CN112435175A - Metallographic image denoising method and system - Google Patents
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Abstract
The invention discloses a metallographic image denoising method and a system, based on a regularization method in a fully robust RPCA, on the basis of a low-rank sparse matrix decomposition algorithm, carrying out L2 norm constraint on low-rank clear data matrix blocks after noise removal, on the basis of realizing local regularization of image block characteristics, carrying out constraint processing on Gaussian noise to obtain an improved low-rank sparse matrix decomposition model, representing the structural information of an image by using the local characteristics of the image, treating the noise as actual noise, improving the problem that image noise information is defaulted to be a sparse matrix when the traditional low-rank sparse matrix decomposition algorithm is used for denoising, reducing the conditions of fuzzy key content, unclear texture details and unclear edges caused by the traditional RPCA, solving the problem that the traditional RPCA only has remarkable effect on pulse noise denoising, and taking a large amount of Gaussian noise caused by interference of surrounding environment and hardware equipment in the actual image data sampling process into account, mixed noise is processed.
Description
Technical Field
The invention belongs to the field of image processing, and particularly relates to a metallographic image denoising method and a system.
Background
Image denoising is a hotspot of research in the field of image processing, and aims to reduce the influence of interference of imaging equipment and external environment noise and the like on digital images in the digitization and transmission processes. The image denoising technology lays a work foundation for metallographic quantitative analysis of metal materials in the industrial industry of the Internet of things, and provides more effective data for carbide segmentation, multiphase structure target detection, grain size measurement and the like of subsequent metallographic images. The higher-quality image is the first requirement for intelligent analysis, and the original metallographic sample is subjected to the preparation processes of sampling, grinding, polishing, erosion and the like, so that noise existing in the microscopic image causes interference to a certain degree in later research. Therefore, the original microscopic image needs to be subjected to denoising pretreatment, the image quality is enhanced, and the analysis accuracy of different data sets is improved.
The conventional low rank sparse matrix decomposition algorithm (Sun W, Liu C, Li J L, et al, Low-rank and sparse matrix decomposition-based analysis detection for hyper-spectral image [ J ]. Journal of Applied Remote Sensing,2014,8(1):083641.) when denoising an image, the contained image noise information is defaulted to a sparse matrix, and when a noise point part is eliminated, a part of the structural characteristics of the image is often regarded as a sparse area, so that the image after denoising is highly likely to have the conditions of blurred main content, texture details and unclear edges, and the RPCA robust principal component analysis (Wright, J., fresh, A., Rao, S., Peng, Y, Ma, Y., Ro. robust principal component analysis: Exacty recovery of real-temporal sampling of the image only by sampling the real-time impulse analysis 2009, a great amount of gaussian noise due to interference of surrounding environment and hardware equipment often occurs, so that the conventional RPCA is not suitable for denoising the actual noise point. Due to the complexity of metallographic structure images, it has been a challenge to provide a denoising pre-processing model with strong denoising capability and weak edge blurring.
Disclosure of Invention
The invention aims to provide a metallographic image denoising method and a system, which are used for overcoming the defects of the prior art.
In order to achieve the purpose, the invention adopts the following technical scheme:
a metallographic image denoising method comprises the following steps:
step 1), on the basis of a regularization method in a fully robust RPCA (resilient packet access), on the basis of a low-rank sparse matrix decomposition algorithm, carrying out L2 norm constraint on blocks of a low-rank clear data matrix after noise removal, and on the basis of realizing local regularization of image block characteristics, carrying out constraint processing on Gaussian noise to obtain an improved low-rank sparse matrix decomposition model;
and step 2), carrying out drying treatment on the metallographic structure image to be dried by using the improved low-rank sparse matrix decomposition model.
Further, the improved low-rank sparse matrix decomposition model is as follows:
e is a noise-containing sparse matrix, D is a noise-containing point image information matrix, A is a low-rank matrix, gamma is a low-rank matrix coefficient, and lambda is a sparse matrix coefficient.
Further, an inaccurate Lagrange multiplier method IALM algorithm is adopted for optimization solution, and the Lagrange function is obtained as follows:
wherein,<Y,D-A-E>＝trace(Y*(D-A-E))，
further, a noise-point image information matrix D obtained by sampling, a penalty factor mu, a low-rank matrix coefficient gamma, a sparse matrix coefficient lambda and a clear original image matrix AkSum noise partial matrix Ek，
Initialization operation: y is0＝D，E0＝0，k＝0，γ0＞0，μ0＞0
When the improved low-rank sparse matrix decomposition model is not converged, alternately performing iterative processing:
(1)
(2)
(3)Yk+1＝Yk+μk(D-Ak+1-Ek+1)；
(4)
(5)k＝k+1；
(6) when | | | D-1-E | | non-woven phosphorF≤ε||D||F,ε＝10-7And when the model is converged, stopping iteration, otherwise, repeating the process until a convergence condition is reached.
And further, taking two microscopic metallographic structure images with different metallographies as the input of the improved low-rank sparse matrix decomposition model to carry out metallographic structure image drying treatment.
Further, for a single-phase metallographic structure: taking a cross-section microscopic metallographic image of hot-rolled 20G steel as original data, dividing the cross-section microscopic metallographic image into five series of atlas data sets A-E according to different carbon contents, and grading each series of images into 1 grade to 5 grades according to different segregation degrees; aiming at a multiphase metallographic structure: the longitudinal section microscopic gold phase diagram of 42CrMo round steel is used as the original data.
Further, the improved low-rank sparse matrix decomposition model is transferred to denoising treatment of a metallographic image, two different metallographic structure images are used as input of the improved low-rank sparse matrix decomposition model, denoising pretreatment is carried out on the two different metallographic structure images by adopting a filtering treatment algorithm, and the two results of the denoising treatment are compared to obtain an effect rating.
Further, circularly iterating each variable in the lagrangian function, we can obtain:
solving for the low rank matrix a:
solving aiming at the noisy sparse matrix E:
for image block matrix AiSolving:
to AiAnd (3) carrying out partial derivative solution, and making the value of the partial derivative solution be zero to solve the extreme value of the above matrix:
image block matrix AiIs the subblock portion of the low rank matrix a.
Further, the iterative process of the matrix Y and the penalty factor μ is:
a metallographic image denoising system comprising a memory, a processor and a computer program stored in said memory and transportable on said processor, said computer program when executed by said processor implementing the steps of the method of claim 1.
Compared with the prior art, the invention has the following beneficial technical effects:
the invention relates to a metallographic image denoising method, which is based on a regularization method in a fully robust RPCA, and is used for constraining a low-rank clear data matrix block subjected to noise removal by an L2 norm on the basis of a low-rank sparse matrix decomposition algorithm, and constraining Gaussian noise to obtain an improved low-rank sparse matrix decomposition model on the basis of realizing local regularization of image block characteristics, and the structural information of an image is represented by the local characteristics of the image. And (3) taking a large amount of Gaussian noise generated due to interference of surrounding environment and hardware equipment in the actual image data sampling process into consideration, and processing the mixed noise. The method can ensure that the grain, the edge detail and the tissue content in the metallographic image are not over fuzzified, has small difference in processing effect on different metallographic images, and has wider application.
Furthermore, relaxation processing of the objective function is carried out, so that the problem of the NP-hard non-deterministic polynomial difficulty is solved.
Furthermore, the above formula is optimally solved by adopting an inaccurate Lagrange multiplier method IALM, and compared with an iterative threshold algorithm IT and an accelerated near-end gradient algorithm APG, the operator has the advantages of higher convergence rate and higher solving precision.
The metallographic image denoising system can rapidly realize the metallographic image denoising treatment through the memory, the processor and the computer program which is stored in the memory and can be conveyed on the processor.
Drawings
FIG. 1 is a flow chart of an implementation of a denoising method based on a low-rank sparse matrix decomposition model in an embodiment of the present invention.
Fig. 2 is a comparison graph of two metallographic structure images and a gray histogram thereof after denoising according to the invention in the embodiment of the invention, fig. 2a is a single-phase metallographic structure gray graph and a gray histogram thereof, fig. 2b is a single-phase metallographic structure image and a gray histogram thereof after denoising through an improved algorithm, fig. 2c is a multiphase metallographic structure gray graph and a gray histogram thereof, and fig. 2d is a multiphase metallographic structure image and a gray histogram thereof after denoising through an improved algorithm.
Detailed Description
The invention is described in further detail below with reference to the accompanying drawings:
as shown in fig. 1, the invention provides a metallographic image denoising method, which comprises the following steps:
step 1), on the basis of a regularization method in a fully robust RPCA (resilient packet access), on the basis of a low-rank sparse matrix decomposition algorithm, carrying out L2 norm constraint on blocks of a low-rank clear data matrix after noise removal, and on the basis of realizing local regularization of image block characteristics, carrying out constraint processing on Gaussian noise to obtain an improved low-rank sparse matrix decomposition model;
the improved low-rank sparse matrix decomposition model is as follows:
e is a noise-containing sparse matrix, D is a noise-containing point image information matrix, A is a low-rank matrix, gamma is a low-rank matrix coefficient, and lambda is a sparse matrix coefficient.
And (3) performing optimized solution on the above formula by adopting an inaccurate Lagrange multiplier method IALM, wherein the operator has higher convergence speed and higher solution precision compared with an iterative threshold algorithm IT and an accelerated near-end gradient algorithm APG.
And performing optimization solution by adopting an inaccurate Lagrange multiplier method IALM algorithm to obtain a Lagrange function as follows:
in this connection, it is possible to use,<Y,D-A-E>＝trace(Y*(D-A-E))，
specifically, a noise-point image information matrix D obtained by sampling, a penalty factor mu, a low-rank matrix coefficient gamma, a sparse matrix coefficient lambda and a clear original image matrix AkSum noise partial matrix Ek，
Initialization operation: y is0＝D，E0＝0，k＝0，γ0＞0，μ0＞0
When the improved low-rank sparse matrix decomposition model is not converged, alternately performing iterative processing:
(1)
(2)
(3)Yk+1＝Yk+μk(D-Ak+1-Ek+1)；
(4)
(5)k＝k+1；
(6) when | | | D-1-E | | non-woven phosphorF≤ε||D||F,ε＝10-7And when the model is converged, stopping iteration, otherwise, repeating the process until a convergence condition is reached.
And transferring the improved low-rank sparse matrix decomposition model to denoising of a metallographic image, taking two different metallographic structure images as the input of the improved low-rank sparse matrix decomposition model, performing denoising pretreatment on the two different metallographic structure images by adopting a filtering treatment algorithm, and comparing two types of denoising treatment results to obtain an effect rating. The specific working process is as follows:
iterating each variable in the lagrange function in a loop, we can obtain:
solving for the low rank matrix a:
solving aiming at the noisy sparse matrix E:
for image block matrix AiSolving:
to AiAnd (3) carrying out partial derivative solution, and making the value of the partial derivative solution be zero to solve the extreme value of the above matrix:
image block matrix AiIs a sub-block portion of the low rank matrix A, so A can be divided intoiCombining the subblocks with the matrix A, and performing further superposition iteration on the matrix A, wherein the iteration process of the matrix Y and the penalty factor mu is as follows:
and step 2), carrying out drying treatment on the metallographic structure image to be dried by using the improved low-rank sparse matrix decomposition model.
And 2) taking two microscopic metallographic structure images with different metallographies as the input of the improved low-rank sparse matrix decomposition model for metallographic structure image drying treatment.
Specifically, for a single-phase metallographic structure: taking a cross-section microscopic metallographic image of hot-rolled 20G steel as original data, dividing the cross-section microscopic metallographic image into five series of atlas data sets A-E according to different carbon contents, and grading each series of images into 1 grade to 5 grades according to different segregation degrees;
aiming at a multiphase metallographic structure: a longitudinal section microscopic golden phase diagram of 42CrMo round steel is used as original data, and LabelImg software is used for manually marking a multiphase tissue target on the image.
The method for generating the image comprises the following steps of:
(1.1) for the original microscopic metallographic structure image, carrying out carbide discrimination, carbon content and segregation degree grading on the single-phase metallographic structure image by manpower, and identifying the morphological characteristics of different structures in the multiphase metallographic structure image;
(1.2) expanding the number of images in the data set by the image turning, image zooming and light and shade changing methods for the two different metallographic structure images in the step (1.1), so as to increase the original data set;
and (1.3) using the added data set in (1.2) in different filtering processes and denoising processes for improving a low-rank sparse matrix decomposition model.
And taking two different metallographic structure images as input, transferring a common filtering processing algorithm to denoising pretreatment of the metallographic images, comparing the improved low-rank sparse matrix decomposition model with the denoising pretreatment algorithm, and grading the denoising algorithm effect. The specific working process is as follows:
(3.1) taking the two microscopic metallographic structure images with different metallographic phases as the input of the improved low-rank sparse matrix decomposition model to obtain a denoising effect graph of the improved low-rank sparse matrix decomposition model;
(3.2) comparing the denoising effect graph of the improved low-rank sparse matrix decomposition model with a common filter processing operator; the result is shown in fig. 2, and it is found that the improved low-rank sparse matrix decomposition model achieves a better denoising effect, and the mean square error MSE, the peak signal-to-noise ratio PSNR, and the structural similarity SSIM value are used as the evaluation indexes of the model, and the results are shown in tables 1 and 2 below. Common filtering processes include spatial filtering and frequency-domain filtering. The spatial filtering selects median filtering, Gaussian filtering and bilateral filtering denoising operators for processing common salt and pepper noise, Gaussian noise, Poisson noise and the like. The frequency domain filtering selects an ideal low-pass filter, a Gaussian low-pass filter and a Butterworth low-pass filter to eliminate noise and improve image quality. Three indexes of mean square error MSE, peak signal-to-noise ratio PSNR and structural similarity SSIM are adopted, so that the image quality of common filtering and the improvement of denoising operator processing by the method is measured. The grain, edge details and all tissue contents in the metallographic image obtained by the method are not over fuzzified, and the method is superior to the existing method.
TABLE 1 index data table corresponding to each filtering processing algorithm of single-phase metallographic structure image
TABLE 2 index data table corresponding to each filter processing algorithm of multiphase metallographic structure image
The embodiments of the present invention have been described above with reference to the accompanying drawings. It will be appreciated by persons skilled in the art that the present invention is not limited by the embodiments described above. On the basis of the technical solution of the present invention, those skilled in the art can make various modifications or variations without creative efforts and still be within the protection scope of the present invention.
Claims (10)
1. A metallographic image denoising method is characterized by comprising the following steps:
step 1), on the basis of a regularization method in a fully robust RPCA (resilient packet access), on the basis of a low-rank sparse matrix decomposition algorithm, carrying out L2 norm constraint on blocks of a low-rank clear data matrix after noise removal, and on the basis of realizing local regularization of image block characteristics, carrying out constraint processing on Gaussian noise to obtain an improved low-rank sparse matrix decomposition model;
and step 2), carrying out drying treatment on the metallographic structure image to be dried by using the improved low-rank sparse matrix decomposition model.
2. The metallographic image denoising method according to claim 1, wherein the improved low-rank sparse matrix decomposition model is:
e is a noise-containing sparse matrix, D is a noise-containing point image information matrix, A is a low-rank matrix, gamma is a low-rank matrix coefficient, and lambda is a sparse matrix coefficient.
3. The metallographic image denoising method according to claim 2, wherein an inexact lagrangian multiplier IALM algorithm is used for optimal solution to obtain a lagrangian function as follows:
wherein,<Y,D-A-E>＝trace(Y*(D-A-E))，
4. the method for denoising the metallographic image according to claim 3, wherein the sampled noisy image information matrix D, penalty factor μ, low rank matrix coefficient γ, sparse matrix coefficient λ, and clear original image matrix AkSum noise partial matrix Ek，
Initialization operation: y is0＝D，E0＝0，k＝0，γ0＞0，μ0＞0
When the improved low-rank sparse matrix decomposition model is not converged, alternately performing iterative processing:
(1)
(2)
(3)Yk+1＝Yk+μk(D-Ak+1-Ek+1)；
(4)
(5)k＝k+1；
(6) when | | | D-1-E | | non-woven phosphorF≤ε||D||F,ε＝10-7And when the model is converged, stopping iteration, otherwise, repeating the process until a convergence condition is reached.
5. The metallographic image denoising method according to claim 1, wherein two metallographic different microscopic metallographic images are taken as input of the improved low-rank sparse matrix decomposition model for metallographic image denoising.
6. The method for denoising the metallographic image according to claim 5, wherein for a single-phase metallographic structure: taking a cross-section microscopic metallographic image of hot-rolled 20G steel as original data, dividing the cross-section microscopic metallographic image into five series of atlas data sets A-E according to different carbon contents, and grading each series of images into 1 grade to 5 grades according to different segregation degrees; aiming at a multiphase metallographic structure: the longitudinal section microscopic gold phase diagram of 42CrMo round steel is used as the original data.
7. The metallographic image denoising method according to claim 1, wherein the improved low-rank sparse matrix decomposition model is transferred to a denoising treatment of the metallographic image, two different metallographic structure images are used as input of the improved low-rank sparse matrix decomposition model, the two different metallographic structure images are subjected to denoising pretreatment by a filtering treatment algorithm, and the two results of the denoising treatment are compared to obtain an effect rating.
8. The method for denoising the metallographic image according to claim 1, wherein each variable in the Lagrangian function is iterated cyclically to obtain:
solving for the low rank matrix a:
solving aiming at the noisy sparse matrix E:
for image block matrix AiSolving:
to AiAnd (3) carrying out partial derivative solution, and making the value of the partial derivative solution be zero to solve the extreme value of the above matrix:
image block matrix AiIs the subblock portion of the low rank matrix a.
9. The method for denoising the metallographic image according to claim 8, wherein the iterative process of the matrix Y and the penalty factor μ is as follows:
10. a metallographic image denoising system comprising a memory, a processor and a computer program stored in said memory and transportable on said processor, said processor implementing the steps of the method according to claim 1 when executing said computer program.
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