavelet decomposition and the defect area are calculated to be 0.992, 0.994, 0.996, and 0.994, respectively, and it can be seen that the high positive correlation is shown between the variation coefficient of the low-frequency component Wavelet coefficient after the Wavelet decomposition of 3 times and the defect size;
in this embodiment, the selected area size may be 140 pixels by 140 pixels, 120 pixels by 120 pixels, 100 pixels by 100 pixels, 80 pixels by 80 pixels, 60 pixels by 60 pixels, and 40 pixels by 40 pixels;
as shown in fig. 3 and 4, a Correlation-coefficient (Correlation-coefficient) curve and a slope (slope) curve are respectively obtained between the variation coefficient of the wavelet coefficient of the low frequency component and the defect area after wavelet decomposition in different size regions;
step 6, comparing according to the correlation coefficient and the slope in the step 5, selecting the optimal wavelet decomposition times, recording as k times, and respectively fitting a mathematical relation between the defect size under the regions with different sizes and the variation coefficient of the wavelet coefficient of the low-frequency component after the wavelet decomposition for k times; wherein k is a positive integer;
in this embodiment, since the defects in the CT image are all circular, the calculation formula of the circular area is used when fitting the defect size: s ═ pi R2S is the area of a circle, R is the radius of the circle, the defect area and the defect size (diameter) are converted, a mathematical relation between the defect size and the variation coefficient of the low-frequency component wavelet coefficient after the wavelet decomposition of k times is directly fitted, and the defect size can be obtained by inputting the variation coefficient of the low-frequency component wavelet coefficient after the wavelet decomposition of k times;
the specific steps for selecting the optimal wavelet decomposition times are as follows:
step 6-1, comparing the correlation coefficient between the variation coefficient of the low-frequency component wavelet coefficient after wavelet decomposition and the defect area in different size areas, and turning to step 6-2 when the correlation coefficient between the variation coefficient of the low-frequency component wavelet coefficient after wavelet decomposition and the defect area is basically larger than a set value in different size areas;
wherein, the value range of the set value of the correlation coefficient in the step 6-1 is 0.99-0.995; in this embodiment, the set value of the correlation coefficient is 0.995, and since it cannot be completely guaranteed in actual operation that the correlation coefficient between the variation coefficient of the low-frequency component wavelet coefficient after a certain wavelet decomposition and the defect area can reach the set value in regions of different sizes, the basic meaning in step 6-1 above is: when the correlation coefficient between the variation coefficient of the low-frequency component wavelet coefficient after a certain wavelet decomposition and the defect area has a% correlation coefficient larger than a set value in different size areas, the correlation coefficient is determined to be basically larger than the set value, and a certain error is allowed, wherein 0< a%, < 1, for example: the value range of a% is 90% -95%;
step 6-2, comparing the slopes between the wavelet coefficients of the low-frequency components after wavelet decomposition and the defect areas which meet the condition of the correlation coefficients in the step 6-1 for all times, and selecting the corresponding wavelet decomposition times when the slope between the wavelet coefficients of the low-frequency components after certain wavelet decomposition and the defect areas is basically the maximum value, and taking the wavelet decomposition times as the optimal wavelet decomposition times; similarly, when the slope between the wavelet coefficient of the low frequency component and the defect area after a certain wavelet decomposition has a maximum value of 90% to 95%, the slope is considered to be substantially the maximum value.
According to the scheme, the optimal wavelet decomposition times are comprehensively analyzed according to the actual situation, according to the analysis of the images in; in this embodiment, k is 3.
And 7, randomly setting the size m x n of the selected region, randomly selecting an m x n region containing a small defect in the CT image of the tested piece, calculating the variation coefficient of the low-frequency component wavelet coefficient after k times of wavelet decomposition of the m x n region, substituting the variation coefficient into the mathematical relation between the defect size of the m x n region in the step 6 and the variation coefficient of the low-frequency component wavelet coefficient after k times of wavelet decomposition, and obtaining the small defect size in the m x n region selected by the tested piece, namely finishing the small defect quantification.
In the embodiment, the fitting method is a linear fitting method, for example, a 304 stainless steel wafer with the diameter of 50mm is used, and a quantitative model (the region is 120 pixels × 120 pixels) with the small defect size is obtained by fitting according to a relation curve between different sizes of the defect and the variation coefficient of the low-frequency component wavelet coefficient after 3 times of wavelet decomposition;
D(cv)＝8.05802cv+0.03342；
wherein D is the diameter size of the small defect, and the unit is: mm; c. CvThe coefficient of variation of the wavelet coefficient of the low-frequency component after 3 times of wavelet decomposition; the fitted correlation coefficient was about 0.995;
therefore, when a region of 120 pixels by 120 pixels containing a small defect is selected from the CT image of the tested piece, the variation coefficient of the low-frequency component wavelet coefficient after 3 times of wavelet decomposition of the region is calculated and substituted into the formula, and the size of the small defect can be obtained.
In order to compare and verify the quantitative effectiveness of the method on the small defect size of the linear array industrial CT image, the method is compared and analyzed with a full width at half maximum method, a PSF convolution iteration method and a statistical equivalent method, and the 3 methods are shown in FIG. 5. When the defect diameter is increased from 0.3mm to 1.1mm, the average relative errors of the measurement results of the coefficient of variation method, the full width at half maximum method, the PSF convolution iteration method and the statistical equivalent method are 4.14%, 7.25%, 10.01% and 5.97%, respectively. It can be seen that the measurement deviation of the coefficient of variation method is minimal. The measurement was carried out using small defects on the test piece which did not participate in the modeling, and the defect diameters were 0.295mm and 0.509mm, respectively, as measured by CLSM. The deviation of each defect diameter was calculated by 4 methods for 2 verification defects, respectively, and the results are shown in table 1.
Table 14 verification of the results of the measurement methods
As can be seen from table 1, the PSF convolution iteration method and the conventional full width at half maximum measurement error are large, and the maximum relative error with the CLSM measurement result is 19.5% and 18.2%, respectively, because in the PSF convolution iteration method, noise has a large influence on both the PSF estimation and the iteration result. The measurement result of the traditional full width at half maximum method is mainly subjective judgment, and the interference of human factors is large. The variation coefficient method and the statistical equivalent method are ideal in stability and measurement accuracy, but the statistical equivalent method requires that a curve region and a reference region (without defects) are simultaneously selected, an equivalent thickness standard deviation coefficient is calculated, and the operation is complex. The variation coefficient method can measure the small defect size only by fixing the local area range, the measurement result is not affected by the defect position, and the practicability is superior to that of a statistical equivalent method.
The foregoing is only a preferred embodiment of the present invention, and it should be noted that, for those skilled in the art, various modifications and decorations can be made without departing from the technical principle of the present invention, and these modifications and decorations should also be regarded as the protection scope of the present invention.
Claims (4)
1. A CT image small defect quantification method based on a coefficient of variation method is characterized by comprising the following steps:
step 1, manufacturing a circular comparison test block with the same material as a tested piece by adopting a mechanical method, and forming circular through holes with various sizes on the comparison test block;
step 2, respectively carrying out linear array industrial CT scanning on the punched comparison test piece and the punched tested piece to obtain CT images of the comparison test piece and the punched tested piece;
step 3, selecting a plurality of M x N regions with the same size from the CT image of the comparison test piece, wherein each selected M x N region image contains a circular through hole or does not contain a circular through hole, the circular through hole corresponds to a small defect, performing wavelet decomposition for t times on the selected small defect region image and non-defect region image with different sizes respectively, and calculating the variation coefficient c of the low-frequency component wavelet coefficient of each selected region image after each wavelet decompositionvtThe calculation formula is as follows:
wherein t is the wavelet decomposition times, t is a positive integer, σtIs the standard deviation of the wavelet coefficients of the low frequency components after the t-th wavelet decomposition, mu is the mean value of the wavelet coefficients of the low frequency components after the t-th wavelet decomposition, ft(i, j) is the value of the coordinate position in the low-frequency component wavelet coefficient after the tth wavelet decomposition as the position (i, j); mtAnd NtRespectively obtaining the length and the width of the region obtained after the t-th wavelet decomposition of the M-N region;
step 4, establishing the relation between the variation coefficient of the wavelet coefficient of the low-frequency component after each wavelet decomposition and the defect area according to the calculation result in the step 3;
step 5, calculating the correlation coefficient and the slope between the variation coefficient of the wavelet coefficient of the low-frequency component and the defect area after wavelet decomposition in the regions with different sizes by using the same method in the step 3 and the step 4;
step 6, comparing according to the correlation coefficient and the slope in the step 5, selecting the optimal wavelet decomposition times, recording as k times, and respectively fitting a mathematical relation between the defect size under the regions with different sizes and the variation coefficient of the wavelet coefficient of the low-frequency component after the wavelet decomposition for k times; wherein k is a positive integer;
and 7, randomly setting the size m x n of the selected region, randomly selecting an m x n region containing a small defect in the CT image of the tested piece, calculating the variation coefficient of the low-frequency component wavelet coefficient of the m x n region subjected to k times of wavelet decomposition, and substituting the variation coefficient into the mathematical relation between the defect size of the m x n region and the variation coefficient of the low-frequency component wavelet coefficient subjected to k times of wavelet decomposition in the step 6 to obtain the small defect size in the m x n region selected by the tested piece, so that the small defect quantification is completed.
2. The method for quantifying the small defects of the CT image based on the coefficient of variation method as claimed in claim 1, wherein: the specific steps in the step 2 are as follows: and attaching the un-punched piece to the back of the punched piece to form an internal artificial hole of the punched piece, and respectively performing linear array CT scanning on the front of the punched piece and the tested piece.
3. The method for quantifying the small defects of the CT image based on the coefficient of variation method as claimed in claim 1, wherein: the specific steps of selecting the optimal wavelet decomposition times in the step 6 are as follows:
step 6-1, comparing the correlation coefficient between the variation coefficient of the low-frequency component wavelet coefficient after wavelet decomposition and the defect area in different size areas, and turning to step 6-2 when the correlation coefficient between the variation coefficient of the low-frequency component wavelet coefficient after wavelet decomposition and the defect area is basically larger than a set value in different size areas;
and 6-2, comparing the slopes of the wavelet coefficients of the low-frequency components after wavelet decomposition and the defect areas which meet the condition of the correlation coefficients in the step 6-1 for all times, selecting the corresponding wavelet decomposition times when the slope between the wavelet coefficients of the low-frequency components after certain wavelet decomposition and the defect areas is basically the maximum value, and taking the wavelet decomposition times as the optimal wavelet decomposition times.
4. The method for quantifying the small defects of the CT image based on the coefficient of variation method as claimed in claim 3, wherein: the value range of the set value of the correlation coefficient in the step 6-1 is 0.99-0.995.
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