CN113808150B - Edge detection new method capable of self-adaptive repair - Google Patents
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- 238000007670 refining Methods 0.000 claims description 8
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- G06T2207/00—Indexing scheme for image analysis or image enhancement
- G06T2207/30—Subject of image; Context of image processing
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Abstract
The invention discloses a new method for edge detection 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 differential operators, carrying out edge extraction on the segmented image by utilizing a Canny edge detection algorithm based on the fractional differential operators to obtain an optimal fractional order, further carrying out edge detection to finally obtain a binary image I only containing edges, calculating a GVF vector field based on a non-maximum suppressed image obtained by a Canny edge detection method of the fractional differential operators of the optimal fractional order, then calculating a curvature value of the image, calculating a curvature value of an 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 an edge point after refinement as 1 to obtain a final edge detection result. The invention solves the problem that the self-adaptive repair of the broken edge cannot be carried out in the existing edge detection.
Description
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 restoration.
Background
In the field of image processing, edge detection is widely used in practical engineering, and in particular, in the field of measurement based on image processing technology, is prominent. 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 still a Sobel operator, so that details of an image edge are difficult to capture, and meanwhile, due to non-maximum suppression and double-threshold detection, the edge detection result of the Canny algorithm has heavy edges, breakage and deletion, so that the accuracy of the detection result is seriously influenced. In recent years, scholars introduce fractional differential operators into the Canny algorithm, and although the edge detection precision of the Canny algorithm is improved through the fractional differential operators, the method aggravates the breakage of the edge. Therefore, how to detect the edge of the silicon single crystal by using a fractional differential Canny algorithm and adaptively repair the broken edge in the detection result so as to obtain a complete contour edge is very important.
Disclosure of Invention
The invention aims to provide a novel edge detection method capable of self-adaptively repairing, which solves the problem that the self-adaptively repairing of broken edges cannot be carried out in the existing edge detection.
The technical scheme adopted by the invention is that a novel edge detection method capable of self-adaptive repair is implemented according to the following steps:
step 1, image segmentation is carried out on an image shot by an image sensor, different fractional orders are brought into fractional differential operators, edge extraction is carried out on the segmented image based on the fractional differential operators by using a Canny edge detection algorithm, an optimal fractional order is obtained by using an evaluation function, edge detection is carried out on the image by using the optimal fractional order, and finally a binary image I only containing edges is obtained, namely, 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 non-maximum value suppressed image obtained by the Canny edge detection method based on the fractional differential operator of the optimal fractional order 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 binarized image I only containing edges, wherein the parameters comprise curvature values of the image I in the restoration process;
step 4, performing iterative restoration on the image I to be restored by using the curvature value obtained by the GVF field calculation and the curvature value of the image I in the restoration process;
and 5, refining the repaired image by using non-maximum suppression 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 specifically as follows:
step 1.1, image segmentation is carried out on an image shot by an image sensor;
by introducing fractional differential operators, the original 4-direction Sobel first-order differential operator is promoted to fractional differential operators according to G-L definition, and the promoted fractional differential operators are shown as follows:
in the method, in the process of the invention,fractional differential operators in the directions of 0, 45, 90 and 135 degrees respectively; v is the order of the fractional order differential operator;
sequentially selecting and bringing fractional orders in v E (0, 2) with a spacing of 0.2 into formulas (1) - (4) to obtain a plurality of groups of fractional order differential operators, and performing 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 as follows: 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 larger than the minimum distance between one inner edge point and one outer edge point under the same abscissa in all pixels, at the moment, the inner edge point and the outer edge point are considered to be single pixel edge points, the abscissa number meeting the condition is recorded as S (v), then the Lagrangian interpolation method is utilized to fit the S (v) -v, and finally the maximum value point of the S (v) is solved to be the optimal fractional order;
step 1.3, introducing the optimal fractional order obtained in the step 1.2 into the formulas (1) - (4) to obtain an optimal fractional order differential operator, and performing edge detection on the image through a Canny algorithm based on the optimal fractional order differential operator, wherein an obtained edge detection result is an extracted binarized image I only containing edges.
The step 2 is specifically as follows:
and (3) calculating a GVF vector field of the image after non-maximum suppression, which is obtained by a Canny edge detection method based on a fractional differential operator of the optimal fractional order according to the following iterative method:
wherein u is x (i, j, t+1) and u y (i, j, t+1) is the GVF vector magnitude in the x and y directions of the midpoint (i, j) of the t+1st iteration, respectively, i.eG is GVF vector field x (i, j) and G y (i, j) are gradients in x and y directions of the non-maxima suppressed image at point (i, j), respectively;
then with GVF vector fieldAs gradient values of the image, curvature values of the image are calculated using the gradient values, as follows:
wherein, kappa GVF The curvature value of the image is suppressed for non-maxima.
The step 3 is specifically as follows:
and 3.1, a diffusion iteration equation using a CDD image restoration model is as follows:
in the method, in the process of the invention,
f is the flux field of the image I,for the divergence, Δt is a numerical time step, and n represents the number of iterations;
step 3.2, solving gradient values of the edge restoration model, and defining gray values at half points by adopting a half-point gradient difference method, wherein the gray values of two adjacent points are averaged to obtain an image half-pointThe gradient value at this point is calculated by the following formula:
in the method, in the process of the invention,at the point +.>Gradient values at, I x And I y Gradient values of the image to be repaired in the x direction and the y direction respectively;
then, the curvature value of the image is solved by utilizing the half-point gradient value, and the second derivative value of the image at the half-point gradient difference is calculated as follows:
in the method, in the process of the invention,and->The second derivatives of the 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 calculation method of the second derivative,
wherein, kappa F Is the curvature value of image I.
Step 4 is specifically as follows, while using the curvature value κ of the image I F And a curvature value kappa of the non-maximum suppressed image GVF ，
Selecting a curvature value and calculating a half-point gradient value according to a formula (13) and a formula (10), and taking the half-point gradient value as a parameter of a model into a formula (8) to carry out iterative solution on the model;
after the maximum iteration number n is reached, obtaining an edge image I (n) The image is refined again by using non-maximum suppression, and the pixel value of the edge point after refinement is set to be 1, so that a final edge detection result is obtained and output.
The invention has the beneficial effects that the novel edge detection method capable of self-adaptive repair is characterized by inheriting the literature by providing the evaluation function suitable for the instance engineering scene [1] The edge detection precision of the multi-directional fractional differential operator in the method is high. And the CDD repair model is improved, and an edge repair model is provided, so that the model can accurately repair broken edges, and the integrity and vision of edge detection results are improvedThe sense of connectivity is of great significance to improving the edge detection accuracy.
Drawings
FIG. 1 is an image of a workpiece in a high Wen Gongre state;
FIG. 2 is an edge detection result of a workpiece image in a high Wen Gongre state using the present invention;
FIG. 3 is an edge detection result of a workpiece image in a high Wen Gongre state by a conventional Canny method;
FIG. 4 is a document showing the use of images of a workpiece in a high Wen Gongre state [1] And (5) detecting a result of the method edge.
Detailed Description
The invention will be described in detail below with reference to the drawings and the detailed description.
The invention discloses a novel edge detection method capable of self-adaptive repair, which is implemented according to the following steps:
step 1, image segmentation is carried out on an image shot by an image sensor, different fractional orders are brought into fractional differential operators, edge extraction is carried out on the segmented image based on the fractional differential operators by using a Canny edge detection algorithm, an optimal fractional order is obtained by using an evaluation function, edge detection is carried out on the image by using the optimal fractional order, and finally a binary image I only containing edges is obtained, namely, 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 specifically as follows:
step 1.1, image segmentation is carried out on an image shot by an image sensor;
by introducing fractional differential operators, the original 4-direction Sobel first-order differential operator is promoted to fractional differential operators according to G-L definition, and the promoted fractional differential operators are shown as follows:
in the method, in the process of the invention,and->Fractional differential operators in the directions of 0, 45, 90 and 135 degrees respectively; v is the order of the fractional order differential operator;
sequentially selecting and bringing fractional orders in v E (0, 2) with a spacing of 0.2 into formulas (1) - (4) to obtain a plurality of groups of fractional order differential operators, and performing 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 as follows: 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 larger than the minimum distance between one inner edge point and one outer edge point under the same abscissa in all pixels, at the moment, the inner edge point and the outer edge point are considered to be single pixel edge points, the abscissa number meeting the condition is recorded as S (v), then the Lagrangian interpolation method is utilized to fit the S (v) -v, and finally the maximum value point of the S (v) is solved to be the optimal fractional order;
step 1.3, introducing the optimal fractional order obtained in the step 1.2 into the formulas (1) - (4) to obtain an optimal fractional order differential operator, and performing edge detection on the image through a Canny algorithm based on the optimal fractional order differential operator, wherein an obtained edge detection result is an extracted binarized image I only containing edges.
Step 2, calculating GVF (Gradient Vector Flow) vector field by using the non-maximum value suppressed image obtained by the Canny edge detection method based on the fractional differential operator of the optimal fractional order in the step 1, and then calculating the curvature value of the image by taking GVF vector field as the gradient value of the image;
the step 2 is specifically as follows:
and (3) calculating a GVF vector field of the image after non-maximum suppression, which is obtained by a Canny edge detection method based on a fractional differential operator of the optimal fractional order according to the following iterative method:
wherein u is x (i, j, t+1) and u y (i, j, t+1) is the GVF vector magnitude in the x and y directions of the midpoint (i, j) of the t+1st iteration, respectively, i.eG is GVF vector field x (i, j) and G y (i, j) are gradients in x and y directions of the non-maxima suppressed image at point (i, j), respectively;
then with GVF vector fieldAs gradient values of the image, curvature values of the image are calculated using the gradient values, as follows:
wherein, kappa GVF The curvature value of the image is suppressed for non-maxima.
Step 3, calculating parameters in a CDD image restoration model of curvature driving diffusion (Curvature Driven Diffusions) by using a binarized image I only containing edges, wherein the parameters comprise curvature values of the image I in the restoration process;
the step 3 is specifically as follows:
and 3.1, a diffusion iteration equation using a CDD image restoration model is as follows:
in the method, in the process of the invention,
f is the flux field of the image I,for the divergence, Δt is a numerical time step, and n represents the number of iterations;
step 3.2, solving gradient values of the edge restoration model, and defining gray values at half points by adopting a half-point gradient difference method, wherein the gray values of two adjacent points are averaged to obtain an image half-pointThe gradient value at this point is calculated by the following formula:
in the method, in the process of the invention,at the point +.>Gradient values at, I x And I y Gradient values of the image to be repaired in the x direction and the y direction respectively;
then, the curvature value of the image is solved by utilizing the half-point gradient value, and the second derivative value of the image at the half-point gradient difference is calculated as follows:
in the method, in the process of the invention,and->The second derivatives of the 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 calculation method of the second derivative,
wherein, kappa F Is the curvature value of image I.
Step 4, performing iterative restoration on the image I to be restored by using the curvature value obtained by the GVF field calculation and the curvature value of the image I in the restoration process;
step 4 is specifically as follows, while using the curvature value κ of the image I F And a curvature value kappa of the non-maximum suppressed image GVF ，
Selecting a curvature value and calculating a half-point gradient value according to a formula (13) and a formula (10), and taking the half-point gradient value as a parameter of a model into a formula (8) to carry out iterative solution on the model;
after the maximum iteration number n is reached, obtaining an edge image I (n) The image is refined again by using non-maximum suppression, and the pixel value of the edge point after refinement is set to be 1, so that a final edge detection result is obtained and output.
And 5, refining the repaired image by using non-maximum suppression 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 Error Rate (OF), an Error Rate (ER), and a 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 of the quality factor 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 index calculations are as follows:
wherein S is c S is the number of correct pixels in the edge detection result total And S is detect Total pixel number d of real edge image and edge detection result respectively i For the shortest distance of the detected edge pixel point to the real edge, α is a penalty parameter, herein α=1/9, and the real edge is obtained empirically by means of off-line calibration.
Examples
The invention is applied to the problem of edge detection of a workpiece in a high Wen Gongre state, as shown in fig. 1.
First, the parameters of the present invention are set as follows: the iteration number of the GVF vector field is 5, a region with the vector amplitude of 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 experiment introduces the traditional Canny algorithm and the method of document [1] respectively to compare the detection results of the invention. The edge detection results of the workpiece image in the high Wen Gongre state by the three methods 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 detection results of the workpiece image in the high Wen Gongre state are shown in table 1. The three performance indexes of the traditional Canny method are the worst in the three methods, the omission factor of the invention 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 invention are obviously improved. Document [1]]Although the error rate is lower than the method, the omission rate is far higher than the invention, so the performance of the invention is better than that of the literature [1] Is a method of (2).
Table 1 detection results of workpiece image in high Wen Gongre state
| Method | OF | ER | FOM |
| The invention is that | 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] Jiang Chaohui, wu Qiaoqun, gui Weihua, poncirus Trifoliata, xie Yongfang. Blast furnace level contour adaptive detection based on fractional order multidirectional differential operators [ J ]. Automation journal, 2017,43 (12): 2115-2126.
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 (1)
1. The novel edge detection method capable of self-adaptive repair is characterized by comprising the following steps of:
step 1, image segmentation is carried out on an image shot by an image sensor, different fractional orders are brought into fractional differential operators, edge extraction is carried out on the segmented image based on the fractional differential operators by using a Canny edge detection algorithm, an optimal fractional order is obtained by using an evaluation function, edge detection is carried out on the image by using the optimal fractional order, and finally a binary image I only containing edges is obtained, namely, the pixel value corresponding to an edge point is 1, and the pixel value corresponding to a background point is 0;
the step 1 specifically comprises the following steps:
step 1.1, image segmentation is carried out on an image shot by an image sensor;
by introducing fractional differential operators, the original 4-direction Sobel first-order differential operator is promoted to fractional differential operators according to G-L definition, and the promoted fractional differential operators are shown as follows:
in the method, in the process of the invention,and->Fractional differential operators in the directions of 0, 45, 90 and 135 degrees respectively; v is the order of the fractional order differential operator;
sequentially selecting and bringing fractional orders in v E (0, 2) with a spacing of 0.2 into formulas (1) - (4) to obtain a plurality of groups of fractional order differential operators, and performing 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 as follows: 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 larger than the minimum distance between one inner edge point and one outer edge point under the same abscissa in all pixels, at the moment, the inner edge point and the outer edge point are considered to be single pixel edge points, the abscissa number meeting the condition is recorded as S (v), then the Lagrangian interpolation method is utilized to fit the S (v) -v, and finally the maximum value point of the S (v) is solved to be the optimal fractional order;
step 1.3, introducing the optimal fractional order obtained in the step 1.2 into the formulas (1) - (4) to obtain an optimal fractional order differential operator, and carrying out edge detection on the image by a Canny algorithm based on the optimal fractional order differential operator, wherein an obtained edge detection result is an extracted binarized image I only containing edges;
step 2, calculating a GVF vector field by using the non-maximum value suppressed image obtained by the Canny edge detection method based on the fractional differential operator of the optimal fractional order 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;
the step 2 specifically comprises the following steps:
and (3) calculating a GVF vector field of the image after non-maximum suppression, which is obtained by a Canny edge detection method based on a fractional differential operator of the optimal fractional order according to the following iterative method:
wherein u is x (i, j, t+1) and u y (i, j, t+1) is the GVF vector magnitude in the x and y directions of the midpoint (i, j) of the t+1st iteration, respectively, i.eG is GVF vector field x (i, j) and G y (i, j) are gradients in x and y directions of the non-maxima suppressed image at point (i, j), respectively;
then with GVF vector fieldAs gradient values of the image, curvature values of the image are calculated using the gradient values, as follows:
wherein, kappa GVF Suppressing the curvature value of the image for a non-maximum value;
step 3, calculating parameters in a curvature-driven diffusion CDD image restoration model by using a binarized image I only containing edges, wherein the parameters comprise curvature values of the image I in the restoration process;
the step 3 specifically comprises the following steps:
and 3.1, a diffusion iteration equation using a CDD image restoration model is as follows:
in the method, in the process of the invention,
f is the flux field of the image I,for the divergence, Δt is a numerical time step, and n represents the number of iterations;
step 3.2, solving gradient values of the edge restoration model, and defining gray values at half points by adopting a half-point gradient difference method, wherein the gray values of two adjacent points are averaged to obtain an image half-pointThe gradient value at this point is calculated by the following formula:
in the method, in the process of the invention,at the point +.>Gradient values at, I x And I y Gradient values of the image to be repaired in the x direction and the y direction respectively;
then, the curvature value of the image is solved by utilizing the half-point gradient value, and the second derivative value of the image at the half-point gradient difference is calculated as follows:
in the method, in the process of the invention,and->The second derivatives of the 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 calculation method of the second derivative,
wherein, kappa F Is the curvature value of the image I;
step 4, performing iterative restoration on the image I to be restored by using the curvature value obtained by the GVF field calculation and the curvature value of the image I in the restoration process;
said step 4 is specifically as follows, while using the curvature value κ of the image I F And a curvature value kappa of the non-maximum suppressed image GVF ，
Selecting a curvature value and calculating a half-point gradient value according to a formula (13) and a formula (10), and taking the half-point gradient value as a parameter of a model into a formula (8) to carry out iterative solution on the model;
after the maximum iteration number n is reached, obtaining an edge image I (n) Refining the image again by using non-maximum value inhibition, setting the pixel value of the edge point after refining as 1, obtaining a final edge detection result and outputting the final edge detection result;
and 5, refining the repaired image by using non-maximum suppression again, and setting the pixel value of the edge point after refining as 1 to obtain a final edge detection result.
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