CN110163881B - Fractional order edge detection method for noise pollution image - Google Patents
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Abstract
The invention discloses a fractional order edge detection method of a noise pollution image, which is characterized by comprising the following steps: the method comprises the following steps: denoising the noise pollution gray level image; the denoised image enters a two-dimensional fractional order differential filter for edge extraction; the denoising processing method comprises the following steps: convolving the gray level image with a fractional order integral filter or a Gaussian filter to obtain a filtering image; the method for extracting the edge comprises the following steps: and (4) convolving the denoised image with a two-dimensional fractional order differential filter mask in the horizontal direction and the vertical direction to obtain a gradient image. The invention adopts the improved two-dimensional fractional order integral filter and the two-dimensional fractional order differential filter, and realizes the characteristics of strong robustness, edge positioning accuracy and edge enhancement of noise when the two are simultaneously used for detecting the edge of a noise image.
Description
Technical Field
The invention relates to the field of image edge detection, in particular to a fractional order edge detection method for a noise pollution image.
Background
Most of the existing edge detection methods adopt integer order difference, and mainly comprise a Robert operator, a Prewitt operator, a Sobel operator, a Canny operator, a Laplace operator and the like. The integer order difference has the advantage of directionality, but because noise and object edges belong to high-frequency signals, when the edge detection is performed on a noise image, the existing algorithm cannot effectively compromise the noise resistance and the edge detection accuracy.
Canny in a computerized approach to edge detection discloses an edge detection operator optimized between noise immunity and accurate positioning, which comprises four steps:
A. smoothing an image
B. Calculating the gradient amplitude in the horizontal direction and the vertical direction of the filtered image
C. Non-maximum suppression of gradient amplitudes
D. Processing and connecting edges with dual thresholds
The Canny operator has fine detection edges, accurate positioning and easy noise interference, generates false edges, and is transitionally dependent on the selection of a threshold, more texture details can be reserved if the selection of a high threshold is too small, and part of the edges can be lost if the selection of a low threshold is too large.
Mathieu B et al, in the article "Fractional differentiation for edge detection", disclose a Fractional order differential mask operator for detecting edges by using an extremum of a gray difference between adjacent upper and lower edge pixels; the domain average is first searched to smooth the noise and then the gradient is calculated.
The CRONE algorithm has certain immunity to noise, but is still limited to the differential principle, the conflict between the detection precision and the noise immunity cannot be solved well, the edge image extracted when the noise image is subjected to edge detection still contains a great deal of noise, and the processing effect is not ideal particularly for images polluted by salt and pepper noise.
Pan X et al, in the document Complex Derivative Edge Detection and Its applications to Edge Detection, propose a Complex Derivative Edge Detection operator, which is the CRONE operator and the Canny operator [3] The combination and improvement of (2) comprises four steps of (a) performing convolution on the fractional order integral filter and the image; b. carrying out convolution on the image subjected to integral filtering and the fractional order differential filter; c. non-maxima suppression; d. and (4) carrying out double-threshold processing.
The composite derivative operator firstly proposes that first-order fractional differentiation and integration are simultaneously used in image edge processing, the interference of part of noise on the noise in the image after edge detection, the target interior and the background area can resist the interference of part of noise, but the image after non-maximum value suppression and threshold processing has discontinuous target edge and the edge is sensitive to the noise.
Fractional calculus can enhance high-frequency signals and keep the characteristics of low-frequency signals, and CRONE operators and compound derivative operators make certain breakthrough in edge detection, but can not well solve the conflict between detection precision and noise resistance.
Disclosure of Invention
The invention aims to: aiming at the existing problems, the fractional order edge detection method for the noise pollution image can effectively compromise the noise immunity and the edge detection accuracy, has strong noise immunity and high detection accuracy, can extract texture details of a target, enhances the edge and has high running speed.
The technical scheme adopted by the invention is as follows:
the invention discloses a fractional order edge detection method of a noise pollution image, which comprises the following steps: denoising the noise pollution gray level image; and (4) enabling the denoised image to enter a two-dimensional fractional order differential filter for edge extraction.
Further, the denoising processing method includes: and (4) convolving the gray level image with a fractional order integral filter or a Gaussian filter to obtain a filtering image.
Further, the fractional order integration filter adopts a two-dimensional fractional order integration filter.
Further, the two-dimensional fractional order integral filter
Wherein, F x 、F y Respectively a horizontal direction filtering template and a vertical direction filtering template, tau epsilon (-1, 0) is an integral order, r is the length of the filtering template, a positive integer larger than 1 is taken, and i is a positive integer smaller than or equal to r.
Further, the method for edge extraction includes: and (4) convolving the denoised image with the masks of the two-dimensional fractional order differential filters in the horizontal direction and the vertical direction to obtain a gradient image.
Further, the method also comprises the following steps: and carrying out binarization processing on the gradient image to obtain an edge detection image.
Further, the two-dimensional fractional order differential filter comprises a horizontal template Mx and a vertical template My,
wherein, a k Is a real number of coefficients of a binomial form,
Further, the thickness degree of the edge is adjusted by changing the template radius of the dimensional fractional order integral filter; and the degree of noise reduction and the edge strength are controlled by adjusting the integral order and the differential order.
In summary, due to the adoption of the technical scheme, the invention has the beneficial effects that: the method is improved on the basis of a CRONE operator and a composite derivative operator;
firstly, convolving a noise image with a two-dimensional fractional order integration filter, and smoothing noise to the maximum extent by controlling an integration order aiming at different images; then convolving the denoised image with fractional order differential filters in the horizontal and vertical directions to obtain a gradient and obtain an image after edge extraction; in the differential filtering process, edge positioning and edge enhancement are realized by controlling the differential order;
when the noise image is subjected to edge detection, the interference of noise can be greatly weakened by coordinating the second-order differential order and the integral order, and compared with the commonly used integral-order Prewitt operator, sobel operator, canny operator, fractional-order CRONE operator and composite derivative operator at present, the noise enhancement effect is obviously improved in the edge detection accuracy and the noise resistance performance of the image subjected to edge detection.
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The invention will now be described, by way of example, with reference to the accompanying drawings, in which:
FIG. 1 is a flowchart illustrating a fractional order edge detection method for a noise-contaminated image according to the present invention.
Fig. 2 is a flowchart of edge detection on a two-dimensional color image in the embodiment.
Fig. 3 is a schematic diagram of a horizontal template of a two-dimensional fractional order differential filter of the present invention.
Fig. 4 is a schematic diagram of a vertical template of a two-dimensional fractional order differential filter of the present invention.
Fig. 5, 6 and 7 are control variable comparison graphs of a fractional order edge detection method of a noise contaminated image according to the present invention.
Detailed Description
All of the features disclosed in this specification, or all of the steps in any method or process so disclosed, may be combined in any combination, except combinations of features and/or steps that are mutually exclusive.
Any feature disclosed in this specification (including any accompanying claims, abstract) may be replaced by alternative features serving equivalent or similar purposes, unless expressly stated otherwise. That is, unless expressly stated otherwise, each feature is only an example of a generic series of equivalent or similar features.
The first embodiment is as follows: a fractional order edge detection method of a noise pollution image comprises the following steps: denoising the noise pollution gray level image; and (4) enabling the denoised image to enter a two-dimensional fractional order differential filter for edge extraction.
Example two: in this embodiment, the method for denoising a noise-contaminated grayscale image includes: convolving the gray level image with a fractional order integral filter to obtain a filtering image; the fractional order integration filter is preferably a two-dimensional fractional order integration filter.
Example three: in this embodiment, the method for edge extraction using a two-dimensional fractional order differential filter includes: convolving the denoised image with a two-dimensional fractional order differential filter mask in the horizontal direction and the vertical direction to obtain a gradient image;
example four: compared with the three phases of the embodiment, in the embodiment, also disclosed are: after the gradient image is obtained, the gradient image is subjected to binarization processing to obtain an edge detection image.
Example five: as shown in fig. 1, in an embodiment, a fractional order edge detection method of a noise contaminated image is disclosed: the noise image is denoised by an integral filter, and the image after integral filtering enters a differential filter for edge extraction.
Example six: in an embodiment, the fractional order integration filter employs a two-dimensional fractional order integration filter; two-dimensional fractional order integral filter
Wherein, F x 、F y Respectively a horizontal direction filtering template and a vertical direction filtering template, tau epsilon (-1, 0) is an integral order, r is the length of the filtering template, a positive integer larger than 1 is taken, and i is a positive integer smaller than or equal to r.
The invention relates to a fractional order integral filtering process and a fractional order differential filtering process, which briefly summarize the derivation process: and (3) a two-dimensional fractional order integral filter derivation process:
the fractional order integral of the τ order (τ e C, R (τ) ≧ 0.) of any integrable function f (x) can be expressed as:
I τ f(x)＝f(x)*I τ δ(x)，
wherein f (x) is a one-dimensional function, I τ Is the integral of order τ, δ (x) is the Dirac pulse function, I τ δ (x) is a one-dimensional τ order fractional integration filter, which has the following formula:
wherein τ is a fractional order of integration.
According to the characteristics of a two-dimensional gray image, a two-dimensional fractional order filtering template is deduced by combining a filter formula, wherein the filtering templates in the horizontal direction and the vertical direction are expressed as follows:
wherein, F x 、F y Respectively a horizontal direction filtering template and a vertical direction filtering template.
Convolving the horizontal filtering template with the vertical filtering template (the convolution sign is
) Obtaining the two-dimensional fractional order integral filter of the operator of the invention:
then, the τ order integral of the two-dimensional image a is:
wherein tau belongs to (-1, 0) as an integral order, r is the length of a filtering template, and a positive integer greater than 1 is taken; 3 × 3 template when r = 2; when r =3, it is a 5 × 5 template; i is a positive integer of r or less, and when i = r, F x ＝0，F y =0, the template size is typically (2 r-1) × (2 r-1).
A two-dimensional fractional order differential filter derivation process:
the first derivative in the positive x-axis direction for an arbitrary derivable function f (x) is:
defining the conversion operator q to satisfy:
q -1 f(x)＝f(x-h)
then it is determined that,
therefore, the v-order derivative of f (x) in the positive x-direction is:
another derivative form of the known derivative function f (x) is:
at this time, the conversion operator q satisfies:
qf(x)＝f(x+h)
then it is determined that,
the v-order derivative of f (x) in the positive x-direction is:
from the two equations for the v-order derivative of f (x) in the positive x-direction:
developed by a Newton binomial equation:
wherein, the first and the second end of the pipe are connected with each other,
similarly, the derivative is obtained along the negative direction of x,
the v-order derivative of f (x) can be expressed as:
wherein the content of the first and second substances,
the two-dimensional fractional order differential operator mask is:
horizontal template
X ν ＝[+a m ...+a k ...+a 1 0-a 1 ...-a k ...-a m ]
Vertical template
Y v ＝[+a m ...+ak...+a 1 0-a 1 ...-a k ...-a m ] T
Wherein the content of the first and second substances,
wherein n is a differential order, and n is between 1 and 2 to improve the edge detection accuracy, and n is between-1 and 1 to improve the immunity to noise.
The invention uses the difference thought according to the horizontal template and the vertical template mask, namely, the gray difference of the upper, lower, left and right adjacent points of a pixel point is solved, the edge of an image is detected by solving an extreme value, and a two-dimensional template of fractional order differential of an FIDM operator is deduced: FIDM horizontal template M x And FIDM vertical template M y As shown in fig. 3 and 4, wherein a k Is a real binomial coefficient
When two groups of 3 x 3 matrixes are taken for detection, namely the transverse direction and the longitudinal direction, the matrixes are convolved with the image I after integral filtering, G x 、G y Respectively representing the images detected by the transverse and longitudinal edges, and the formula is as follows：
Example seven: as shown in fig. 2, in an embodiment, the step of performing edge detection on a two-dimensional image according to the present invention includes: inputting a two-dimensional color image containing noise; converting the input color image into a gray image through a gray algorithm formula; convolving the gray image with an integral filter to obtain an integral filtering image; convolving the integral filtering image with fractional order differential filtering masks in the horizontal direction and the vertical direction to obtain a gradient image; carrying out binarization processing on the gradient image to obtain an edge detection image;
the method specifically comprises the following steps:
the first step, converting the two-dimensional color image into a gray image:
I 1 (x，y)＝R(x，y)*0.299+G(x，y)*0.587+B(x，y)*0.114
wherein, I 1 (x, y) represents a gray value at a two-dimensional image coordinate (x, y), and R (x, y), G (x, y), B (x, y) represent three channel components of red, green, and blue at the coordinate (x, y);
and secondly, performing fractional order integral filtering operation on the gray level image:
in the formula, fx and Fy are respectively horizontal and vertical integral filtering templates, I 2 Is an integrated filtered image; thirdly, performing fractional order differential mask calculation on the integrated image:
wherein, M x And M y The horizontal and vertical forms shown in fig. 3 and 4, respectively.
Step four, calculating the gradient size:
obtaining a gradient value through differential filtering results in the horizontal direction and the vertical direction to obtain an edge detection result G;
and fifthly, performing binarization processing on the edge detection result, wherein a binarization processing formula is as follows:
wherein, T is a binary threshold value, and I is an edge detection final result.
Example eight:
in the above technical implementation process, the fractional order integration filter in the specific implementation process can be replaced by a gaussian filter, but the effect of removing noise by the gaussian filter is not as good as that of the fractional order integration filter, so the fractional order integration filter is a preferable scheme.
In the fractional order edge detection of the noise pollution image, as shown in fig. 5, in the differential filtering process, the radius r =2 of an integral template and the integral order τ =0.3 are controlled, and the edge location and the edge intensity are controlled by adjusting the differential order n; as shown in fig. 6, the radius r =2 of the integral template and the differential order n =0.7 are controlled, and the degree of noise reduction is controlled by adjusting the integral order τ; as shown in fig. 7, the degree of edge thickness is adjusted by changing the radius r of the integration template by controlling the integration order τ =0.3 and the differentiation order n = 0.7; by coordinating the differentiation order and the integration order, the interference of noise can be greatly weakened.
The invention is not limited to the foregoing embodiments. The invention extends to any novel feature or any novel combination of features disclosed in this specification, and to any novel method or process steps or any novel combination of steps disclosed.
Claims (3)
1. A fractional order edge detection method of a noise pollution image is characterized by comprising the following steps: the method comprises the following steps:
denoising the noise pollution gray level image: convolving the gray level image with a fractional order integral filter to obtain an image after integral filtering
Wherein the fractional order integration filter adopts a two-dimensional fractional order integration filter
= 
，
Respectively a horizontal direction filtering template and a vertical direction filtering template,
in order to convolve the symbols with each other,
is a gray-scale image and is,
selecting a positive integer larger than 1 and i as a positive integer smaller than or equal to r, wherein the epsilon (-1, 0) is an integral order, r is the length of a filtering template;
the denoised image enters a two-dimensional fractional order differential filter for edge extraction: the denoised image is two-dimensionally related to the horizontal direction and the vertical directionPerforming convolution on the mask of the fractional order differential filter to obtain a gradient image; the method specifically comprises the following steps: and (3) performing fractional order differential mask calculation on the integrated image:
，
wherein, in the step (A),
is a horizontal template, and is characterized in that,
is a vertical template; calculating the gradient to obtain the edge detection result
And carrying out binarization processing on the edge detection result to obtain a final edge detection result.
2. The method of fractional order edge detection of noise contaminated images according to claim 1, characterized in that: the horizontal template
And a vertical template
Respectively as follows:
3. The method of fractional order edge detection of noise contaminated images according to claim 1 or 2, characterized by: adjusting the thickness degree of the edge by changing the template radius of the two-dimensional fractional order integral filter; and the degree of noise reduction and the edge strength are controlled by adjusting the integral order and the differential order.
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