CN103247047A - Image edge detection method based on fractional order partial differential - Google Patents
Image edge detection method based on fractional order partial differential Download PDFInfo
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Abstract
The invention discloses an image edge detection method based on fractional order partial differential, which comprises the following steps: the Sobel operator and a 3*3 pixel neighborhood with the gray-scale function of F (x, y) are subjected to convolution; the convolution sum is subjected to central difference to obtain an integral order differential expression; the integral order differential expression is replaced by a v order differential expression; based on definition of fractional differential, first three items of the fractional differential expression of a digital image substitute values in the v order differential expression; and different results can be obtained through regulation parameter, namely the differential order v. The method can satisfactorily extract edge contour information, has an excellent effect on texture detail detection, is superior to conventional edge detection methods, and satisfactorily achieves the purpose of image edge detection.
Description
Technical field
The present invention relates to the Image Edge-Detection field, relate in particular to a kind of method for detecting image edge based on the fractional order partial differential.
Background technology
Image Edge-Detection is one of important topic of Digital Image Processing research field, and existing method for detecting image edge is more, and has relative merits separately.
Carrying out rim detection with the Sobel operator is a kind of of partial differential method rim detection, has not been a kind of new edge detection method.Its basic detection principle is directly to utilize horizontal gradient operator and vertical gradient operator to calculate this pixel value, choosing suitable threshold carries out emulation experiment and just can obtain the result, this method can realize soon on Matlab software, and ready-made program code is arranged.Be with the code typing in this method implementation procedure, even copy to paste and just can finish.But the effect that this method realizes is unsatisfactory.
As a kind of popularization of integer rank differential theory, the fractional order differential theory had applied to the image processing rapidly in recent years, and obtained certain achievement.Possessing on the differential basis, integer rank, and definition and the character of fractional order differential have been grasped, and the fractional order differential image is handled relevant document, important references documents such as " based on the rim detection of fractional order differential ", " based on the figure image intensifying of fractional order differential ", " based on the image denoising new model of fractional order partial differential " particularly, after understanding the fractional order differential image processing method, we combine fractional order differential and derive and make new advances with the Sobel operator rim detection model.
We know that the anti-noise ability of Sobel operator is better, can understand the fractional order differential computing can keep image as much as possible when carrying out Image Edge-Detection grain details by read documents.
But the unsatisfactory problem of detection effect that existing method for detecting image edge exists, particularly detected image edge and grain details exist can be improved aspect.
Summary of the invention
The object of the present invention is to provide a kind of method for detecting image edge, this method is effective, can not only quite good detecting go out edge of image, can also detect a large amount of grain details.
For reaching this purpose, the present invention by the following technical solutions:
A kind of method for detecting image edge based on the fractional order partial differential may further comprise the steps:
A, with Sobel operator and gray scale function be F (x, 3 * 3 neighborhood of pixels y) are done convolution;
B, obtain integer rank differential expressions with convolution with central difference again;
C, integer rank differential is replaced with v rank differential;
D, from the definition of fractional order differential, in the first three items substitution v rank differential expressions with the fractional order differential expression formula of digital picture, and can obtain different results by regulating parameter differential exponent number v.
Preferably, integer rank differential is replaced with v rank differential among the described step C, wherein v is greater than 0 and less than 1.
Preferably, integer rank differential is replaced with v rank differential among the described step C, wherein v equals at 0.7 o'clock, and effect is best.
Beneficial effect of the present invention is: this kind extracts edge contour information well based on the method for detecting image edge of fractional order partial differential, detection effect to grain details is also fine, be better than existing other several edge detection methods, reach the purpose of Image Edge-Detection well.
Description of drawings
Fig. 1 is new fractional order row gradient and the row gradient former of the embodiment of the invention;
Fig. 2 is the corresponding differential mask of the embodiment of the invention;
Fig. 3 is the rim detection rose figure of the different differential exponent numbers of new model of the embodiment of the invention;
Fig. 4 is new model and other edge detection methods experiment contrast palace figure of the embodiment of the invention;
Fig. 5 be the embodiment of the invention to the girl figure lab diagram that superposes;
Fig. 6 is the palace figure rim detection objective evaluation index of the embodiment of the invention.
Embodiment
Further specify technical scheme of the present invention below in conjunction with accompanying drawing and by embodiment.
Be that (x, 3 * 3 neighborhood of pixels y) are done convolution to F, and then obtain integer rank differential expressions with convolution with central difference with Sobel operator and gray scale function at first.Again integer rank differential is replaced (0＜v＜1) with v rank differential, at last from the definition of fractional order differential, in the first three items substitution v rank differential expressions with the fractional order differential expression formula of digital picture, and can obtain different experimental results by regulating parameter differential exponent number v.This has just obtained the Image Edge-Detection new model based on the fractional order partial differential, new fractional order row gradient and row gradient former such as Fig. 1, corresponding differential mask such as Fig. 2.
At first experimentize by choosing different differential exponent number v, as shown in Figure 3.(a) being original image, (b)～(f) is that this paper model is chosen the edge detection results that different fractional order parameters obtains.When 0＜v＜1, experiment effect improves gradually with the increase of parameter v; Be not difficult to find out that when v=0.7, experiment effect is best, can not only quite good detecting go out edge of image, can also detect a large amount of grain details, shown in Fig. 3 (d).
As can be seen from Figure 4, Sobel operator, Canny operator, LOG operator edge detection method shortcoming separately are not easy to overcome, and the rim detection effect is relatively poor; Existing [8] are that the definition with the fractional order differential method defines the mask operator and carries out Image Edge-Detection as template, though the fractional order differential method can better detect grain details, but the lifting to some edge is not enough, therefore easy lost part edge.New model can extract edge contour information well, and is also fine to the detection effect of grain details, is better than existing other several edge detection methods, reaches the purpose of Image Edge-Detection well.
Below will continue to do the validity of proving new method, be the accuracy that outline map after example will detect and original graph superpose to verify the new method bearing accuracy with girl figure.From the result of Fig. 5 as can be seen, new method is accurate to the edge detection and location.
Below also will come review new initiative to the superiority of rim detection from objective experimental data.At the objective evaluation of rim detection, objective evaluation standard commonly used has linear connection degree L, fallout ratio N and loss F.The connection degree L of efficient frontier is more high, and the edge evaluation is more high; Fallout ratio N is more little, and the edge evaluation is more high; Loss F is more little, and the edge evaluation is more high.3 indexs of objective evaluation are combined, define new edge evaluation tolerance M
e, M
eWeighted mean by 3 indexs obtains, and is shown below.
M
e=α L+ β (1-N)+γ (1-F) is wherein: alpha+beta+γ=1, α, β, γ three numbers represent that the different evaluation index is to estimating the influence degree of tolerance.
We are the example contrast that experimentizes with palace figure, and we might as well get
Result of calculation as shown in Figure 6.Can draw objectively from Fig. 6,3 evaluation indexes of new model rim detection all are better than all the other SOME METHODS, and loss F is 0, can well detect the edge of image grain details; Compare with additive method, the linearity connection degree L of this method model is higher, and fallout ratio N is lower, on the basis of fractional order differential certain improvement is arranged, and obviously is better than existing integer rank differential algorithm.
The above; only for the preferable embodiment of the present invention, but protection scope of the present invention is not limited thereto, and anyly is familiar with the people of this technology in the disclosed technical scope of the present invention; the variation that can expect easily or replacement all should be encompassed within protection scope of the present invention.Therefore, protection scope of the present invention should be as the criterion with the protection domain of claim.
Claims (3)
1. the method for detecting image edge based on the fractional order partial differential is characterized in that, may further comprise the steps:
A, with Sobel operator and gray scale function be F (x, 3 * 3 neighborhood of pixels y) are done convolution;
B, obtain integer rank differential expressions with convolution with central difference again;
C, integer rank differential is replaced with v rank differential;
D, from the definition of fractional order differential, in the first three items substitution v rank differential expressions with the fractional order differential expression formula of digital picture, and can obtain different results by regulating parameter differential exponent number v.
2. a kind of method for detecting image edge based on the fractional order partial differential as claimed in claim 1 is characterized in that, integer rank differential is replaced with v rank differential among the described step C, and wherein v is greater than 0 and less than 1.
3. a kind of method for detecting image edge based on the fractional order partial differential as claimed in claim 1 is characterized in that, integer rank differential is replaced with v rank differential among the described step C, and wherein v equals 0.7.
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| CN103927725A (en) * | 2014-05-07 | 2014-07-16 | 哈尔滨工业大学 | Movie nuclear magnetic resonance image sequence motion field estimation method based on fractional order differential |
| CN104680548A (en) * | 2015-03-20 | 2015-06-03 | 福州大学 | Omnidirectional M-type kinetocardiogram detection method |
| CN107223266A (en) * | 2017-04-27 | 2017-09-29 | 香港应用科技研究院有限公司 | Kernel approximation for the fractional order differential operator of rim detection |
| CN107424121A (en) * | 2017-06-30 | 2017-12-01 | 中原智慧城市设计研究院有限公司 | A kind of blurred picture ultra-resolution ratio reconstructing method based on fractional order differential |
| WO2018196018A1 (en) * | 2017-04-27 | 2018-11-01 | Hong Kong Applied Science and Technology Research Institute Company Limited | Kernel approximation on fractional differential operator for edge detection |
| CN110599509A (en) * | 2019-08-02 | 2019-12-20 | 西安理工大学 | Edge detection method based on eight-direction fractional order differential operator |
| CN111402204A (en) * | 2020-02-26 | 2020-07-10 | 哈尔滨工业大学 | Chip appearance defect detection method based on multi-order fractional order wavelet packet transformation |
| CN111724318A (en) * | 2020-06-15 | 2020-09-29 | 石家庄铁道大学 | Image denoising method based on mixed high-order partial differential equation model |
| CN112179813A (en) * | 2020-08-26 | 2021-01-05 | 清华大学 | Liquid contact angle on-line measurement method based on experimental image |
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Cited By (15)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN103927725A (en) * | 2014-05-07 | 2014-07-16 | 哈尔滨工业大学 | Movie nuclear magnetic resonance image sequence motion field estimation method based on fractional order differential |
| CN103927725B (en) * | 2014-05-07 | 2017-04-26 | 哈尔滨工业大学 | Movie nuclear magnetic resonance image sequence motion field estimation method based on fractional order differential |
| CN104680548A (en) * | 2015-03-20 | 2015-06-03 | 福州大学 | Omnidirectional M-type kinetocardiogram detection method |
| US10210616B2 (en) | 2017-04-27 | 2019-02-19 | Hong Kong Applied Science And Technology Research Institute Co., Ltd. | Kernal approximation on fractional differential operator for edge detection |
| WO2018196018A1 (en) * | 2017-04-27 | 2018-11-01 | Hong Kong Applied Science and Technology Research Institute Company Limited | Kernel approximation on fractional differential operator for edge detection |
| CN107223266A (en) * | 2017-04-27 | 2017-09-29 | 香港应用科技研究院有限公司 | Kernel approximation for the fractional order differential operator of rim detection |
| CN107223266B (en) * | 2017-04-27 | 2020-07-07 | 香港应用科技研究院有限公司 | Kernel approximation of fractional order differential operators for edge detection |
| CN107424121A (en) * | 2017-06-30 | 2017-12-01 | 中原智慧城市设计研究院有限公司 | A kind of blurred picture ultra-resolution ratio reconstructing method based on fractional order differential |
| CN110599509A (en) * | 2019-08-02 | 2019-12-20 | 西安理工大学 | Edge detection method based on eight-direction fractional order differential operator |
| CN110599509B (en) * | 2019-08-02 | 2021-10-08 | 西安理工大学 | Edge detection method based on eight-direction fractional order differential operator |
| CN111402204A (en) * | 2020-02-26 | 2020-07-10 | 哈尔滨工业大学 | Chip appearance defect detection method based on multi-order fractional order wavelet packet transformation |
| CN111402204B (en) * | 2020-02-26 | 2021-07-06 | 哈尔滨工业大学 | Chip appearance defect detection method based on multi-order fractional order wavelet packet transformation |
| CN111724318A (en) * | 2020-06-15 | 2020-09-29 | 石家庄铁道大学 | Image denoising method based on mixed high-order partial differential equation model |
| CN111724318B (en) * | 2020-06-15 | 2022-04-08 | 石家庄铁道大学 | Image denoising method based on mixed high-order partial differential equation model |
| CN112179813A (en) * | 2020-08-26 | 2021-01-05 | 清华大学 | Liquid contact angle on-line measurement method based on experimental image |
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Application publication date: 20130814 |