CN114359076A - Self-adaptive weighted Gaussian curvature filtering method based on image edge indication function - Google Patents

Self-adaptive weighted Gaussian curvature filtering method based on image edge indication function Download PDF

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CN114359076A
CN114359076A CN202111576705.4A CN202111576705A CN114359076A CN 114359076 A CN114359076 A CN 114359076A CN 202111576705 A CN202111576705 A CN 202111576705A CN 114359076 A CN114359076 A CN 114359076A
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邢远秀
徐红阳
李军贤
龚谊承
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Wuhan University of Science and Engineering WUSE
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Abstract

The invention provides an adaptive weighted Gaussian curvature filtering method based on an image edge indication function, which improves the Gaussian curvature filtering algorithm in the curvature filtering algorithm, adopts the edge indication function to construct an adaptive fractional order-integer order energy functional and a local weighted projection operator, and adaptively and accurately controls the iterative update of the weighted projection operator through a minimized energy functional, thereby improving the denoising performance and better keeping the texture details of the image. The invention adopts a self-adaptive mode to adjust the fractional order and the weight of each item in the energy functional, can accurately control the iterative update of the projection operator, and effectively prevents the image from denoising incompletely or being smoothed excessively.

Description

Self-adaptive weighted Gaussian curvature filtering method based on image edge indication function
Technical Field
The invention relates to the technical field of digital image processing, in particular to an adaptive weighted Gaussian curvature filtering method based on an image edge indication function.
Background
Noise often appears as isolated pixel points or pixel blocks causing strong visual effects on images, and subsequent processing tasks such as image analysis and understanding are directly influenced. The purpose of image denoising is to reduce noise in an image and simultaneously keep edge texture details of the image from being damaged as much as possible, but denoising and edge maintenance are often contradictory processes, and how to find a better balance point on noise removal and detail preservation is a key point of image denoising research.
The current image denoising method mainly comprises methods based on deep learning, transform domain, sparse dictionary, non-local self-similar prior, partial differential equation and the like. The image denoising method based on deep learning has a good effect, but needs a large number of noise image and clean image sample pairs as training data, and the denoising performance is greatly influenced under the condition that a clean image is difficult to obtain. Transform domain based denoising methods rely on transform models and thresholds and tend to result in excessive smoothing of edges and texture portions. The sparse dictionary-based denoising method needs to construct an over-complete dictionary, and the quality of the dictionary directly influences the denoising performance. The denoising method based on the non-local self-similar prior generally utilizes redundant information existing in an image to remove noise, and the algorithm has a good denoising effect on Gaussian noise under the condition of known noise intensity, but has a poor denoising effect on salt-pepper noise, and has high algorithm complexity and low denoising efficiency.
The denoising method based on the partial differential equation restrains image information through a minimum energy function, and is a popular image denoising method in recent years due to the characteristics of local self-adaption, easy numerical value realization and the like. The model based on anisotropic diffusion can better solve the contradiction between edge preservation and denoising, but has poor denoising effect and incomplete noise removal when isolated noise or noise intensity is high. The denoising method based on the total variation model is simple, noise can be removed, meanwhile edge textures can be effectively protected, the image is regarded as a segmented continuous function in a bounded variation space through a classical Total Variation (TV) method, the purpose of smooth denoising is achieved through minimizing an image energy function, a fractional order total variation regularization term, an integer order total variation regularization term and a tight frame sparse regularization term are added to an energy functional of the subsequent total variation denoising model, and sparsity of the denoised image is improved. Although the fully-variant denoising model can well represent the image edge, the method is long in time consumption, and the denoised image is easy to generate step artifacts. In order to improve the denoising performance, some algorithms adopt a full-variant model of gaussian curvature or differential curvature, such as local weighted gaussian curvature as a variant regularization term, or adopt fast fourier transform to solve the involved partial differential equation problem in curvature filtering, but the algorithms need to explicitly calculate the gradient of an energy functional and have slow convergence in minimizing the energy functional. Then some algorithms improve the denoising efficiency by solving an approximate solution of the variation problem, for example, by constructing a filtering projection operator, curvature filtering is performed on the image by implicitly utilizing the curvature information of the image, then some algorithms modify the projection operator and use local variance to correct the energy function of the regularization term to enhance the denoising capability, and some algorithms adopt a median gray level similarity function to weight the curvature projection operator to rapidly reduce the curvature filtering energy. The algorithm can realize rapid blind image denoising without knowing the noise intensity, but does not distinguish the noise points and the edge pixel points, so that the noise points and the edge pixel points are influenced mutually, and meanwhile, under the condition of high noise intensity, the algorithm has the problem of incomplete denoising or excessively smooth edges.
Disclosure of Invention
Aiming at the existing technical problems, the invention aims to provide an adaptive weighted Gaussian curvature filtering method based on an image edge indication function, which improves the Gaussian curvature filtering algorithm in the curvature filtering algorithm, adopts the edge indication function to construct an adaptive fractional order-integer order energy functional and a local weighted projection operator, and adaptively and accurately controls the iterative update of the weighted projection operator through the minimized energy functional, thereby improving the denoising performance and better keeping the texture details of the image.
The technical scheme of the invention is an adaptive weighted Gaussian curvature filtering method based on an image edge indication function, which comprises the following steps:
step 1, performing image space decomposition on a current noise image to obtain four types of disjoint and staggered areas, calculating an edge indicated value of each pixel point, and calculating the weight of a neighborhood pixel of a central pixel point according to the edge indicated value;
step 2, selecting triangular tangent planes of the central pixel points to construct Gaussian weighted projection operators, and calculating weighted projection distances from the central pixel points to M tangent planes according to the pixel weights in the step 1;
step 3, selecting the minimum projection distance to update the central pixel point according to the weighted projection distance calculated in the step 2, and finishing one-time updating of the image after all pixel points in the image are updated;
and 4, calculating the total energy of the denoised image obtained in the step 3 by adopting a self-adaptive Gaussian energy functional formula, if the total energy is less than the total energy of the image before updating, turning to the step 1, otherwise, stopping updating, and outputting the denoised image.
Further, in step 1, a curvature filtering algorithm is used to perform image space decomposition on the input noise image U, and the image is divided into white circles omegaWCBlack circle omegaBCWhite triangle omegaWTAnd black triangle omegaBTFour types of disjoint and interleaved regions eliminate dependencies between neighboring pixels.
Further, the two-dimensional image edge indication value D of the pixel point p of each region is defined in the step 1pAnd normalized edge indicator values
Figure BDA0003425427400000021
Comprises the following steps:
Figure BDA0003425427400000022
wherein, the image U is a noise image,
Figure BDA0003425427400000031
representing the second derivative of the image U in the direction of the gradient, UxFor the first derivative of the image in the x-direction, UyFor the first derivative of the image in the y-direction, UxxFor the second derivative of the image in the x-direction, UyyFor the second derivative of the image in the y-direction, UxyThe second-order partial derivative of the image in the xy direction;
Figure BDA0003425427400000032
represents the second derivative of the image U in the vertical direction; | represents an absolute value; omega represents the set of pixels of the entire image,
Figure BDA0003425427400000033
and the maximum value in the two-dimensional image edge indication values of all the pixel points in the omega region is represented.
Further, in step 1, the weights of the neighborhood pixels of the central pixel point are obtained as follows;
when the image is denoised, a weighted projection operator is adopted to update a pixel point p, and the weight of a neighborhood pixel point q is defined as:
Figure BDA0003425427400000034
wherein, p ═ i, (j) is a central pixel point;
Figure BDA0003425427400000035
a normalized edge indication value of p;
Figure BDA0003425427400000036
a normalized edge indicator value of a neighborhood pixel q;
if p is an edge pixel, when q is an edge pixel, then wqThe value is large, when q is noise or flat area pixel point, wqThe value is small; if p is a noise pixel or a flat region pixel, when q is an edge pixel, wqThe value is small, when q is noise or flat area pixel point, wqThe value is large; through wqThe method can inhibit the diffusion of surrounding pixel points to edges, accelerate the diffusion of noise points, and better keep the texture details of the image while improving the denoising performance, and the weight matrix calculated by adopting a 3 multiplied by 3 pixel neighborhood is shown as follows through the weight of a defined neighborhood pixel point q:
Figure BDA0003425427400000037
wherein, wi,jThe weight of the central pixel point p is equal to the weight of (i, j), and the other values are the weights of the neighborhood pixels of the central pixel point.
Further, 4 half-window tangent planes containing 5 pixel points and 4 triangular tangent planes containing 3 pixel points are selected in the step 2, and 8 tangent planes are used for constructing the weighted projection operator.
Further, in step 2, the calculation mode of the weighted projection distances from the central pixel point to the 8 tangent planes is as follows;
according to the weight of the neighborhood of the central pixel point obtained in the step 1, calculating the weighted projection distance d from the central pixel point to 8 tangent planesi(i ═ 1,2, …,8) where d is1To d4Weighted projection distances, d, from the central pixel to the 4 half-window tangent planes, respectively5To d8The weighted projection distances from the central pixel to the 4 triangular tangent planes are respectively, and the weighted projection operator of the pixel point p ═ i, j is shown as the formula:
Figure BDA0003425427400000041
Figure BDA0003425427400000042
Figure BDA0003425427400000043
Figure BDA0003425427400000044
Figure BDA0003425427400000045
Figure BDA0003425427400000046
Figure BDA0003425427400000047
Figure BDA0003425427400000048
wherein, w·Weight, U, of neighborhood pixel calculated for formula (3) in step 2i,jIs the pixel value of the pixel point at coordinate (i, j); sumi(i ═ 1, …,8) is the sum of the weights of the required neighborhood pixels; by using
Figure BDA0003425427400000051
Normalizing the weight; d1,…,d8Is a weighted projection distance.
Further, the step 3 is implemented by selecting the projection distance d causing the minimum intensity change of the central pixel point from the weighted projection distances of the developable approximate tangent planes of the M local pixel neighborhoods calculated in the step 2min：
|dmin|＝min{|d1|,|d2|,…,|dM|}
Updating the pixel value of the p point to
Figure BDA0003425427400000052
Wherein U ispThe original pixel value of the p-point,
Figure BDA0003425427400000053
and repeating the operation on all pixel points in the image for the updated pixel value to finish one-time updating of the image.
Further, the energy functional of the adaptive weighted gaussian curvature filtering algorithm in step 4 is defined as follows:
Figure BDA0003425427400000054
wherein the content of the first and second substances,
Figure BDA0003425427400000055
and
Figure BDA0003425427400000056
respectively a denoised image and an input image after normalization; eGCIs the total Gaussian energy;
Figure BDA0003425427400000057
fitting terms to the adaptive fractional order data;
Figure BDA0003425427400000058
is a Gaussian regularization term;
Figure BDA0003425427400000059
regularizing terms for tight frames;
Figure BDA00034254274000000510
the order of the adaptive fractional order of the term is fitted to the data,
Figure BDA00034254274000000511
representing normalized edge indication values;
Figure BDA00034254274000000512
is the weight of the Gaussian regularization term;
Figure BDA00034254274000000513
representing a gaussian curvature;
Figure BDA00034254274000000514
weights for tight frame regularization terms; w is a tight frame operator, which satisfies WTW is I; | · | represents the absolute value, p represents a pixel point, and Ω represents the set of pixel points of the whole image;
computing
Figure BDA00034254274000000515
Respectively as follows:
Figure BDA00034254274000000516
Figure BDA00034254274000000517
Figure BDA00034254274000000518
Figure BDA00034254274000000519
wherein the content of the first and second substances,
Figure BDA00034254274000000520
is composed of
Figure BDA00034254274000000521
The first derivative in the x-direction,
Figure BDA00034254274000000522
is composed of
Figure BDA00034254274000000523
The first derivative in the y-direction,
Figure BDA00034254274000000524
is composed of
Figure BDA00034254274000000525
The second derivative in the x-direction,
Figure BDA00034254274000000526
is composed of
Figure BDA00034254274000000527
The second derivative in the y-direction,
Figure BDA00034254274000000528
is composed of
Figure BDA00034254274000000529
Second order partial derivatives in the xy direction; adaptive fractional order of data fitting term
Figure BDA00034254274000000530
Gauss regularization term coefficients
Figure BDA00034254274000000531
Tight frame regularization term coefficients
Figure BDA00034254274000000532
Adjustment coefficient mu1、μ2Is a constant.
The invention has the following advantages and positive effects:
(1) the method adopts the edge indication function to judge whether the central pixel point is an edge pixel point, a noise point or a flat point, calculates the weight of the neighborhood pixel point according to the types of the central pixel point and the neighborhood pixel point, inhibits the diffusion of the edge, and accelerates the diffusion of the noise point, thereby realizing the denoising and simultaneously keeping the edge texture detail;
(2) according to the method, the image is locally approximated by using the developable surface to reduce the regularization term energy, and the image is updated by adopting the weighted projection operator, so that the image denoising can be rapidly carried out, and the operation efficiency of the algorithm is improved;
(3) the energy functional comprises three parts, namely a fractional order data fitting term, a variation regularization term and a tight frame regularization term, so that the sparsity of the image is effectively improved;
(4) the invention adopts a self-adaptive mode to adjust the fractional order and the weight of each item in the energy functional, can accurately control the iterative update of the projection operator, and effectively prevents the image from denoising incompletely or being smoothed excessively.
Drawings
Fig. 1 is an exploded view of an image space according to an embodiment of the present invention.
FIG. 2 is a schematic diagram of a Gaussian filter tangent plane according to an embodiment of the invention.
Fig. 3 is a schematic diagram illustrating a distance between a center pixel and a tangent plane according to an embodiment of the present invention.
Detailed Description
The technical scheme of the invention is explained in detail in the following by combining the drawings and the embodiment.
The technical scheme of the invention can adopt a computer software technology to realize an automatic operation process, and the process of the self-adaptive weighted curvature filtering algorithm based on the image edge indication function provided by the embodiment sequentially comprises the following steps:
1. and performing image space decomposition on the input noise image, calculating an edge indication value of a pixel and performing weight distribution on neighborhood pixels of a central pixel point.
The invention firstly carries out image space decomposition on an input noise image U by utilizing a curvature filtering algorithm, and divides the image into white circles omegaWCBlack circle omegaBCWhite triangle omegaWTAnd black triangle omegaBT4 types of disjoint and interleaved regions to eliminate dependencies between neighboring pixels, as shown in fig. 1.
The embodiment effectively distinguishes pixel points in the image into edge points, isolated noise points and flat points based on the edge indication function of the two-dimensional image with differential curvature, and defines the edge indication value D of the two-dimensional image of the pixel point ppAnd normalized edge indicator values
Figure BDA0003425427400000061
Comprises the following steps:
Figure BDA0003425427400000062
wherein
Figure BDA0003425427400000071
Representing the second derivative of the image U in the direction of the gradient, UxFor the first derivative of the image in the x-direction, UyFor the first derivative of the image in the y-direction, UxxAs an imageSecond derivative in x-direction, UyyFor the second derivative of the image in the y-direction, UxyThe second-order partial derivative of the image in the xy direction;
Figure BDA0003425427400000072
represents the second derivative of the image U in the vertical direction; | represents an absolute value; omega represents the set of pixels of the entire image,
Figure BDA0003425427400000073
and the maximum value in the two-dimensional image edge indication values of all the pixel points in the omega region is represented.
The experimental result shows that if p is the edge pixel point, | UhhGreat | value, | UξξThe value of | is smaller, therefore
Figure BDA0003425427400000074
The value is large; if p is a pixel point of a flat region, | UhhI and I UξξAll values of | are small, and therefore
Figure BDA0003425427400000075
The value is small; if p is a noise point, | UhhI and I UξξThe value of | is large and the difference is small, so
Figure BDA0003425427400000076
The value is small. According to
Figure BDA0003425427400000077
The magnitude of the values can better distinguish image edges, flat areas and noise points.
The embodiment defines the weight of the neighborhood pixel point q of the central pixel p as:
Figure BDA0003425427400000078
wherein, p ═ i, (j) is a central pixel point;
Figure BDA0003425427400000079
a normalized edge indication value of p;
Figure BDA00034254274000000710
is the normalized edge indicator value of the neighborhood pixel q.
The experimental result shows that if p is the edge pixel point, when q is the edge pixel point, then wqThe value is large, when q is noise or flat area pixel point, wqThe value is small; if p is a noise pixel or a flat region pixel, when q is an edge pixel, wqThe value is small, when q is noise or flat area pixel point, wqThe value is large. Through wqThe method can inhibit the diffusion of surrounding pixel points to edges and accelerate the diffusion of noise points, so that the algorithm can better keep the texture details of the image while improving the denoising performance. The weight matrix calculated by the present embodiment using the 3 × 3 pixel neighborhood is as follows:
Figure BDA00034254274000000711
wherein, wi,jThe weight of the central pixel point p is equal to the weight of (i, j), and the other values are the weights of the neighborhood pixels of the central pixel point.
2. And calculating the weighted projection distance from the pixel point to the tangent plane by using a weighted Gaussian curvature filtering algorithm.
In the curvature filtering process, in order to avoid explicitly calculating Gaussian curvature and differential curvature, the segmentation developability is satisfied by directly adjusting the pixel value of each point to be positioned on the tangent plane of the adjacent pixels. Aiming at the problem that the Gaussian curvature filtering algorithm is not ideal for the details of the edge texture of the image after denoising, 8 tangent planes are selected to calculate corresponding weighted projection operators. According to fig. 2, 4 half-window tangent planes containing 5 pixels and 4 triangular tangent planes containing 3 pixels are selected, and 8 tangent planes are used for enhancing the projection operator. Then, adopting an edge indication function to calculate the weighted projection distance from the central pixel point to 8 tangent planes, wherein d1To d4Respectively the weighted projection distances of the central pixel to the 4 half-window tangent planes,d5to d8Respectively, the weighted projection distances of the center pixel to the 4 trigonometric planes. The weighted projection operator of the pixel point p ═ i, j is shown as the following formula:
Figure BDA0003425427400000081
Figure BDA0003425427400000082
Figure BDA0003425427400000083
Figure BDA0003425427400000084
Figure BDA0003425427400000085
Figure BDA0003425427400000086
Figure BDA0003425427400000087
Figure BDA0003425427400000091
wherein, w·Weight, U, of neighborhood pixel calculated for formula (3) in step 2i,jIs the pixel value of the pixel point at coordinate (i, j); sumi(i ═ 1, …,8) is the sum of the weights of the required neighborhood pixels; by using
Figure BDA0003425427400000092
Normalizing the weight; d1,…,d8Is a weighted projection distance.
3. And finding the minimum projection distance from the pixel point to the tangent plane, and updating the image.
Any developable surface can be locally approximated with its tangent plane, so the present invention uses the locally developable surface to approximate the image to reduce the regularization term energy. And (3) selecting the projection distance with the minimum intensity change from the central pixel point in the projection distances of the developable approximate tangent planes of the 8 local pixel neighborhoods selected in the step (2), namely using the minimum absolute distance as the minimum projection distance from the central pixel point to the tangent plane. The minimum projection distance is defined as:
|dmin|＝min{|d1|,|d2|,…,|d8|} (12)
the invention updates the pixel value of the p point to be
Figure BDA0003425427400000093
Wherein U ispThe original pixel value of the p-point,
Figure BDA0003425427400000094
is the updated pixel value. And solving the minimum projection distance of all pixel points in the image, and updating the image once.
Experimental results show that when the Gaussian noise intensity reaches 50, the image denoising task can be completed through 6 iterative updating at most, and when the salt-pepper noise intensity reaches 0.1, the denoising task can be completed through 5 iterative updating at most, so that the algorithm is proved to have higher convergence speed, and the edge texture details of the image are kept better while denoising is performed.
4. And calculating the total energy according to a self-adaptive Gaussian energy functional formula, comparing the total energy of the image after updating with the total energy before updating, and controlling the filtering of the image through the minimized energy functional.
In the curvature filtering process, a minimized energy functional needs to be found, the curvature filtering iteration is controlled to be updated, and the phenomena that denoising is incomplete or an image is excessively smooth and the like are avoided. The invention is based on an edge indication function, adopts a self-adaptive weighted Gaussian curvature energy functional, and the energy functional is defined as follows:
Figure BDA0003425427400000095
wherein the content of the first and second substances,
Figure BDA0003425427400000096
and
Figure BDA0003425427400000097
respectively a denoised image and an input image after normalization; eGCIs the total Gaussian energy;
Figure BDA0003425427400000098
fitting terms to the adaptive fractional order data;
Figure BDA0003425427400000099
is a Gaussian regularization term;
Figure BDA00034254274000000910
regularizing terms for tight frames;
Figure BDA00034254274000000911
the order of the adaptive fractional order of the term is fitted to the data,
Figure BDA00034254274000000912
representing normalized edge indication values;
Figure BDA00034254274000000913
is the weight of the Gaussian regularization term;
Figure BDA00034254274000000914
representing a gaussian curvature;
Figure BDA00034254274000000915
weights for tight frame regularization terms; w is a tight frame operator, which satisfies WTW is I; | · | represents the absolute value, p represents the pixel point, and Ω represents the set of pixel points of the entire image.
Computing
Figure BDA0003425427400000101
Respectively as follows:
Figure BDA0003425427400000102
Figure BDA0003425427400000103
Figure BDA0003425427400000104
Figure BDA0003425427400000105
wherein the content of the first and second substances,
Figure BDA0003425427400000106
is composed of
Figure BDA0003425427400000107
The first derivative in the x-direction,
Figure BDA0003425427400000108
is composed of
Figure BDA0003425427400000109
The first derivative in the y-direction,
Figure BDA00034254274000001010
is composed of
Figure BDA00034254274000001011
The second derivative in the x-direction,
Figure BDA00034254274000001012
is composed of
Figure BDA00034254274000001013
The second derivative in the y-direction,
Figure BDA00034254274000001014
is composed of
Figure BDA00034254274000001015
Second order partial derivatives in the xy direction; adaptive fractional order of data fitting term
Figure BDA00034254274000001016
Gauss regularization term coefficients
Figure BDA00034254274000001017
Tight frame regularization term coefficients
Figure BDA00034254274000001018
The experimental result proves that when the noise is removed by the self-adaptive Gaussian energy functional, in the filtering iteration process of the image,
Figure BDA00034254274000001019
while the value of (A) is unchanged or increased
Figure BDA00034254274000001020
And
Figure BDA00034254274000001021
is constant or decreases. According to the adaptive gaussian energy functional proposed herein, when removing noise,
Figure BDA00034254274000001022
increasing the value will suppress the data fitting term energy
Figure BDA00034254274000001023
While rising, at the same time
Figure BDA00034254274000001024
Increasing the value will accelerate the regularization term energy
Figure BDA00034254274000001025
And
Figure BDA00034254274000001026
so that the total energy EGCIn a downward trend; when the image is to be over-smoothed,
Figure BDA00034254274000001027
and
Figure BDA00034254274000001028
value reduction, fitting acceleration data to term energy
Figure BDA00034254274000001029
Suppressing regularization term energy
Figure BDA00034254274000001030
And
Figure BDA00034254274000001031
so that the total energy EGCIn an upward trend. Therefore, the updating of the image U can be effectively controlled according to the change of the total energy, thereby ensuring better noise removal and simultaneously preventing the image from being over-smooth.
In the embodiment, when the total energy is calculated by using the energy functional, the coefficient mu is adjusted1And mu2Is constant and takes values of 35 and 10.5 respectively. Comparing the updated images
Figure BDA00034254274000001032
Total energy of
Figure BDA00034254274000001033
And total energy E before updateGCThe magnitude of (U) if total energy
Figure BDA00034254274000001034
Less than the total energy E before updateGC(U), then order
Figure BDA00034254274000001035
Repeating the steps, updating the image again, otherwise stopping iteration and outputting the denoised image
Figure BDA00034254274000001036
Experiments prove that the adaptive weighted Gaussian curvature energy functional provided by the invention can accurately control the update iteration of the image, ensure better noise removal and prevent the image from being over smooth.
The experimental result shows that the technical scheme can effectively remove the noise in the image and better keep the edge texture details of the image, compared with the existing curvature filtering method, the algorithm improves the peak signal-to-noise ratio and the structural similarity index of the de-noised image, and has self-adaptability and higher operation efficiency.
The specific embodiments described herein are merely illustrative of the invention. Various modifications or additions may be made to the described embodiments or alternatives may be employed by those skilled in the art without departing from the spirit or ambit of the invention as defined in the appended claims.

Claims (8)

1. An adaptive weighted Gaussian curvature filtering method based on an image edge indication function is characterized by comprising the following steps:
step 1, performing image space decomposition on a current noise image to obtain four types of disjoint and staggered areas, calculating an edge indicated value of each pixel point, and calculating the weight of a neighborhood pixel of a central pixel point according to the edge indicated value;
step 2, selecting triangular tangent planes of the central pixel points to construct Gaussian weighted projection operators, and calculating weighted projection distances from the central pixel points to M tangent planes according to the pixel weights in the step 1;
step 3, selecting the minimum projection distance to update the central pixel point according to the weighted projection distance calculated in the step 2, and finishing one-time updating of the image after all pixel points in the image are updated;
and 4, calculating the total energy of the denoised image obtained in the step 3 by adopting a self-adaptive Gaussian energy functional formula, if the total energy is less than the total energy of the image before updating, turning to the step 1, otherwise, stopping updating, and outputting the denoised image.
2. The method of adaptive weighted gaussian curvature filtering based on image edge indication function according to claim 1, wherein: in step 1, a curvature filtering algorithm is used for carrying out image space decomposition on an input noise image U, and the image is divided into white circles omegaWCBlack circle omegaBCWhite triangle omegaWTAnd black triangle omegaBTFour types of disjoint and interleaved regions eliminate dependencies between neighboring pixels.
3. The method of adaptive weighted gaussian curvature filtering based on image edge indication function according to claim 1, wherein: defining two-dimensional image edge indication values D of pixel points p of each region in step 1pAnd normalized edge indicator values
Figure FDA0003425427390000011
Comprises the following steps:
Figure FDA0003425427390000012
wherein, the image U is a noise image,
Figure FDA0003425427390000013
representing the second derivative of the image U in the direction of the gradient, UxFor the first derivative of the image in the x-direction, UyFor the first derivative of the image in the y-direction, UxxFor the second derivative of the image in the x-direction, UyyFor the image in the y directionSecond derivative of, UxyThe second-order partial derivative of the image in the xy direction;
Figure FDA0003425427390000014
represents the second derivative of the image U in the vertical direction; | represents an absolute value; omega represents the set of pixels of the entire image,
Figure FDA0003425427390000015
and the maximum value in the two-dimensional image edge indication values of all the pixel points in the omega region is represented.
4. The method of claim 3, wherein the adaptive weighted Gaussian curvature filtering method based on the image edge indication function comprises: in the step 1, the weight of the neighborhood pixel of the central pixel point is obtained in the following way;
when the image is denoised, a weighted projection operator is adopted to update a pixel point p, and the weight of a neighborhood pixel point q is defined as:
Figure FDA0003425427390000021
wherein, p ═ i, (j) is a central pixel point;
Figure FDA0003425427390000022
a normalized edge indication value of p;
Figure FDA0003425427390000023
a normalized edge indicator value of a neighborhood pixel q;
if p is an edge pixel, when q is an edge pixel, then wqThe value is large, when q is noise or flat area pixel point, wqThe value is small; if p is a noise pixel or a flat region pixel, when q is an edge pixel, wqThe value is small, when q is noise or flat area pixel point, wqThe value is large; through wqCan suppress the peripheral pixel point to edgeThe diffusion of the noise points is accelerated, the denoising performance is improved, meanwhile, the texture details of the image are better kept, and through the weight of a defined neighborhood pixel point q, a weight matrix calculated by adopting a 3 multiplied by 3 pixel neighborhood is as follows:
Figure FDA0003425427390000024
wherein, wi,jThe weight of the central pixel point p is equal to the weight of (i, j), and the other values are the weights of the neighborhood pixels of the central pixel point.
5. The method of adaptive weighted gaussian curvature filtering based on image edge indication function according to claim 1, wherein: and (3) selecting 4 half-window tangent planes containing 5 pixel points and 4 triangular tangent planes containing 3 pixel points in the step (2), and constructing a weighted projection operator by using 8 tangent planes.
6. The method of adaptive weighted Gaussian curvature filtering based on image edge indication function according to claim 4, characterized in that: in the step 2, the calculation mode of the weighted projection distance from the central pixel point to 8 tangent planes is as follows;
according to the weight of the neighborhood of the central pixel point obtained in the step 1, calculating the weighted projection distance d from the central pixel point to 8 tangent planesi(i ═ 1,2, …,8) where d is1To d4Weighted projection distances, d, from the central pixel to the 4 half-window tangent planes, respectively5To d8The weighted projection distances from the central pixel to the 4 triangular tangent planes are respectively, and the weighted projection operator of the pixel point p ═ i, j is shown as the formula:
Figure FDA0003425427390000031
Figure FDA0003425427390000032
Figure FDA0003425427390000033
Figure FDA0003425427390000034
Figure FDA0003425427390000035
Figure FDA0003425427390000036
Figure FDA0003425427390000037
Figure FDA0003425427390000038
wherein, w·Weight, U, of neighborhood pixel calculated for formula (3) in step 2i,jIs the pixel value of the pixel point at coordinate (i, j); sumi(i ═ 1, …,8) is the sum of the weights of the required neighborhood pixels; by using
Figure FDA0003425427390000039
Normalizing the weight; d1,…,d8Is a weighted projection distance.
7. The method of adaptive weighted gaussian curvature filtering based on image edge indication function according to claim 1, wherein: step 3 is implemented by the weighted projection of the developable approximate tangent plane of the M local pixel neighborhoods calculated in step 2Selecting the projection distance d causing the minimum intensity change of the central pixel point in the distancemin：
|dmin|＝min{|d1|,|d2|,…,|dM|}
Updating the pixel value of the p point to
Figure FDA0003425427390000041
Wherein U ispThe original pixel value of the p-point,
Figure FDA0003425427390000042
and repeating the operation on all pixel points in the image for the updated pixel value to finish one-time updating of the image.
8. The method of adaptive weighted gaussian curvature filtering based on image edge indication function according to claim 1, wherein: the energy functional of the adaptive weighted gaussian curvature filtering algorithm in step 4 is defined as follows:
Figure FDA0003425427390000043
wherein the content of the first and second substances,
Figure FDA0003425427390000044
and
Figure FDA0003425427390000045
respectively a denoised image and an input image after normalization; eGCIs the total Gaussian energy;
Figure FDA0003425427390000046
fitting terms to the adaptive fractional order data;
Figure FDA0003425427390000047
is a Gaussian regularization term;
Figure FDA0003425427390000048
regularizing terms for tight frames;
Figure FDA0003425427390000049
the order of the adaptive fractional order of the term is fitted to the data,
Figure FDA00034254273900000410
representing normalized edge indication values;
Figure FDA00034254273900000411
is the weight of the Gaussian regularization term;
Figure FDA00034254273900000412
representing a gaussian curvature;
Figure FDA00034254273900000413
weights for tight frame regularization terms; w is a tight frame operator, which satisfies WTW is I; | · | represents the absolute value, p represents a pixel point, and Ω represents the set of pixel points of the whole image;
computing
Figure FDA00034254273900000414
Respectively as follows:
Figure FDA00034254273900000415
Figure FDA00034254273900000416
Figure FDA00034254273900000417
Figure FDA00034254273900000418
wherein the content of the first and second substances,
Figure FDA00034254273900000419
is composed of
Figure FDA00034254273900000420
The first derivative in the x-direction,
Figure FDA00034254273900000421
is composed of
Figure FDA00034254273900000422
The first derivative in the y-direction,
Figure FDA00034254273900000423
is composed of
Figure FDA00034254273900000424
The second derivative in the x-direction,
Figure FDA00034254273900000425
is composed of
Figure FDA00034254273900000426
The second derivative in the y-direction,
Figure FDA00034254273900000427
is composed of
Figure FDA00034254273900000428
Second order partial derivatives in the xy direction; adaptive fractional order of data fitting term
Figure FDA00034254273900000429
Gauss regularization term coefficients
Figure FDA00034254273900000430
Tight frame regularization term coefficients
Figure FDA00034254273900000431
Adjustment coefficient mu1、μ2Is a constant.
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