CN114881991A - Method and system for automatically judging defects of laser dislocation speckle images - Google Patents

Method and system for automatically judging defects of laser dislocation speckle images Download PDF

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CN114881991A
CN114881991A CN202210569455.XA CN202210569455A CN114881991A CN 114881991 A CN114881991 A CN 114881991A CN 202210569455 A CN202210569455 A CN 202210569455A CN 114881991 A CN114881991 A CN 114881991A
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image
circle
point
points
defect
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陈佳慧
郑雪鹏
王飞
金翠娥
陈杰
陆彦辰
涂俊
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Shanghai Shenjian Precision Machinery Technology Co ltd
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00Image analysis
    • G06T7/0002Inspection of images, e.g. flaw detection
    • G06T7/0004Industrial image inspection
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T5/00Image enhancement or restoration
    • G06T5/20Image enhancement or restoration by the use of local operators
    • G06T5/30Erosion or dilatation, e.g. thinning
    • G06T5/70
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00Image analysis
    • G06T7/10Segmentation; Edge detection
    • G06T7/136Segmentation; Edge detection involving thresholding
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00Image analysis
    • G06T7/60Analysis of geometric attributes
    • G06T7/62Analysis of geometric attributes of area, perimeter, diameter or volume
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00Image analysis
    • G06T7/60Analysis of geometric attributes
    • G06T7/66Analysis of geometric attributes of image moments or centre of gravity
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/20Special algorithmic details
    • G06T2207/20024Filtering details
    • G06T2207/20032Median filtering

Abstract

The invention provides a method and a system for automatically judging defects of laser dislocation speckle images, which comprises the following steps: step S1: carrying out image denoising pretreatment on the laser dislocation speckle defect image by using sine and cosine filtering; step S2: performing threshold segmentation on the preprocessed image, and performing defect judgment; step S3: and carrying out contour searching and minimum circle searching operation on the defect judgment result image to complete defect positioning and defect equivalent size measurement. The invention can realize automatic judgment of the defects, can quantitatively measure the positions of the defects with high precision and automatically calculate the size of the removed defects; the invention has good real-time performance and high automation degree; the method is beneficial to improving the detection efficiency of the laser dislocation speckle image defects, meets the application requirements of non-contact, high resolution, high positioning precision and real-time rapid detection of aerospace products, and lays the foundation for the wide engineering popularization and application of the laser dislocation speckle detection technology in the fields of weapons, new energy automobiles and the like.

Description

Method and system for automatically judging defects of laser dislocation speckle images
Technical Field
The invention relates to the field of nondestructive testing, in particular to a method and a system for automatically judging defects by laser dislocation speckle images.
Background
The laser dislocation speckle interference is used as a new nondestructive testing technology, has the advantages of large area, full field, non-contact, low vibration isolation requirement, simple structure and the like, and is widely applied to nondestructive testing of composite materials. At present, the laser dislocation speckle interference defect judgment technology mainly depends on manual auxiliary judgment, but in the practical application process, the phase image contrast obtained by the laser dislocation speckle is often lower, great difficulty is brought to the accurate delineation of the defect boundary, the defect size measurement of the phase depends on manual judgment, the accurate measurement cannot be achieved, and the requirement of large-scale industrial production detection is difficult to meet. The detection result of the laser dislocation speckle technology is given in an image form, and the method is particularly critical for automatically judging the defect from a complex detection image and accurately measuring the size of the defect, rather than depending on the experience judgment and manual measurement of detection personnel.
Patent document CN112362700A (application number: CN202011065157.4) discloses a method for verifying detection sensitivity of laser dislocation speckle equipment based on a thermal loading method; firstly, selecting a black frosted acrylic plate, and processing M rows and N rows of blind holes for simulating defects on the same surface of the black frosted acrylic plate, wherein M, N are positive integers larger than 2, the blind holes in the row pitch direction are different in aperture and the burial depth, and the blind holes in the row pitch direction are same in aperture and the burial depth, so as to obtain a sensitivity calibration test block; then uniformly spraying a thin layer of white developing powder on the surface of the prepared sensitivity check test block by using a developer spraying tank for penetration detection, and clamping and fixing the sensitivity check test block by using a bracket after the developing powder is dried; and then, carrying out test operation and analyzing and judging the test structure to realize nondestructive verification. But the invention does not allow automatic determination of defects.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a method and a system for automatically judging the defects of laser dislocation speckle images.
The invention provides a method for automatically judging defects of laser dislocation speckle images, which comprises the following steps:
step S1: carrying out image denoising pretreatment on the laser dislocation speckle defect image by using sine and cosine filtering;
step S2: performing threshold segmentation on the preprocessed image, and performing defect judgment;
step S3: and carrying out contour searching and minimum circle searching operation on the defect judgment result image to complete defect positioning and defect equivalent size measurement.
Preferably, in the step S1:
converting discontinuous phase information in the fringe pattern into continuous values by utilizing the continuity of a sine-cosine function, performing sine and cosine transformation on the phase pattern respectively to avoid information loss of phase pattern jump, performing median filtering on the transformed phase pattern respectively, and performing arc tangent processing on the filtered sine phase pattern and cosine phase pattern;
the image I (x, y) is sine and cosine transformed, respectively:
Figure BDA0003659659750000021
in the formula, I (x, y) is the gray value of the original image of the wrapped phase map, s (x, y) is the gray value of the image after sine transformation, and c (x, y) is the gray value after cosine transformation.
Preferably, median filtering is respectively carried out on the images obtained after transformation;
the phase diagram is divided into two components, then the calculation is carried out by adopting mean filtering respectively, any pixel point (i, j) in the mean filtering is taken as a central point, and the size of a window is 3 multiplied by 3:
s′(x i ,y j )=median[s(x i-1 ,y j-1 ),s(x i ,y j-1 ),s(x i+1 ,y j-1 ),s(x i-1 ,y j ),s(x i ,y j ),s(x i+1 ,y j ),s(x i-1 ,y j+1 ),s(x i ,y j+1 ),s(x i ,y j+1 )]
c′(x i ,y j )=median[c(x i-1 ,y j-1 ),c(x i ,y j-1 ),c(x i+1 ,y j-1 ),c(x i-1 ,y j ),c(x i ,y j ),c(x i+1 ,y j ),c(x i-1 ,y j+1 ),c(x i ,y j+1 ),c(x i ,y j+1 )]
s ' (x, y) is a sine phase map filtered image, c ' (x, y) is a cosine phase map filtered image, s ' (x) i ,y j ) Is the pixel value at coordinate (i, j), c' (x), in image s i ,y j ) Is the pixel value at coordinate (i, j) in image c', s (x) i ,y j ) Is the pixel value at coordinate (i, j) in image s, c (x) i ,y j ) Is the pixel value at coordinate (i, j) in image c;
and performing arc tangent operation on the filtered image:
Figure BDA0003659659750000022
in the formula I 1 And (x, y) is the image after smoothing the edge texture after denoising.
Preferably, in the step S2:
the defect judgment needs to be carried out by utilizing image segmentation and image expansion corrosion morphological operation:
firstly, threshold segmentation is carried out on an image:
Figure BDA0003659659750000031
in the formula I 1 (x i ,y j ) For the denoised image obtained in step 1, I 2 (x i ,y j ) For thresholded images, T 1 To set a low threshold, T 2 For a set high threshold value, after the image is divided and binarized, in order to eliminate the influence of scattered noise, performing morphological operation of firstly expanding and then corroding on the image;
image I 2 The expansion with structural unit K can be expressed as:
Figure BDA0003659659750000032
in the formula, symbol
Figure BDA0003659659750000033
Is the dilation operator, l' 2 For the expanded image, K (x,y) Indicating that when the origin of K is moved to point (X, y), X represents the binarized image I 2 A connected domain of (c);
etching image I 'with structural unit K' 2 Can be expressed as:
Figure BDA0003659659750000034
in the formula, symbol
Figure BDA0003659659750000035
For corrosion operator, I 3 For post-etch images, K (x,y) When the origin of K is moved to a point (X, y), X represents the binarized image I 2 A connected domain of (c);
performing multiple iterative operations, and comparing the image I with the structural unit K 2 Firstly carrying out n times of expansion and then carrying out n times of corrosion to obtain an image I 3
Preferably, in the step S3:
a. for image I 3 And carrying out contour searching and minimum circle searching operation to finish defect positioning and defect size measurement:
b. traversing all the points, and finding out four points of the leftmost point, the rightmost point, the uppermost point and the lowermost point, which are respectively represented by A, B, C, D;
c. finding the center and radius of a minimum circle C1 surrounding A, B, C, D four points;
d. the first iteration, going through all points, checks if there is a point out of bounds, i.e. not within and on the boundary of circle C1;
e. if no boundary point exists, the circle is finally solved; if the out-of-bounds point exists, entering the step f;
f. if the point farthest from the center of the circle C1 in the boundary points is E, the following four combinations are tried in sequence: (1) A/B/C/E; (2) A/B/D/E; (3) A/C/D/E; (4) B/C/D/E;
if the minimum enclosing circle of the four points in the combination is C2, and the remaining points outside the combination are detected to be in the circle C2, then the center and the radius of the point E and the circle C2 are recorded;
g. the second iteration, traversing all the points, checking whether out-of-bounds points exist, namely not in the circle C2 and not on the boundary, if not, the solved circle C2 is the final solved; if the out-of-bounds point exists, the step h is operated;
h. if F is the point farthest from the center of the circle C2 in the boundary points, the following four combinations are tried in sequence: (I) A/B/D/F; (II) A/B/E/F; (III) A/D/E/F; (IV) B/D/E/F; sequentially processing the four combinations to obtain a minimum enclosing circle of four points in the combinations, obtaining a circle C3 if the combinations are detected, detecting the remaining points except the combinations in the circle C3, and recording the centers and the radiuses of the point F and the circle C3;
i. and (4) repeating g and h for the third iteration, until all the point results are found to be in the newly solved circle boundary after traversing, determining that the circle is the finally solved circle, and exiting the iteration.
The invention provides a system for automatically judging defects of laser dislocation speckle images, which comprises:
module M1: carrying out image denoising pretreatment on the laser dislocation speckle defect image by using sine and cosine filtering;
module M2: performing threshold segmentation on the preprocessed image, and performing defect judgment;
module M3: and carrying out contour searching and minimum circle searching operation on the defect judgment result image to complete defect positioning and defect equivalent size measurement.
Preferably, in said module M1:
converting discontinuous phase information in the fringe pattern into continuous values by utilizing the continuity of a sine-cosine function, performing sine and cosine transformation on the phase pattern respectively to avoid information loss of phase pattern jump, performing median filtering on the transformed phase pattern respectively, and performing arc tangent processing on the filtered sine phase pattern and cosine phase pattern;
the image I (x, y) is sine and cosine transformed, respectively:
Figure BDA0003659659750000041
in the formula, I (x, y) is the gray value of the original image of the wrapped phase map, s (x, y) is the gray value of the image after sine transformation, and c (x, y) is the gray value after cosine transformation.
Preferably, median filtering is respectively carried out on the images obtained after transformation;
the phase diagram is divided into two components, then the calculation is carried out by adopting mean filtering respectively, any pixel point (i, j) in the mean filtering is taken as a central point, and the size of a window is 3 multiplied by 3:
s′(x i ,y j )=median[s(x i-1 ,y j-1 ),s(x i ,y j-1 ),s(x i+1 ,y j-1 ),s(x i-1 ,y j ),s(x i ,y j ),s(x i+1 ,y j ),s(x i-1 ,y j+1 ),s(x i ,y j+1 ),s(x i ,y j+1 )]
c′(x i ,y j )=median[c(x i-1 ,y j-1 ),c(x i ,y j-1 ),c(x i+1 ,y j-1 ),c(x i-1 ,y j ),c(x i ,y j ),c(x i+1 ,y j ),c(x i-1 ,y j+1 ),c(x i ,y j+1 ),c(x i ,y j+1 )]
s ' (x, y) is a sine phase map filtered image, c ' (x, y) is a cosine phase map filtered image, s ' (x) i ,y j ) Is the pixel value at coordinate (i, j), c' (x), in image s i ,y j ) Is the pixel value at coordinate (i, j) in image c', s (x) i ,y j ) Is the pixel value at coordinate (i, j) in image s, c (x) i ,y j ) Is the pixel value at coordinate (i, j) in image c;
and performing arc tangent operation on the filtered image:
Figure BDA0003659659750000051
in the formula I 1 And (x, y) is the image after smoothing the edge texture after denoising.
Preferably, in said module M2:
the defect judgment needs to be carried out by utilizing image segmentation and image dilation corrosion morphological operation:
firstly, threshold segmentation is carried out on an image:
Figure BDA0003659659750000052
in the formula I 1 (x i ,y j ) For the denoised image obtained in step 1, I 2 (x i ,y j ) For thresholded images, T 1 To set a low threshold, T 2 For a set high threshold value, after the image is divided and binarized, in order to eliminate the influence of scattered noise, performing morphological operation of firstly expanding and then corroding on the image;
image I 2 By expansion of the structural unit KComprises the following steps:
Figure BDA0003659659750000053
in the formula, symbol
Figure BDA0003659659750000054
Is the dilation operator, l' 2 For the expanded image, K (x,y) Indicating that when the origin of K is moved to point (X, y), X represents the binarized image I 2 A connected domain of (c);
etching image I 'with structural unit K' 2 Can be expressed as:
Figure BDA0003659659750000055
in the formula, symbol
Figure BDA0003659659750000056
For corrosion operator, I 3 For post-etch images, K (x,y) When the origin of K is moved to a point (X, y), X represents the binarized image I 2 A connected domain of (c);
performing multiple iterative operations, and comparing the image I with the structural unit K 2 Firstly carrying out n times of expansion and then carrying out n times of corrosion to obtain an image I 3
Preferably, in said module M3:
a. for image I 3 And carrying out contour searching and minimum circle searching operation to finish defect positioning and defect size measurement:
b. traversing all the points, and finding out four points of the leftmost point, the rightmost point, the uppermost point and the lowermost point, which are respectively represented by A, B, C, D;
c. finding the center and radius of a minimum circle C1 surrounding A, B, C, D four points;
d. the first iteration, going through all points, checks if there is a point out of bounds, i.e. not within and on the boundary of circle C1;
e. if no boundary point exists, the circle is finally solved; if the out-of-bounds point exists, entering the step f;
f. if the point farthest from the center of the circle C1 in the boundary points is E, the following four combinations are tried in sequence: (1) A/B/C/E; (2) A/B/D/E; (3) A/C/D/E; (4) B/C/D/E;
if the minimum enclosing circle of the four points in the combination is C2, and the remaining points outside the combination are detected to be in the circle C2, then the center and the radius of the point E and the circle C2 are recorded;
g. the second iteration, traversing all the points, checking whether out-of-bounds points exist, namely not in the circle C2 and not on the boundary, if not, the solved circle C2 is the final solved; if the out-of-bounds point exists, the step h is operated;
h. if F is the point farthest from the center of the circle C2 in the boundary points, the following four combinations are tried in sequence: (I) A/B/D/F; (II) A/B/E/F; (III) A/D/E/F; (IV) B/D/E/F; sequentially processing the four combinations to obtain a minimum enclosing circle of four points in the combination, if the combination is used for obtaining a circle C3, detecting the remaining points outside the combination to be in the circle C3, and recording the centers and the radiuses of the point F and the circle C3;
i. and (4) repeating g and h for the third iteration, until all the point results are found to be in the newly solved circle boundary after traversing, determining that the circle is the finally solved circle, and exiting the iteration.
Compared with the prior art, the invention has the following beneficial effects:
1. the invention can realize automatic judgment of defects: the existing laser dislocation speckle interference defect judgment technology mainly depends on manual auxiliary judgment and is difficult to meet the requirement of mass industrial production detection, and the invention can directly and automatically judge the defects from complex detection images;
2. the invention can quantitatively measure the position of the defect with high precision and automatically calculate the size of the defect; in the practical application process, the phase image contrast obtained by laser dislocation speckle is often low, great difficulty is brought to accurate delineation of the defect boundary, and accurate positioning is difficult to achieve due to the fact that corresponding defect size measurement depends on manual judgment and manual measurement;
3. the invention has good real-time performance and high automation degree; the automatic detection method has the advantages that the automatic detection of the defects can be realized, the detection efficiency of the laser dislocation speckle image defects is greatly improved, the real-time performance is good, and the automation degree is high;
4. the method is beneficial to improving the detection efficiency of the laser dislocation speckle image defects, meets the application requirements of non-contact, high resolution, high positioning precision and real-time rapid detection of aerospace products, and is a basis for the wide engineering popularization and application of the laser dislocation speckle detection technology in the fields of weapons, new energy automobiles and the like.
Drawings
Other features, objects and advantages of the invention will become more apparent upon reading of the detailed description of non-limiting embodiments with reference to the following drawings:
FIG. 1 is a flow chart of the method of the present invention.
Detailed Description
The present invention will be described in detail with reference to specific examples. The following examples will assist those skilled in the art in further understanding the invention, but are not intended to limit the invention in any way. It should be noted that it would be obvious to those skilled in the art that various changes and modifications can be made without departing from the spirit of the invention. All falling within the scope of the present invention.
Example 1:
aiming at the defects of the laser dislocation speckle defect detection method at the present stage, the invention provides a method for automatically realizing the defect detection and the size measurement of the laser dislocation speckle defect image by using the laser dislocation speckle image. Decomposing a laser dislocation speckle image into a sine image and a cosine image, respectively carrying out median filtering on the sine image and the cosine image, and inversely converting the filtered images into a filtered image; carrying out threshold segmentation on the filtered image, and carrying out multiple expansion and corrosion operations to complete defect detection; and finally, judging the contour, searching a minimum circle surrounding the contour, and determining the circle center and the radius to finish defect positioning and defect size measurement. The method provided by the invention obtains the accurate outline of the defect according to the gray distribution information of the defect, thereby completing the automatic judgment of the characteristic defect and the accurate measurement of the size of the defect and realizing the automatic detection of the defect.
The method for automatically judging the defects of the laser dislocation speckle images, as shown in figure 1, comprises the following steps:
step S1: carrying out image denoising pretreatment on the laser dislocation speckle defect image by using sine and cosine filtering;
specifically, in the step S1:
converting discontinuous phase information in the fringe pattern into continuous values by utilizing the continuity of a sine-cosine function, performing sine and cosine transformation on the phase pattern respectively to avoid information loss of phase pattern jump, performing median filtering on the transformed phase pattern respectively, and performing arc tangent processing on the filtered sine phase pattern and cosine phase pattern;
the image I (x, y) is sine and cosine transformed, respectively:
Figure BDA0003659659750000081
in the formula, I (x, y) is the gray value of the original image of the wrapped phase map, s (x, y) is the gray value of the image after sine transformation, and c (x, y) is the gray value after cosine transformation.
Specifically, median filtering is respectively carried out on the images obtained after transformation;
the phase diagram is divided into two components, then the calculation is carried out by adopting mean filtering respectively, any pixel point (i, j) in the mean filtering is taken as a central point, and the size of a window is 3 multiplied by 3:
s′(x i ,y j )=median[s(x i-1 ,y j-1 ),s(x i ,y j-1 ),s(x i+1 ,y j-1 ),s(x i-1 ,y j ),s(x i ,y j ),s(x i+1 ,y j ),s(x i-1 ,y j+1 ),s(x i ,y j+1 ),s(x i ,y j+1 )]
c′(x i ,y j )=median[c(x i-1 ,y j-1 ),c(x i ,y j-1 ),c(x i+1 ,y j-1 ),c(x i-1 ,y j ),c(x i ,y j ),c(x i+1 ,y j ),c(x i-1 ,y j+1 ),c(x i ,y j+1 ),c(x i ,y j+1 )]
s ' (x, y) is a sine phase map filtered image, c ' (x, y) is a cosine phase map filtered image, s ' (x) i ,y j ) Is the pixel value at coordinate (i, j), c' (x), in image s i ,y j ) Is the pixel value at coordinate (i, j) in image c', s (x) i ,y j ) Is the pixel value at coordinate (i, j) in image s, c (x) i ,y j ) Is the pixel value at coordinate (i, j) in image c;
and performing arc tangent operation on the filtered image:
Figure BDA0003659659750000082
in the formula I 1 And (x, y) is the image after smoothing the edge texture after denoising.
Step S2: performing threshold segmentation on the preprocessed image, and performing defect judgment;
specifically, in the step S2:
the defect judgment needs to be carried out by utilizing image segmentation and image expansion corrosion morphological operation:
firstly, threshold segmentation is carried out on an image:
Figure BDA0003659659750000083
in the formula I 1 (x i ,y j ) For the denoised image obtained in step 1, I 2 (x i ,y j ) For thresholded images, T 1 To set a low threshold, T 2 For a set high threshold value, after the image is divided and binarized, in order to eliminate the influence of scattered noise, performing morphological operation of firstly expanding and then corroding on the image;
image I 2 The expansion with structural unit K can be expressed as:
Figure BDA0003659659750000091
in the formula, symbol
Figure BDA0003659659750000092
Is the dilation operator, l' 2 For the expanded image, K (x,y) Indicating that when the origin of K is moved to point (X, y), X represents the binarized image I 2 A connected domain of (c);
etching image I 'with structural unit K' 2 Can be expressed as:
Figure BDA0003659659750000093
in the formula, symbol
Figure BDA0003659659750000094
For corrosion operator, I 3 For post-etch images, K (x,y) When the origin of K is moved to a point (X, y), X represents the binarized image I 2 A connected domain of (c);
performing multiple iterative operations, and comparing the image I with the structural unit K 2 Firstly carrying out n times of expansion and then n times of corrosion to obtain an image I 3
Step S3: and carrying out contour searching and minimum circle searching operation on the defect judgment result image to complete defect positioning and defect equivalent size measurement.
Specifically, in the step S3:
a. for image I 3 And carrying out contour searching and minimum circle searching operation to finish defect positioning and defect size measurement:
b. traversing all the points, and finding out four points of the leftmost point, the rightmost point, the uppermost point and the lowermost point, which are respectively represented by A, B, C, D;
c. finding the center and radius of a minimum circle C1 surrounding A, B, C, D four points;
d. the first iteration, going through all points, checks if there is a point out of bounds, i.e. not within and on the boundary of circle C1;
e. if no boundary point exists, the circle is finally solved; if the out-of-bounds point exists, entering the step f;
f. if the point farthest from the center of the circle C1 in the boundary points is E, the following four combinations are tried in sequence: (1) A/B/C/E; (2) A/B/D/E; (3) A/C/D/E; (4) B/C/D/E;
if the minimum enclosing circle of the four points in the combination is C2, and the remaining points outside the combination are detected to be in the circle C2, then the center and the radius of the point E and the circle C2 are recorded;
g. the second iteration, traversing all the points, checking whether out-of-bounds points exist, namely not in the circle C2 and not on the boundary, if not, the solved circle C2 is the final solved; if the out-of-bounds point exists, the step h is operated;
h. if F is the point farthest from the center of the circle C2 in the boundary points, the following four combinations are tried in sequence: (I) A/B/D/F; (II) A/B/E/F; (III) A/D/E/F; (IV) B/D/E/F; sequentially processing the four combinations to obtain a minimum enclosing circle of four points in the combination, if the combination is used for obtaining a circle C3, detecting the remaining points outside the combination to be in the circle C3, and recording the centers and the radiuses of the point F and the circle C3;
i. and (4) repeating g and h for the third iteration, until all the point results are found to be in the newly solved circle boundary after traversing, determining that the circle is the finally solved circle, and exiting the iteration.
Example 2:
example 2 is a preferred example of example 1, and the present invention will be described in more detail.
The method for automatically judging the defect by using the laser misplaced speckle image provided by the invention can be understood as a specific implementation manner of a system for automatically judging the defect by using the laser misplaced speckle image, namely the system for automatically judging the defect by using the laser misplaced speckle image can be realized by executing the step flow of the method for automatically judging the defect by using the laser misplaced speckle image.
The invention provides a system for automatically judging defects of laser dislocation speckle images, which comprises:
module M1: carrying out image denoising pretreatment on the laser dislocation speckle defect image by using sine and cosine filtering;
specifically, in the module M1:
converting discontinuous phase information in the fringe pattern into continuous values by utilizing the continuity of a sine-cosine function, performing sine and cosine transformation on the phase pattern respectively to avoid information loss of phase pattern jump, performing median filtering on the transformed phase pattern respectively, and performing arc tangent processing on the filtered sine phase pattern and cosine phase pattern;
the image I (x, y) is sine and cosine transformed, respectively:
Figure BDA0003659659750000101
in the formula, I (x, y) is the gray value of the original image of the wrapped phase map, s (x, y) is the gray value of the image after sine transformation, and c (x, y) is the gray value after cosine transformation.
Specifically, median filtering is respectively carried out on the images obtained after transformation;
the phase diagram is divided into two components, then the calculation is carried out by adopting mean filtering respectively, any pixel point (i, j) in the mean filtering is taken as a central point, and the size of a window is 3 multiplied by 3:
s′(x i ,y j )=median[s(x i-1 ,y j-1 ),s(x i ,y j-1 ),s(x i+1 ,y j-1 ),s(x i-1 ,y j ),s(x i ,y j ),s(x i+1 ,y j ),s(x i-1 ,y j+1 ),s(x i ,y j+1 ),s(x i ,y j+1 )]
c′(x i ,y j )=median[c(x i-1 ,y j-1 ),c(x i ,y j-1 ),c(x i+1 ,y j-1 ),c(x i-1 ,y j ),c(x i ,y j ),c(x i+1 ,y j ),c(x i-1 ,y j+1 ),c(x i ,y j+1 ),c(x i ,y j+1 )]
s ' (x, y) is a sine phase map filtered image, c ' (x, y) is a cosine phase map filtered image, s ' (x) i ,y j ) Is the pixel value at coordinate (i, j), c' (x), in image s i ,y j ) Is the pixel value at coordinate (i, j) in image c', s (x) i ,y j ) Is the pixel value at coordinate (i, j) in image s, c (x) i ,y j ) Is the pixel value at coordinate (i, j) in image c;
and performing arc tangent operation on the filtered image:
Figure BDA0003659659750000111
in the formula I 1 And (x, y) is the image after smoothing the edge texture after denoising.
Module M2: performing threshold segmentation on the preprocessed image, and performing defect judgment;
specifically, in the module M2:
the defect judgment needs to be carried out by utilizing image segmentation and image expansion corrosion morphological operation:
firstly, threshold segmentation is carried out on an image:
Figure BDA0003659659750000112
in the formula I 1 (x i ,y j ) For the denoised image obtained in step 1, I 2 (x i ,y j ) For thresholded images, T 1 To set a low threshold, T 2 For a set high threshold value, after the image is divided and binarized, in order to eliminate the influence of scattered noise, performing morphological operation of firstly expanding and then corroding on the image;
image I 2 The expansion with structural unit K can be expressed as:
Figure BDA0003659659750000113
in the formula, symbol
Figure BDA0003659659750000114
Is the dilation operator, l' 2 For the expanded image, K (x,y) Indicating that when the origin of K is moved to point (X, y), X represents the binarized image I 2 A connected domain of (c);
etching image I 'with structural unit K' 2 Can be expressed as:
Figure BDA0003659659750000115
in the formula, symbol
Figure BDA0003659659750000116
For corrosion operator, I 3 For post-etch images, K (x,y) When the origin of K is moved to a point (X, y), X represents the binarized image I 2 A connected domain of (c);
performing multiple iterative operations, and comparing the image I with the structural unit K 2 Firstly carrying out n times of expansion and then carrying out n times of corrosion to obtain an image I 3
Module M3: and carrying out contour searching and minimum circle searching operation on the defect judgment result image to complete defect positioning and defect equivalent size measurement.
Specifically, in the module M3:
a. for image I 3 Proceed to find the outline sumFinding the minimum circle operation to finish defect positioning and defect size measurement:
b. traversing all the points, and finding out four points of the leftmost point, the rightmost point, the uppermost point and the lowermost point, which are respectively represented by A, B, C, D;
c. finding the center and radius of a minimum circle C1 surrounding A, B, C, D four points;
d. the first iteration, going through all points, checks if there is a point out of bounds, i.e. not within and on the boundary of circle C1;
e. if no boundary point exists, the circle is finally solved; if the out-of-bounds point exists, entering the step f;
f. if the point farthest from the center of the circle C1 in the boundary points is E, the following four combinations are tried in sequence: (1) A/B/C/E; (2) A/B/D/E; (3) A/C/D/E; (4) B/C/D/E;
finding the minimum enclosing circle of four points in the combination, if the minimum enclosing circle of the four points in the combination is C2, and detecting the remaining points outside the combination to be in the circle C2, then recording the center and the radius of the point E and the circle C2;
g. the second iteration, traversing all the points, checking whether out-of-bounds points exist, namely not in the circle C2 and not on the boundary, if not, the solved circle C2 is the final solved; if the out-of-bounds point exists, the step h is operated;
h. if F is the point farthest from the center of the circle C2 in the boundary points, the following four combinations are tried in sequence: (I) A/B/D/F; (II) A/B/E/F; (III) A/D/E/F; (IV) B/D/E/F; sequentially processing the four combinations to obtain a minimum enclosing circle of four points in the combination, if the combination is used for obtaining a circle C3, detecting the remaining points outside the combination to be in the circle C3, and recording the centers and the radiuses of the point F and the circle C3;
i. and (4) repeating g and h for the third iteration, until all the point results are found to be in the newly solved circle boundary after traversing, determining that the circle is the finally solved circle, and exiting the iteration.
Example 3:
example 3 is a preferred example of example 1, and the present invention will be described in more detail.
The method comprises the steps of firstly carrying out sine and cosine filtering pretreatment on a laser dislocation speckle image, then carrying out image segmentation and expansion corrosion morphological transformation to realize defect detection, and finally searching a contour and a minimum circle to finish defect positioning and defect equivalent size measurement. The method can realize automatic judgment of the defects, is beneficial to improving the detection efficiency of the laser dislocation speckle image defects, meets the application requirements of non-contact, high resolution, high positioning precision and real-time rapid detection of aerospace products, and lays the foundation for the wide engineering popularization and application of the laser dislocation speckle detection technology in the fields of weapons, new energy automobiles and the like.
The invention discloses a method for automatically judging defects of laser dislocation speckle images, which is mainly shown in a flow chart 1 and comprises the following specific steps:
(1) carrying out image denoising pretreatment on the laser dislocation speckle defect image by using sine and cosine filtering:
and converting discontinuous phase information in the fringe pattern into continuous values by utilizing the continuity of a sine-cosine function by utilizing a sine-cosine filtering method, namely performing sine and cosine transformation on the phase pattern respectively, then performing median filtering respectively, and finally performing arc tangent processing on the filtered sine phase pattern and cosine phase pattern.
The input laser dislocation speckle defect image I 1 Performing sine transform and cosine transform to obtain I 1s And I 1c
For image I 1 (x, y) sine and cosine transforms:
Figure BDA0003659659750000131
in the formula I 1 (x, y) is the gray value of the original image of the wrapped phase map, I 1s (x, y) is the image gray value after sinusoidal transformation, I 1c And (x, y) are gray values after cosine transformation, and median filtering is respectively carried out on the images obtained after the transformation.
At this time, the phase diagram is divided into two components, and then the average filtering is adopted to calculate, taking any pixel point (i, j) in the average filtering as the central point, the window size is 3 x 3,
I′ 1s (x i ,y j )=median[I 1s (x i-1 ,y j-1 ),I 1s (x i ,y j-1 ),s(x i+1 ,y j-1 ),I 1s (x i-1 ,y j ),I 1s (x i ,y j ),I 1s (x i+1 ,y j ),I 1s (x i-1 ,y j+1 ),I 1s (x i ,y j+1 ),I 1s (x i ,y j+1 )]
I′ 1c (x i ,y j )=median[I 1c (x i-1 ,y j-1 ),I 1c (x i ,y j-1 ),I 1c (x i+1 ,y j-1 ),I 1c (x i-1 ,y j ),I 1c (x i ,y j ),I 1c (x i+1 ,y j ),I 1c (x i-1 ,y j+1 ),I 1c (x i ,y j+1 ),I 1c (x i ,y j+1 )]
I' 1s (x i ,y j ) Is a sine phase map filtered image, I' 1c (x i ,y j ) Is a cosine phase map filtered image. And performing arc tangent operation on the filtered image:
Figure BDA0003659659750000132
in the formula I 2 (x, y) is the denoised image.
(2) And (3) utilizing image segmentation and image expansion corrosion morphological operation to judge defects:
the image is first subjected to a threshold segmentation,
Figure BDA0003659659750000133
in the formula I 2 (x i ,y j ) For the denoised image obtained in step 1, I 3 (x i ,y j ) The image is divided by a threshold value. After the image is divided and binarized, in order to eliminate the influence of scattered noise, the image is subjected to morphological operation of firstly expanding and then corroding.
In order to obtain better effect, the invention carries out multiple iterative operations, and uses the structural unit K to firstly carry out image I 3 Firstly carrying out n times of expansion and then carrying out n times of corrosion to obtain an image I 4
For example, this time for image I 3 3 expansions and 3 more erosions were performed.
Image I 3 The expansion 3 times by the structural unit K can be respectively expressed as:
Figure BDA0003659659750000134
Figure BDA0003659659750000135
Figure BDA0003659659750000141
in the formula, symbol
Figure BDA0003659659750000142
Is the dilation operator, I' 3 Shown as 3 post-dilation images.
To image I 'with structural unit K' 3 The 3 times of etching can be expressed as:
Figure BDA0003659659750000143
Figure BDA0003659659750000144
Figure BDA0003659659750000145
in the formula, symbol
Figure BDA0003659659750000146
For corrosion operator, I 4 Indicated as 3 post-etch images.
(3) And (3) performing contour searching and minimum circle searching operation on the result image in the step (2) to finish defect positioning and defect size measurement, wherein the method comprises the following steps:
1) all points are traversed to find four points, represented by A, B, C, D, at the leftmost, rightmost, uppermost and lowermost points.
2) The center and radius of a minimum circle C1 surrounding these four points are found.
3) The first iteration. Traversing all points, check if there is a point out of bounds, i.e., not within and not on the boundary of circle C1. If no point is defined, the circle is finally determined. If the out-of-bounds point exists, go to the fourth step.
4) Assuming that E is the point farthest from the center of the circle C1 among the out-of-bounds points, the following four combinations are tried in turn: (1) A/B/C/E (2) A/B/D/E (3) A/C/D/E (4) B/C/D/E. The minimum circle of enclosure of four points in the combination is found. Assuming that the minimum enclosing circle of the combination (1) A, B, C, E is C2, then the remaining points D are detected as not being within C2, for example, the minimum enclosing circle C3 of four points A, B, D, E is calculated for the combination (2), the remaining points C are detected and found to be within the circle C3, and then the center and radius of the point E and the circle C3 are recorded.
5) And (5) performing second iteration. All points are traversed to check if there is an out-of-bounds point, i.e., not within and not on the boundary of circle C3. If no point is defined, the circle C3 is finally determined. If there is an out-of-bounds point, go to the next step.
6) Assuming that F is the point of the out-of-bounds points farthest from the center of the circle C3, the following four combinations are tried in turn: (1) A/B/D/F (2) A/B/E/F (3) A/D/E/F (4) B/D/E/F. The four combinations are processed in sequence to find the minimum circle of enclosure of the four points in the combination. Assuming that the combination (1) obtains the circle C4, the center and radius of the point F and the circle C4 are recorded in the circle C4 at the detection point E.
7) And (5) carrying out a third iteration. And then repeating the steps 5 and 6 until all the point traversal results are found to be in the newly solved circle boundary, so that the circle is the finally solved circle, and exiting the iteration.
And (3) performing the operation of the steps 1-7 on each defect, and outputting all circle center coordinates and corresponding radius values, wherein the circle center coordinates are the positions of the defects, and the radius is the equivalent size of the defects.
Those skilled in the art will appreciate that, in addition to implementing the systems, apparatus, and various modules thereof provided by the present invention in purely computer readable program code, the same procedures can be implemented entirely by logically programming method steps such that the systems, apparatus, and various modules thereof are provided in the form of logic gates, switches, application specific integrated circuits, programmable logic controllers, embedded microcontrollers and the like. Therefore, the system, the device and the modules thereof provided by the present invention can be considered as a hardware component, and the modules included in the system, the device and the modules thereof for implementing various programs can also be considered as structures in the hardware component; modules for performing various functions may also be considered to be both software programs for performing the methods and structures within hardware components.
The foregoing description of specific embodiments of the present invention has been presented. It is to be understood that the present invention is not limited to the specific embodiments described above, and that various changes or modifications may be made by one skilled in the art within the scope of the appended claims without departing from the spirit of the invention. The embodiments and features of the embodiments of the present application may be combined with each other arbitrarily without conflict.

Claims (10)

1. A method for automatically judging defects of laser dislocation speckle images is characterized by comprising the following steps:
step S1: carrying out image denoising pretreatment on the laser dislocation speckle defect image by using sine and cosine filtering;
step S2: performing threshold segmentation on the preprocessed image, and performing defect judgment;
step S3: and carrying out contour searching and minimum circle searching operation on the defect judgment result image to complete defect positioning and defect equivalent size measurement.
2. The method for automatically determining the defects by using the laser misplaced speckle images as claimed in claim 1, wherein in the step S1:
converting discontinuous phase information in the fringe pattern into continuous values by utilizing the continuity of a sine-cosine function, performing sine and cosine transformation on the phase pattern respectively to avoid information loss of phase pattern jump, performing median filtering on the transformed phase pattern respectively, and performing arc tangent processing on the filtered sine phase pattern and cosine phase pattern;
the image I (x, y) is sine and cosine transformed, respectively:
Figure FDA0003659659740000011
in the formula, I (x, y) is the gray value of the original image of the wrapped phase map, s (x, y) is the gray value of the image after sine transformation, and c (x, y) is the gray value after cosine transformation.
3. The method for automatically determining the defects of the laser misplaced speckle images according to claim 2, wherein:
performing median filtering on the images obtained after transformation respectively;
the phase diagram is divided into two components, then the calculation is carried out by adopting mean filtering respectively, any pixel point (i, j) in the mean filtering is taken as a central point, and the size of a window is 3 multiplied by 3:
s′(x i ,y j )=median[s(x i-1 ,y j-1 ),s(x i ,y j-1 ),s(x i+1 ,y j-1 ),s(x i-1 ,y j ),s(x i ,y j ),s(x i+1 ,y j ),s(x i-1 ,y j+1 ),s(x i ,y j+1 ),s(x i ,y j+1 )]
c′(x i ,y j )=median[c(x i-1 ,y j-1 ),c(x i ,y j-1 ),c(x i+1 ,y j-1 ),c(x i-1 ,y j ),c(x i ,y j ),c(x i+1 ,y j ),c(x i-1 ,y j+1 ),c(x i ,y j+1 ),c(x i ,y j+1 )]
s ' (x, y) is a sine phase map filtered image, c ' (x, y) is a cosine phase map filtered image, s ' (x) i ,y j ) Is the pixel value at coordinate (i, j), c' (x), in image s i ,y j ) Is the pixel value at coordinate (i, j) in image c', s (x) i ,y j ) Is the pixel value at coordinate (i, j) in image s, c (x) i ,y j ) Is the pixel value at coordinate (i, j) in image c;
and performing arc tangent operation on the filtered image:
Figure FDA0003659659740000021
in the formula I 1 And (x, y) is the image after smoothing the edge texture after denoising.
4. The method for automatically determining the defects by using the laser misplaced speckle images as claimed in claim 1, wherein in the step S2:
the defect judgment needs to be carried out by utilizing image segmentation and image expansion corrosion morphological operation:
firstly, threshold segmentation is carried out on an image:
Figure FDA0003659659740000022
in the formula I 1 (x i ,y j ) For the denoised image obtained in step 1, I 2 (x i ,y j ) For thresholded images, T 1 To set a low threshold, T 2 In order to set a high threshold value, after the image is segmented and binarized, performing morphological operation of firstly expanding and then corroding on the image in order to eliminate the influence of scattered noise;
image I 2 The expansion with structural unit K can be expressed as:
Figure FDA0003659659740000023
in the formula, symbol
Figure FDA0003659659740000024
Is the dilation operator, l' 2 For the expanded image, K (x,y) Indicating that when the origin of K is moved to point (X, y), X represents the binarized image I 2 A connected domain of (c);
etching image I 'with structural unit K' 2 Can be expressed as:
Figure FDA0003659659740000025
in the formula, symbol
Figure FDA0003659659740000026
For corrosion operator, I 3 For post-etch images, K (x,y) Indicating that when the origin of K is moved to point (X, y), X represents the binarized image I 2 A connected domain of (c);
performing multiple iterative operations, and comparing the image I with the structural unit K 2 Firstly carrying out n times of expansion and then n times of corrosion to obtain an image I 3
5. The method for automatically determining the defects by using the laser misplaced speckle images as claimed in claim 1, wherein in the step S3:
a. for image I 3 Performing contour searching and minimum circle searching operation to complete defect positioning andand (3) measuring the size of the defect:
b. traversing all the points, and finding out four points of the leftmost point, the rightmost point, the uppermost point and the lowermost point, which are respectively represented by A, B, C, D;
c. finding the center and radius of a minimum circle C1 surrounding A, B, C, D four points;
d. the first iteration, going through all points, checks if there is a point out of bounds, i.e. not within and on the boundary of circle C1;
e. if no boundary point exists, the circle is finally solved; if the out-of-bounds point exists, entering the step f;
f. if the point farthest from the center of the circle C1 in the boundary points is E, the following four combinations are tried in sequence: (1) A/B/C/E; (2) A/B/D/E; (3) A/C/D/E; (4) B/C/D/E;
if the minimum enclosing circle of the four points in the combination is C2, and the remaining points outside the combination are detected to be in the circle C2, then the center and the radius of the point E and the circle C2 are recorded;
g. the second iteration, traversing all the points, checking whether out-of-bounds points exist, namely not in the circle C2 and not on the boundary, if not, the solved circle C2 is the final solved; if the out-of-bounds point exists, the step h is operated;
h. if F is the point farthest from the center of the circle C2 in the boundary points, the following four combinations are tried in sequence: (I) A/B/D/F; (II) A/B/E/F; (III) A/D/E/F; (IV) B/D/E/F; sequentially processing the four combinations to obtain a minimum enclosing circle of four points in the combination, if the combination is used for obtaining a circle C3, detecting the remaining points outside the combination to be in the circle C3, and recording the centers and the radiuses of the point F and the circle C3;
i. and (4) repeating g and h for the third iteration, until all the point results are found to be in the newly solved circle boundary after traversing, determining that the circle is the finally solved circle, and exiting the iteration.
6. A system for automatically judging defects of laser dislocation speckle images is characterized by comprising:
module M1: carrying out image denoising pretreatment on the laser dislocation speckle defect image by using sine and cosine filtering;
module M2: performing threshold segmentation on the preprocessed image, and performing defect judgment;
module M3: and carrying out contour searching and minimum circle searching operation on the defect judgment result image to complete defect positioning and defect equivalent size measurement.
7. The system for automatically determining defects according to laser misplaced speckle images of claim 6, wherein in module M1:
converting discontinuous phase information in the fringe pattern into continuous values by utilizing the continuity of a sine-cosine function, performing sine and cosine transformation on the phase pattern respectively to avoid information loss of phase pattern jump, performing median filtering on the transformed phase pattern respectively, and performing arc tangent processing on the filtered sine phase pattern and cosine phase pattern;
the image I (x, y) is sine and cosine transformed, respectively:
Figure FDA0003659659740000031
in the formula, I (x, y) is the gray value of the original image of the wrapped phase map, s (x, y) is the gray value of the image after sine transformation, and c (x, y) is the gray value after cosine transformation.
8. The system for automatically determining defects according to laser misplaced speckle images of claim 7, wherein:
performing median filtering on the images obtained after transformation respectively;
the phase diagram is divided into two components, and then average filtering is adopted for calculation, any pixel point (i, j) in the average filtering is taken as a central point, and the size of a window is 3 multiplied by 3:
s′(x i ,y j )=median[s(x i-1 ,y j-1 ),s(x i ,y j-1 ),s(x i+1 ,y j-1 ),s(x i-1 ,y j ),s(x i ,y j ),s(x i+1 ,y j ),s(x i-1 ,y j+1 ),s(x i ,y j+1 ),s(x i ,y j+1 )]
c′(x i ,y j )=median[c(x i-1 ,y j-1 ),c(x i ,y j-1 ),c(x i+1 ,y j-1 ),c(x i-1 ,y j ),c(x i ,y j ),c(x i+1 ,y j ),c(x i-1 ,y j+1 ),c(x i ,y j+1 ),c(x i ,y j+1 )]
s ' (x, y) is a sine phase map filtered image, c ' (x, y) is a cosine phase map filtered image, s ' (x) i ,y j ) Is the pixel value at coordinate (i, j), c' (x), in image s i ,y j ) Is the pixel value at coordinate (i, j) in image c', s (x) i ,y j ) Is the pixel value at coordinate (i, j) in image s, c (x) i ,y j ) Is the pixel value at coordinate (i, j) in image c;
and performing arc tangent operation on the filtered image:
Figure FDA0003659659740000041
in the formula I 1 And (x, y) is the image after smoothing the edge texture after denoising.
9. The system for automatically determining defects according to laser misplaced speckle images of claim 6, wherein in module M2:
the defect judgment needs to be carried out by utilizing image segmentation and image expansion corrosion morphological operation:
firstly, threshold segmentation is carried out on an image:
Figure FDA0003659659740000042
in the formula I 1 (x i ,y j ) For the denoised image obtained in step 1, I 2 (x i ,y j ) For thresholded images, T 1 To set a low threshold, T 2 In order to set a high threshold value, after the image is segmented and binarized, performing morphological operation of firstly expanding and then corroding on the image in order to eliminate the influence of scattered noise;
image I 2 The expansion with structural unit K can be expressed as:
Figure FDA0003659659740000043
in the formula, symbol
Figure FDA0003659659740000044
Is the dilation operator, l' 2 For the expanded image, K (x,y) Indicating that when the origin of K is moved to point (X, y), X represents the binarized image I 2 A connected domain of (c);
etching image I 'with structural unit K' 2 Can be expressed as:
Figure FDA0003659659740000045
in the formula, symbol
Figure FDA0003659659740000051
For corrosion operator, I 3 For post-etch images, K (x,y) When the origin of K is moved to a point (X, y), X represents the binarized image I 2 A connected domain of (c);
performing multiple iterative operations, and comparing the image I with the structural unit K 2 Firstly carrying out n times of expansion and then carrying out n times of corrosion to obtain an image I 3
10. The system for automatically determining defects according to laser misplaced speckle images of claim 6, wherein in module M3:
a. for image I 3 And carrying out contour searching and minimum circle searching operation to finish defect positioning and defect size measurement:
b. traversing all the points, and finding out four points of the leftmost point, the rightmost point, the uppermost point and the lowermost point, which are respectively represented by A, B, C, D;
c. finding the center and radius of a minimum circle C1 surrounding A, B, C, D four points;
d. the first iteration, going through all points, checks if there is a point out of bounds, i.e. not within and on the boundary of circle C1;
e. if no boundary point exists, the circle is finally solved; if the out-of-bounds point exists, entering the step f;
f. if the point farthest from the center of the circle C1 in the boundary points is E, the following four combinations are tried in sequence: (1) A/B/C/E; (2) A/B/D/E; (3) A/C/D/E; (4) B/C/D/E;
if the minimum enclosing circle of the four points in the combination is C2, and the remaining points outside the combination are detected to be in the circle C2, then the center and the radius of the point E and the circle C2 are recorded;
g. the second iteration, traversing all the points, checking whether out-of-bounds points exist, namely not in the circle C2 and not on the boundary, if not, the solved circle C2 is the final solved; if the out-of-bounds point exists, the step h is operated;
h. if F is the point farthest from the center of the circle C2 in the boundary points, the following four combinations are tried in sequence: (I) A/B/D/F; (II) A/B/E/F; (III) A/D/E/F; (IV) B/D/E/F; sequentially processing the four combinations to obtain a minimum enclosing circle of four points in the combination, if the combination is used for obtaining a circle C3, detecting the remaining points outside the combination to be in the circle C3, and recording the centers and the radiuses of the point F and the circle C3;
i. and (4) repeating g and h for the third iteration, until all the point results are found to be in the newly solved circle boundary after traversing, determining that the circle is the finally solved circle, and exiting the iteration.
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