CN113808150A - Novel edge detection method capable of self-adaptive repairing - Google Patents

Novel edge detection method capable of self-adaptive repairing Download PDF

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CN113808150A
CN113808150A CN202111009401.XA CN202111009401A CN113808150A CN 113808150 A CN113808150 A CN 113808150A CN 202111009401 A CN202111009401 A CN 202111009401A CN 113808150 A CN113808150 A CN 113808150A
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fractional order
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CN113808150B (en
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张新雨
林鹏逸
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Xian University of Technology
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    • G06T2207/00—Indexing scheme for image analysis or image enhancement
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Abstract

The invention discloses a novel edge detection method capable of self-adaptive restoration, which comprises the steps of firstly carrying out image segmentation on an image shot by an image sensor, bringing different fractional orders into fractional order differential operators, carrying out edge extraction on the segmented image based on the fractional order differential operators by utilizing a Canny edge detection algorithm to obtain an optimal fractional order, further carrying out edge detection to obtain a binary image I only containing edges, obtaining an image after non-maximum value inhibition by using a Canny edge detection method based on the fractional order differential operators of the optimal fractional order, calculating a GVF vector field, then calculating a curvature value of the image, calculating a curvature value of the image I in a curvature-driven diffusion CDD image restoration model, carrying out iterative restoration and refinement on the image I to be restored, and setting a pixel value of a refined edge point to be 1 to obtain a final edge detection result. The invention solves the problem that the self-adaptive repair of the fractured edge cannot be carried out in the existing edge detection.

Description

Novel edge detection method capable of self-adaptive repairing
Technical Field
The invention belongs to the technical field of image processing, and particularly relates to a novel edge detection method capable of self-adaptive repairing.
Background
In the field of image processing, edge detection is widely applied to practical engineering, and is particularly prominent in the field of measurement based on image processing technology. For example, diameter detection of a metal workpiece, crystal diameter detection during growth of a Czochralski silicon single crystal. The Canny algorithm is a relatively common edge detection algorithm and has the characteristics of high anti-interference performance and high robustness, but a first-order differential operator adopted by the Canny algorithm is a Sobel operator, so that the details of the image edge are difficult to capture, and meanwhile, due to the introduction of non-maximum value inhibition and dual-threshold detection, the edge detection result of the Canny algorithm has heavy edges, breakage and deficiency, which seriously affects the precision of the detection result. In recent years, researchers introduce fractional order differential operators into the Canny algorithm, and although the edge detection accuracy of the Canny algorithm is improved through the fractional order differential operators, the method accelerates the edge breakage. Therefore, how to detect the edge of the silicon single crystal by using the fractional differential Canny algorithm and carry out self-adaptive repair on the fracture edge in the detection result so as to obtain a relatively complete contour edge is very important.
Disclosure of Invention
The invention aims to provide a novel edge detection method capable of self-adaptively repairing, and solves the problem that the self-adaptively repairing of a broken edge cannot be carried out in the conventional edge detection.
The technical scheme adopted by the invention is that a novel edge detection method capable of self-adaptive repairing is implemented according to the following steps:
step 1, carrying out image segmentation on an image shot by an image sensor, bringing different fractional orders into fractional order differential operators, carrying out edge extraction on the segmented image based on the fractional order differential operators by utilizing a Canny edge detection algorithm, obtaining an optimal fractional order by utilizing an evaluation function, and carrying out edge detection on the image by utilizing the optimal fractional order to finally obtain a binary image I only containing edges, wherein the pixel value corresponding to an edge point is 1, and the pixel value corresponding to a background point is 0;
step 2, calculating a GVF vector field by using the image after non-maximum suppression, which is obtained by the Canny edge detection method based on the optimal fractional order differential operator in the step 1, and then calculating the curvature value of the image by taking the GVF vector field as the gradient value of the image;
step 3, calculating parameters in a curvature-driven diffusion CDD image restoration model by using a binary image I only containing edges, wherein the parameters comprise curvature values of the image I in the restoration process;
step 4, performing iterative repair on the image I to be repaired by simultaneously using the curvature value obtained by the calculation of the GVF field and the curvature value of the image I in the repair process;
and 5, refining the repaired image by using non-maximum value inhibition again, and setting the pixel value of the edge point after refining as 1 to obtain a final edge detection result.
The present invention is also characterized in that,
the step 1 is as follows:
step 1.1, carrying out image segmentation on an image shot by an image sensor;
by introducing a fractional order differential operator, the original 4-direction Sobel first order differential operator is popularized to the fractional order according to the G-L definition, and the popularized fractional order differential operator is as follows:
Figure BDA0003238101790000021
Figure BDA0003238101790000031
Figure BDA0003238101790000032
Figure BDA0003238101790000033
in the formula (I), the compound is shown in the specification,
Figure BDA0003238101790000034
fractional order differential operators in the directions of 0 °, 45 °, 90 ° and 135 ° respectively; v is the order of the fractional order differential operator;
sequentially selecting the fractional orders in the v epsilon (0,2) with the distance of 0.2 and bringing the fractional orders into the formulas (1) - (4) to obtain a plurality of groups of fractional order differential operators, and carrying out edge detection on the image by using the fractional order differential operators through a Canny algorithm to obtain edge image detection results under different fractional orders;
step 1.2, defining an evaluation function S (v), wherein the evaluation function S (v) is calculated by the following method: in the detection result corresponding to the fractional order v, if there are only two edge points on one abscissa of the edge image and the absolute value of the subtraction of the ordinate of the two edge points is greater than the minimum distance between one inner edge point and one outer edge point in the same abscissa of all pixels, the inner edge point and the outer edge point are considered to be single-pixel edge points at the moment, the number of the abscissas meeting the condition is recorded as S (v), then the Lagrange interpolation method is used for fitting S (v) -v, and finally the maximum value point of the S (v) is solved to be the optimal fractional order;
and step 1.3, carrying out the optimal fractional order differential operators obtained in the optimal fractional order banding formulas (1) to (4) obtained in the step 1.2, and carrying out edge detection on the image through a Canny algorithm based on the optimal fractional order differential operators to obtain an edge detection result, namely the extracted edge-only binary image I.
The step 2 is as follows:
calculating the GVF vector field of the image after non-maximum suppression, which is obtained by a Canny edge detection method based on the fractional order differential operator of the optimal fractional order, according to the following iterative formula:
Figure BDA0003238101790000041
Figure BDA0003238101790000042
in the formula ux(i, j, t +1) and uy(i, j, t +1) is the GVF vector magnitude of the point (i, j) in the x and y directions of the t +1 th iteration respectively, i.e. the GVF vector magnitude
Figure BDA0003238101790000043
Is the GVF vector field, Gx(i, j) and Gy(i, j) are eachThe gradient in the x and y directions of the non-maxima suppressed image at point (i, j);
then using GVF vector field
Figure BDA0003238101790000044
The curvature value of the image is calculated as a gradient value of the image according to the gradient value, and the calculation mode is as follows:
Figure BDA0003238101790000045
in the formula, κGVFCurvature values of the image are suppressed for non-maxima.
The step 3 is as follows:
step 3.1, using the diffusion iteration equation of the CDD image restoration model as follows:
Figure BDA0003238101790000046
in the formula (I), the compound is shown in the specification,
Figure BDA0003238101790000047
f is the flux field of the image I,
Figure BDA0003238101790000048
is divergence, delta t is a numerical time step, and n represents the iteration number;
3.2, solving the gradient value of the edge repairing model by adopting a half-point gradient difference method, defining the gray value at the half point to be obtained by averaging the gray values of two adjacent points, and then obtaining the image half point
Figure BDA0003238101790000051
The gradient value of (d) is calculated by:
Figure BDA0003238101790000052
in the formula (I), the compound is shown in the specification,
Figure BDA0003238101790000053
for image I at point
Figure BDA0003238101790000059
A gradient value of (a)xAnd IyRespectively are gradient values of the image to be restored in the x direction and the y direction;
then, the curvature value of the image is solved by using the half-point gradient value, and the second derivative value of the gradient difference of the image at the half point is calculated as follows:
Figure BDA0003238101790000054
in the formula (I), the compound is shown in the specification,
Figure BDA0003238101790000055
and
Figure BDA0003238101790000056
second derivatives of image I in the x and y directions, respectively;
the curvature value of the image to be repaired at the half point can be calculated by the following formula through the calculation method of the second derivative,
Figure BDA0003238101790000057
in the formula, κFIs the curvature value of the image I.
Step 4 is detailed below, while using the curvature value κ of the image IFAnd curvature value k of non-maxima suppressed imageGVF，
Figure BDA0003238101790000058
Selecting a curvature value according to an equation (13) and calculating a half-point gradient value according to an equation (10), and taking the half-point gradient value as a parameter of the model to be brought into an equation (8) to carry out iterative solution on the model;
when the maximum iteration number n is reached, obtaining an edge image I(n)And thinning the image by using non-maximum value inhibition again, setting the pixel value of the edge point after thinning as 1, obtaining and outputting the final edge detection result.
The method has the advantages that the novel edge detection method capable of self-adaptively repairing inherits the literature by firstly providing the evaluation function suitable for the instance engineering situation[1]The method has the advantage of high edge detection precision of the multidirectional fractional order differential operator. And the CDD repairing model is improved, and the edge repairing model is provided, so that the model can accurately repair the broken edge, the integrity and the visual connectivity of the edge detection result are improved, and the method has important significance for improving the edge detection precision.
Drawings
FIG. 1 is an image of a workpiece in a high temperature red hot state;
FIG. 2 is an edge detection result of a workpiece image in a high temperature red hot state using the present invention;
FIG. 3 is a result of edge detection of a workpiece image in a high temperature red hot state using a conventional Canny method;
FIG. 4 is a document for use of an image of a workpiece in a high temperature red hot state[1]And (5) detecting the edge.
Detailed Description
The present invention will be described in detail below with reference to the accompanying drawings and specific embodiments.
The invention relates to a novel edge detection method capable of self-adaptive repairing, which is implemented according to the following steps:
step 1, carrying out image segmentation on an image shot by an image sensor, bringing different fractional orders into fractional order differential operators, carrying out edge extraction on the segmented image based on the fractional order differential operators by utilizing a Canny edge detection algorithm, obtaining an optimal fractional order by utilizing an evaluation function, and carrying out edge detection on the image by utilizing the optimal fractional order to finally obtain a binary image I only containing edges, wherein the pixel value corresponding to an edge point is 1, and the pixel value corresponding to a background point is 0;
the step 1 is as follows:
step 1.1, carrying out image segmentation on an image shot by an image sensor;
by introducing a fractional order differential operator, the original 4-direction Sobel first order differential operator is popularized to the fractional order according to the G-L definition, and the popularized fractional order differential operator is as follows:
Figure BDA0003238101790000071
Figure BDA0003238101790000072
Figure BDA0003238101790000073
Figure BDA0003238101790000074
in the formula (I), the compound is shown in the specification,
Figure BDA0003238101790000075
and
Figure BDA0003238101790000076
fractional order differential operators in the directions of 0 °, 45 °, 90 ° and 135 ° respectively; v is the order of the fractional order differential operator;
sequentially selecting the fractional orders in the v epsilon (0,2) with the distance of 0.2 and bringing the fractional orders into the formulas (1) - (4) to obtain a plurality of groups of fractional order differential operators, and carrying out edge detection on the image by using the fractional order differential operators through a Canny algorithm to obtain edge image detection results under different fractional orders;
step 1.2, defining an evaluation function S (v), wherein the evaluation function S (v) is calculated by the following method: in the detection result corresponding to the fractional order v, if there are only two edge points on one abscissa of the edge image and the absolute value of the subtraction of the ordinate of the two edge points is greater than the minimum distance between one inner edge point and one outer edge point in the same abscissa of all pixels, the inner edge point and the outer edge point are considered to be single-pixel edge points at the moment, the number of the abscissas meeting the condition is recorded as S (v), then the Lagrange interpolation method is used for fitting S (v) -v, and finally the maximum value point of the S (v) is solved to be the optimal fractional order;
and step 1.3, carrying out the optimal fractional order differential operators obtained in the optimal fractional order banding formulas (1) to (4) obtained in the step 1.2, and carrying out edge detection on the image through a Canny algorithm based on the optimal fractional order differential operators to obtain an edge detection result, namely the extracted edge-only binary image I.
Step 2, calculating a GVF (gradient Vector flow) Vector field by using the image after non-maximum suppression, which is obtained by the Canny edge detection method based on the optimal fractional order differential operator in the step 1, and then calculating the curvature value of the image by using the GVF Vector field as the gradient value of the image;
the step 2 is as follows:
calculating the GVF vector field of the image after non-maximum suppression, which is obtained by a Canny edge detection method based on the fractional order differential operator of the optimal fractional order, according to the following iterative formula:
Figure BDA0003238101790000081
Figure BDA0003238101790000082
in the formula ux(i, j, t +1) and uy(i, j, t +1) is the GVF vector magnitude of the point (i, j) in the x and y directions of the t +1 th iteration respectively, i.e. the GVF vector magnitude
Figure BDA0003238101790000083
Is the GVF vector field, Gx(i, j) and Gy(i, j) the gradient in the x and y directions of the non-maxima suppressed image at point (i, j), respectively;
then using GVF vector field
Figure BDA0003238101790000084
The curvature value of the image is calculated as a gradient value of the image according to the gradient value, and the calculation mode is as follows:
Figure BDA0003238101790000085
in the formula, κGVFCurvature values of the image are suppressed for non-maxima.
Step 3, calculating parameters in a Curvature Driven diffusion (Curvature drive diffusion) CDD image restoration model by using the binary image I only containing edges, wherein the parameters comprise the Curvature value of the image I in the restoration process;
the step 3 is as follows:
step 3.1, using the diffusion iteration equation of the CDD image restoration model as follows:
Figure BDA0003238101790000091
in the formula (I), the compound is shown in the specification,
Figure BDA0003238101790000092
f is the flux field of the image I,
Figure BDA0003238101790000093
is divergence, delta t is a numerical time step, and n represents the iteration number;
3.2, solving the gradient value of the edge repairing model by adopting a half-point gradient difference method, defining the gray value at the half point to be obtained by averaging the gray values of two adjacent points, and then obtaining the image half point
Figure BDA0003238101790000094
The gradient value of (d) is calculated by:
Figure BDA0003238101790000095
in the formula (I), the compound is shown in the specification,
Figure BDA0003238101790000096
for image I at point
Figure BDA0003238101790000097
A gradient value of (a)xAnd IyRespectively are gradient values of the image to be restored in the x direction and the y direction;
then, the curvature value of the image is solved by using the half-point gradient value, and the second derivative value of the gradient difference of the image at the half point is calculated as follows:
Figure BDA0003238101790000098
in the formula (I), the compound is shown in the specification,
Figure BDA0003238101790000101
and
Figure BDA0003238101790000102
second derivatives of image I in the x and y directions, respectively;
the curvature value of the image to be repaired at the half point can be calculated by the following formula through the calculation method of the second derivative,
Figure BDA0003238101790000103
in the formula, κFIs the curvature value of the image I.
Step 4, performing iterative repair on the image I to be repaired by simultaneously using the curvature value obtained by the calculation of the GVF field and the curvature value of the image I in the repair process;
step 4 is as followsWhile using the curvature value kappa of the image IFAnd curvature value k of non-maxima suppressed imageGVF，
Figure BDA0003238101790000104
Selecting a curvature value according to an equation (13) and calculating a half-point gradient value according to an equation (10), and taking the half-point gradient value as a parameter of the model to be brought into an equation (8) to carry out iterative solution on the model;
when the maximum iteration number n is reached, obtaining an edge image I(n)And thinning the image by using non-maximum value inhibition again, setting the pixel value of the edge point after thinning as 1, obtaining and outputting the final edge detection result.
And 5, refining the repaired image by using non-maximum value inhibition again, and setting the pixel value of the edge point after refining as 1 to obtain a final edge detection result.
The edge detection result is objectively evaluated, and three evaluation indexes OF an undetected Rate (Omission Factor, OF), an Error Rate (ER) and a quality Factor (Figure OF Merit, FOM) are introduced. The quality factor mainly describes the distance between the detection result and the real edge, and the closer the value is to 1, the closer the detection result is to the real edge; the omission factor mainly describes the integrity of the detection result; the false detection rate mainly describes the accuracy of the detection result. The three quantitative indices were calculated as follows:
Figure BDA0003238101790000111
Figure BDA0003238101790000112
Figure BDA0003238101790000113
in the formula, ScAs a result of edge detectionNumber of correct pixel points, StotalAnd SdetectTotal number of pixel points, d, for the true edge image and edge detection result, respectivelyiAnd alpha is a penalty parameter, which is the shortest distance from the detected edge pixel point to the real edge, and in this document, alpha is 1/9, and the real edge is obtained by an offline calibration mode according to experience.
Examples
The invention is applied to the problem of edge detection of workpieces in a high-temperature red hot state, as shown in figure 1.
Firstly, the parameters of the invention are set as follows: the iteration number of the GVF vector field is 5, the area of which the vector amplitude is not 0 in the GVF field is set as a mask image of the CDD model, and the maximum diffusion iteration number of the improved CDD model is 40.
Secondly, the traditional Canny algorithm and the method of the document [1] are respectively introduced into the experiment to compare the detection results of the invention. The results of the three methods for detecting the edge of the workpiece image in the high-temperature red-hot state are shown in fig. 2, 3 and 4.
Then, the detection results of the three methods are objectively evaluated by using the three evaluation indexes. The results of the inspection of the workpiece image in the high-temperature red hot state are shown in table 1. The three performance indexes of the traditional Canny method are the worst in the three methods, the missing detection rate of the method is the lowest, the FOM is the highest, and compared with the traditional Canny method, the integrity and the accuracy of the edge detection result of the method are obviously improved. Document [1]]Although the error rate of the method is lower than that of the method, the omission ratio of the method is far higher than that of the invention, so the performance of the invention is better than that of the literature[1]The method of (1).
TABLE 1 inspection results of workpiece images in high temperature Red-Hot State
Method OF ER FOM
The invention 42.46％ 69.53％ 0.9011
Traditional Canny method 49.03％ 37.59％ 0.6894
Literature[1]Method 63.89％ 69.83％ 0.8434
Document [1] Jiangchui, Wuqiao group, Guiweihua, Yangchunhua, Xieyangfang, blast furnace burden surface profile adaptive detection based on a fractional order multidirectional differential operator [ J ] automated science report, 2017,43(12):2115 and 2126.
Jiang Z H,Wu Q Q,Gui W H,Yang C H,Xie Y F.Adaptive detection of blast furnace surface contour with fractional multi-directional differential operator[J].Acta Automatica Sinica,2017,43(12):2115-2126.

Claims (5)

1. A novel edge detection method capable of self-adaptive repairing is characterized by being implemented according to the following steps:
step 1, carrying out image segmentation on an image shot by an image sensor, bringing different fractional orders into fractional order differential operators, carrying out edge extraction on the segmented image based on the fractional order differential operators by utilizing a Canny edge detection algorithm, obtaining an optimal fractional order by utilizing an evaluation function, and carrying out edge detection on the image by utilizing the optimal fractional order to finally obtain a binary image I only containing edges, wherein the pixel value corresponding to an edge point is 1, and the pixel value corresponding to a background point is 0;
step 2, calculating a GVF vector field by using the image after non-maximum suppression, which is obtained by the Canny edge detection method based on the optimal fractional order differential operator in the step 1, and then calculating the curvature value of the image by taking the GVF vector field as the gradient value of the image;
step 3, calculating parameters in a curvature-driven diffusion CDD image restoration model by using a binary image I only containing edges, wherein the parameters comprise curvature values of the image I in the restoration process;
step 4, performing iterative repair on the image I to be repaired by simultaneously using the curvature value obtained by the calculation of the GVF field and the curvature value of the image I in the repair process;
and 5, refining the repaired image by using non-maximum value inhibition again, and setting the pixel value of the edge point after refining as 1 to obtain a final edge detection result.
2. The method according to claim 1, wherein the step 1 specifically comprises the following steps:
step 1.1, carrying out image segmentation on an image shot by an image sensor;
by introducing a fractional order differential operator, the original 4-direction Sobel first order differential operator is popularized to the fractional order according to the G-L definition, and the popularized fractional order differential operator is as follows:
Figure FDA0003238101780000021
Figure FDA0003238101780000022
Figure FDA0003238101780000023
Figure FDA0003238101780000024
in the formula (I), the compound is shown in the specification,
Figure FDA0003238101780000025
and
Figure FDA0003238101780000026
fractional order differential operators in the directions of 0 °, 45 °, 90 ° and 135 ° respectively; v is the order of the fractional order differential operator;
sequentially selecting the fractional orders in the v epsilon (0,2) with the distance of 0.2 and bringing the fractional orders into the formulas (1) - (4) to obtain a plurality of groups of fractional order differential operators, and carrying out edge detection on the image by using the fractional order differential operators through a Canny algorithm to obtain edge image detection results under different fractional orders;
step 1.2, defining an evaluation function S (v), wherein the evaluation function S (v) is calculated by the following method: in the detection result corresponding to the fractional order v, if there are only two edge points on one abscissa of the edge image and the absolute value of the subtraction of the ordinate of the two edge points is greater than the minimum distance between one inner edge point and one outer edge point in the same abscissa of all pixels, the inner edge point and the outer edge point are considered to be single-pixel edge points at the moment, the number of the abscissas meeting the condition is recorded as S (v), then the Lagrange interpolation method is used for fitting S (v) -v, and finally the maximum value point of the S (v) is solved to be the optimal fractional order;
and step 1.3, carrying out the optimal fractional order differential operators obtained in the optimal fractional order banding formulas (1) to (4) obtained in the step 1.2, and carrying out edge detection on the image through a Canny algorithm based on the optimal fractional order differential operators to obtain an edge detection result, namely the extracted edge-only binary image I.
3. The new edge detection method capable of adaptive repairing according to claim 2, wherein the step 2 is as follows:
calculating the GVF vector field of the image after non-maximum suppression, which is obtained by a Canny edge detection method based on the fractional order differential operator of the optimal fractional order, according to the following iterative formula:
Figure FDA0003238101780000031
Figure FDA0003238101780000032
in the formula ux(i, j, t +1) and uy(i, j, t +1) is the GVF vector magnitude of the point (i, j) in the x and y directions of the t +1 th iteration respectively, i.e. the GVF vector magnitude
Figure FDA0003238101780000033
Is the GVF vector field, Gx(i, j) and Gy(i, j) the gradient in the x and y directions of the non-maxima suppressed image at point (i, j), respectively;
then using GVF vector field
Figure FDA0003238101780000034
The curvature value of the image is calculated as a gradient value of the image according to the gradient value, and the calculation mode is as follows:
Figure FDA0003238101780000035
in the formula, κGVFCurvature values of the image are suppressed for non-maxima.
4. The method according to claim 3, wherein the step 3 is as follows:
step 3.1, using the diffusion iteration equation of the CDD image restoration model as follows:
Figure FDA0003238101780000041
in the formula (I), the compound is shown in the specification,
Figure FDA0003238101780000042
f is the flux field of the image I,
Figure FDA0003238101780000043
is divergence, delta t is a numerical time step, and n represents the iteration number;
3.2, solving the gradient value of the edge repairing model by adopting a half-point gradient difference method, defining the gray value at the half point to be obtained by averaging the gray values of two adjacent points, and then obtaining the image half point
Figure FDA0003238101780000044
The gradient value of (d) is calculated by:
Figure FDA0003238101780000045
in the formula (I), the compound is shown in the specification,
Figure FDA0003238101780000046
for image I at point
Figure FDA0003238101780000047
A gradient value of (a)xAnd IyRespectively are gradient values of the image to be restored in the x direction and the y direction;
then, the curvature value of the image is solved by using the half-point gradient value, and the second derivative value of the gradient difference of the image at the half point is calculated as follows:
Figure FDA0003238101780000048
in the formula (I), the compound is shown in the specification,
Figure FDA0003238101780000049
and
Figure FDA00032381017800000410
second derivatives of image I in the x and y directions, respectively;
the curvature value of the image to be repaired at the half point can be calculated by the following formula through the calculation method of the second derivative,
Figure FDA00032381017800000411
in the formula, κFIs the curvature value of the image I.
5. The method of claim 4, wherein the step 4 is implemented by using the curvature value κ of the image IFAnd curvature value k of non-maxima suppressed imageGVF，
Figure FDA0003238101780000051
Selecting a curvature value according to an equation (13) and calculating a half-point gradient value according to an equation (10), and taking the half-point gradient value as a parameter of the model to be brought into an equation (8) to carry out iterative solution on the model;
when the maximum iteration number n is reached, obtaining an edge image I(n)And thinning the image by using non-maximum value inhibition again, setting the pixel value of the edge point after thinning as 1, obtaining and outputting the final edge detection result.
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