CN107944497A - Image block method for measuring similarity based on principal component analysis - Google Patents
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Abstract
The invention belongs to computer graphics, to realize image noise reduction, lifting digital picture quality.For this reason, the technical solution adopted by the present invention is, a kind of image block method for measuring similarity based on principal component analysis, comprises the steps of：Step 1：Mathematical model is built using principal component analysis PCA algorithms；Step 2：To given image V, M pixel is randomly choosed in the picture to build the dictionary of PCA, the method standardized using standard deviation is pre-processed, and is established covariance matrix, is obtained the characteristic value of sample and corresponding feature vector；Step 3：Primitive character is projected in a sub-spaces, builds new feature, and similitude between pixel is calculated with this feature；Step 4：Its overall situation can be obtained by stratification orthogonal matching pursuit algorithm and aid in similar point set, simplify the Similarity measures of target pixel points and auxiliary pixel point, simplify similarity measurement and calculate.Present invention is mainly applied to computer graphical processing occasion.
Description
Technical Field
The invention belongs to the field of computer graphics and computer vision, relates to the technologies of image processing, image noise reduction and the like, can be widely applied to multiple aspects of computer vision, such as feature extraction, target monitoring, image segmentation and the like, and particularly relates to an image block similarity measurement method based on principal component analysis. In particular to a knowledge recommendation method based on time migration.
Background
Image noise reduction is a technical means for improving the quality of digital images, and is widely applied to multiple aspects of computer vision. Aiming at the problem of image noise reduction, a series of effective noise reduction algorithms are proposed by a plurality of researchers at home and abroad and can be divided into a spatial domain filtering algorithm and a transform domain filtering algorithm.
The spatial domain filtering algorithm directly processes the image, can generally avoid introducing artifacts in the noise reduction process, generally uses a certain filtering template, takes a target pixel point as a template center, performs convolution operation on the template and the target pixel point, and takes a convolution result as a noise reduction value of the pixel point. Common filtering templates include mean filtering, median filtering, and the like.
The transform domain filtering algorithm is to perform certain transform on an image, map the image to a transform domain space, and adjust a transform coefficient in a switch domain according to the assumption that a noise spectrum and a real signal are intensively distributed in different frequency bands, so as to realize the aim of signal-noise separation.
In the methods, the value of a target point subjected to noise reduction is estimated through pixel points in a neighborhood by utilizing the spatial position relationship among pixels, and the estimated value is locally restricted by the neighborhood. When the image structure is complex and the detail structure is small, the noise reduction algorithms are difficult to obtain a good noise reduction effect.
Disclosure of Invention
In order to overcome the defects of the prior art, the invention aims to provide an image block similarity measurement method based on principal component analysis, which is used for realizing image noise reduction and improving the quality of a digital image. Therefore, the invention adopts the technical scheme that the image block similarity measurement method based on principal component analysis comprises the following steps:
the method comprises the following steps: a Principal Component Analysis (PCA) algorithm is adopted to construct a mathematical model: giving a d-dimensional random vector x, considering the estimation of the random vector, transforming a sample x into a new vector Y through a linear transformation operator to reconstruct an original vector, and defining a reconstructed mean square error;
step two: for a given image V, randomly selecting M pixel points in the image to construct a dictionary of PCA, preprocessing by adopting a standard deviation standardization method, establishing a covariance matrix, and obtaining a characteristic value of a sample and a corresponding characteristic vector;
step three: projecting the original features into a subspace, constructing new features, and calculating the similarity between pixel points by using the features;
step four: the global auxiliary similarity point set can be obtained through a hierarchical orthogonal matching pursuit algorithm, similarity calculation of the target pixel point and the auxiliary pixel points is simplified, and similarity measurement calculation is simplified.
And (3) adopting an evaluation standard based on pixel point errors and an evaluation standard based on human visual characteristics to test the effectiveness of the measuring method.
The steps in one embodiment include:
step S0101: given a d-dimensional random vector x = (x) 1 ，x 2 ，…，x d ) The random variables are estimated by the PCA algorithm using a covariance matrix defined as shown in equation (1) where m X Is the mean value of the samples, S X The elements on the diagonal represent each random variable x i The off-diagonal elements represent covariance:
S X ＝E[(X-m X )(X-m X ) T ] (1)
the matrix A is a linear transformation operator, the operator transforms any sample X into a new vector Y, and the transformation process is expressed as formula (2):
Y＝A T (X-m x ) (2)
correspondingly, the inverse transformation process of the PCA can be expressed as shown in formula (3), where the matrix A is a linear transformation operator and m is a linear transformation operator X Is the mean of the samples.
X＝AY+m X (3)
Step S0102: in reconstruction, the first M columns of the linear operator A are adopted to construct a new transformation matrix A', and the PCA reconstruction result of the original vector X is shown in formula (4) by using the new transformation operator, whereinRepresents the reconstructed vector:
step S0201: for a pixel point i in a given image V, taking a gray value feature vector fi of a square neighborhood taking the point as a center as an original feature vector, marking the size of the square neighborhood as S, and using the SRepresenting all pixel points in the image V, where f i The expression dimension is S 2 The neighborhood feature vector of the pixel is based on the principal component analysis, the basic unit of the feature extraction method of the principal component analysis is the pixel, and the same method is used for extracting the features of the pixel in the measurement of global similarity constraint and local similarity constraint;
step S0202: randomly selecting M pixel points in the image V to construct a dictionary of PCA (principal component analysis)To represent the original feature vector set of the M pixel points, so that the original data sample set has a dimension S 2 X M, preprocessing by standard deviation standardization, establishing covariance matrix, and obtaining sample eigenvalue { lambda i A sum pairA corresponding feature vector;
step S0301:representing a slave setAccording to the feature vector f of the corresponding feature value, and then the original feature vector f i Projected into the K-dimensional PCA subspace, the constructed new features are represented as shown in equation (5), wherein,<f i ,λ j &and gt, representing the projection length of the original feature vector of the pixel point i on the jth PCA subspace basis vector:
step S0401: subspace basis vectorsThe distances between the pixel point i and the pixel point m in the PCA subspace can be simplified as shown in formula (6), dist (i, m) represents the distance between the pixel point i and the pixel point m,<f m ,λ i &the projection length of the original characteristic vector of the pixel point m on the ith PCA subspace basis vector is expressed;
step S0402: using Dist (i, m) to replace the conventional similarity measurement method, the similarity calculation manner between the target pixel point i and the auxiliary pixel point m can be represented as formula (7), where exp () function represents an exponential function with e as the base, h is a weight attenuation coefficient, and is related to the noise level:
step S0403: given pixel point i, a global auxiliary similar point set can be obtained through a layering orthogonal matching tracking algorithmFor auxiliary pixel pointThe global similarity constraint is defined as shown in equation (8):
wherein f is i Representing the domain feature vector of the pixel point i, | · | | luminance 2 Representing the euclidean distance between the feature vectors, when z = n,if not, then,
the invention has the characteristics and beneficial effects that:
in the method, in order to improve the noise reduction level of the image, the characteristics of the pixel points are extracted by using a Principal Component Analysis (PCA) method, and the similarity measurement of the target pixel points and the auxiliary pixel points is simplified by using dot product operation. The experimental result shows that the image block similarity measurement method based on principal component analysis can filter noise and simultaneously describe pixel point information more accurately by using fewer feature dimensions in the aspect of feature extraction.
Description of the drawings:
fig. 1 is a flowchart of the present invention, and it can be seen from the diagram that a principal component analysis method is used to perform correlation processing on pixel points of an image block, and the feature after dimension reduction is used as a feature of similarity measurement.
Fig. 2 shows a noise reduction contrast chart when the noise standard deviation σ = 20. From left to right the images are Lena, boat, barbarara and Man, respectively. The clear image, the noise image and the noise reduction result image are respectively arranged from top to bottom.
Fig. 2 shows the image denoising result when the noise standard deviation is 20. As can be seen from the figure, the image after noise reduction has high fidelity and is closer to the original pure image. At a noise level with a standard deviation of 20, detail information in the Lena image in a face flat area and at a hat is well protected, and boundary information is clearly visible. The Boat image shows clear hull and better recovery of the blocks on the ground. The main structural information in the image can still be kept after the image is subjected to noise reduction overall.
Detailed Description
The invention aims to extract the characteristics of pixel points by using a Principal Component Analysis (PCA) method and simplify the similarity measurement between a target pixel point and an auxiliary pixel point by using dot product operation. For a pixel point, the gray value set of the pixel block taking the point as the center is used as an original characteristic, the original artificial characteristic of the pixel point is projected into a subspace, and a more characteristic is constructed through a PCA algorithm and used for similarity measurement.
In order to achieve the above object, the present invention provides an image block similarity measurement method based on principal component analysis, comprising the following steps:
the method comprises the following steps: and constructing a mathematical model according to the core idea of the PCA algorithm. Given a d-dimensional random vector x, the random vector is considered to be estimated, and the PCA algorithm uses a covariance matrix to estimate a random variable more accurately, so that the influence of a related variable on an estimation result is reduced. The original vector is reconstructed by transforming the sample x into a new vector Y by a linear transformation operator and the reconstructed mean square error is defined.
Step two: for a given image V, according to the principle of PCA, M pixel points are randomly selected in the image to construct a dictionary of PCA. And preprocessing by adopting a standard deviation standardization method, establishing a covariance matrix, and obtaining the eigenvalue of the sample and the corresponding eigenvector.
Step three: and projecting the original features into a subspace, constructing new features, and calculating the similarity between pixel points by using the features.
Step four: a global auxiliary similar point set can be obtained through a layering orthogonal matching tracking algorithm, similarity calculation of a target pixel point and auxiliary pixel points is simplified, and similarity measurement calculation is simplified.
In the task of image noise reduction, the quality evaluation of the noise-reduced result image is an important process of algorithm analysis. And judging the quality of the noise-reduced image through different evaluation criteria, thereby checking the effectiveness of the method.
1. Evaluation standard based on pixel point error
The evaluation standard judges the quality of the noise reduction algorithm by comparing the gray value difference between corresponding pixel points of the original pure image and the noise-reduced image, and common indicators are as follows: mean Square Error (MSE) and peak signal-to-noise ratio (PSNR). In general, the smaller the MSE value, the larger the PSNR, and the higher the accuracy.
2. Evaluation criterion based on human visual characteristics
Based on the human visual perception system model, the most typical measurement index is Structural Similarity (SSIM). The SSIM index explicitly unifies image brightness, contrast and structural factors into one model to improve accuracy of an evaluation result. The higher the SSIM index is, the better the structural information in the pure image is kept in the noise-reduced image.
The experiment used an image noise reduction standard data set to test the performance of the algorithm, and the image size was 512 x 512, including 16 basic images. The comparison experiment includes noise reduction processing under three different levels of noise levels, and additive white gaussian noise with standard deviation sigma of 20, 30 and 40 is respectively added to each image in the standard data set to serve as a test image. And optimizing parameters in the feature selection process based on principal component analysis by comparing the noise reduction results of the algorithm in the parameter training data set. In the test process, the values of parameters involved in the generation of the global auxiliary points are as follows: the downsampling rate r =2, the number of downsampling layers T =4, and the global assist point number | Ng | =5. The parameters involved in the feature selection process take values as follows: the original gray value vector is composed of 7 × 7 image blocks, the reconstruction error θ =0, and the number M =10000 of selected pixels during pca initialization. According to the experimental results, the new feature dimension based on principal component analysis is generally 6.
In the aspect of feature extraction, the image block similarity measurement based on principal component analysis can extract main features of a pixel point geometric structure while filtering noise, and more accurately describe pixel point information by using fewer feature dimensions. The NLMPCA algorithm simplifies calculation by utilizing a subspace mapping method, simplifies similarity measurement in the standard NLM algorithm by the orthogonal property of PCA basis vectors, and performs rapid operation by using an inner product. According to experimental results, feature dimensions screened out using PCA are generally between 5 and 7, which reduces the computational load in the similarity measure by 80% compared to the original feature dimension of 25.
Table 1 shows the SSIM index comparison of various algorithms when the noise standard deviation is 20, and it can be seen from the table that the SSIM index is superior to other improved algorithms on 10 images, and the PCA algorithm achieves better performance.
Table 1 σ =20 SSIM indices of different noise reduction algorithms
The invention extracts the characteristics of the pixel points by using a principal component analysis method, and simplifies the similarity measurement of a target pixel point and an auxiliary pixel point by using dot product operation, comprising the following steps of:
step S0101: given a d-dimensional random vector x = (x) 1 ，x 2 ，…，x d ) Consider estimating a random vector. The method uses the covariance matrix to estimate the random variable more accurately through the PCA algorithm, and reduces the influence of the related variable on the estimation result. The covariance matrix is defined as shown in formula (1), where m X Is the mean value of the samples, S X The elements on the diagonal represent each random variable x i The off-diagonal elements represent covariance.
S X ＝E[(X-m X )(X-m X ) T ] (1)
Note that the matrix a is a linear transformation operator, which can transform any sample X into a new vector Y, and the transformation process can be expressed as shown in formula (2).
Y＝A T (X-m x ) (2)
Correspondingly, the inverse transformation process of the PCA can be expressed as shown in formula (3), where the matrix A is a linear transformation operator and m is a linear transformation operator X Is the mean of the samples.
X＝AY+m X (3)
Step S0102: in reconstruction, assuming that the first M columns of the linear operator A are taken to construct a new transformation matrix A', the new transformation operator is used, and the PCA reconstruction result of the original vector X is shown in formula (4), whereinRepresenting the reconstructed vector.
Step S0201: for a pixel point i in a given image V, a gray value feature vector fi of a square neighborhood taking the point as a center is used as an original feature vector, and the size of the square neighborhood is recorded as S. Randomly selecting M pixel points in the image V to construct a dictionary of PCA, and using the dictionaryTo represent the original feature vector set of the M pixel points. Thus, the original data sample set has dimension S 2 Xm, pre-treatment using standard deviation normalization. Establishing a covariance matrix to obtain the eigenvalue { lambda ] of the sample i And the corresponding feature vectors.
Step S0301：Representing a slave setThe feature vector combinations are selected and arranged according to the descending order of the corresponding feature values. Then the original feature vector f i Projected into the K-dimensional PCA subspace, the constructed new features can be expressed as shown in equation (5), where,<f i ,λ j &and gt, representing the projection length of the original feature vector of the pixel point i on the jth PCA subspace basis vector.
Step S0401: subspace basis vectorsThe distances between the pixel point i and the pixel point m in the PCA subspace can be simplified, and the calculation process can be simplified as shown in formula (6), wherein,<f m ,λ i &and gt represents the projection length of the original feature vector of the pixel point m on the ith PCA subspace basis vector.
Step S0402: using Dist (i, m) to replace the traditional similarity measurement method, the similarity calculation method between the target pixel point i and the auxiliary pixel point m can be expressed as shown in formula (7), where the exp () function represents an exponential function with e as the base, and h is a weight attenuation coefficient, which is related to the noise level.
Step S0403: given pixel point i, pass hierarchyThe orthogonal matching pursuit algorithm can obtain the global auxiliary similar point setFor auxiliary pixel pointThe global similarity constraint is defined as shown in equation (8), where f i The field feature vector representing the pixel point i, | | ground | | 2 Representing the euclidean distance between the feature vectors. When z = n, the number of the n-th planes is zero,if not, then the mobile terminal can be switched to the normal mode,
in the method, in order to improve the noise reduction level of the image, the characteristics of the pixel points are extracted by using a Principal Component Analysis (PCA) method, and the similarity measurement of the target pixel points and the auxiliary pixel points is simplified by using dot product operation. The experimental result shows that the image block similarity measurement method based on principal component analysis can filter noise and simultaneously use less feature dimensions to more accurately describe pixel point information in the aspect of feature extraction.
Claims (3)
1. An image block similarity measurement method based on principal component analysis is characterized by comprising the following steps:
the method comprises the following steps: a Principal Component Analysis (PCA) algorithm is adopted to construct a mathematical model: giving a d-dimensional random vector x, considering the estimation of the random vector, transforming a sample x into a new vector Y through a linear transformation operator to reconstruct an original vector, and defining a reconstructed mean square error;
step two: for a given image V, randomly selecting M pixel points in the image to construct a dictionary of PCA, preprocessing by adopting a standard deviation standardization method, establishing a covariance matrix, and obtaining a characteristic value of a sample and a corresponding characteristic vector;
step three: projecting the original features into a subspace, constructing new features, and calculating the similarity between pixel points by using the features;
step four: a global auxiliary similar point set can be obtained through a layering orthogonal matching tracking algorithm, similarity calculation of a target pixel point and auxiliary pixel points is simplified, and similarity measurement calculation is simplified.
2. The image block similarity measurement method based on principal component analysis according to claim 1, wherein the effectiveness of the measurement method is verified by using an evaluation criterion based on pixel point errors and an evaluation criterion based on human visual characteristics.
3. The principal component analysis-based image block similarity measurement method of claim 1, wherein the detailed steps in a specific example are as follows:
step S0101: given a d-dimensional random vector x = (x) 1 ，x 2 ，...，x d ) The random variables are estimated by the PCA algorithm using a covariance matrix defined as formula (1), where m X Is the mean value of the samples, S X The elements on the diagonal represent each random variable x i The off-diagonal elements represent covariance:
S X ＝E[(X-m X )(X-m X ) T ] (1)
the matrix A is a linear transformation operator, the operator transforms any sample X into a new vector Y, and the transformation process is expressed as formula (2):
Y＝A T (X-m x ) (2)
correspondingly, the inverse transformation process of PCA can be expressed as shown in formula (3), where matrix A is a linear transformation operator and m is X Is the mean of the samples.
X＝AY+m X (3)
Step S0102: during reconstruction, the first M columns of the linear operator A are adopted to construct a new transformation matrix A', and the PCA reconstruction result of the original vector X is shown in formula (4) by using the new transformation operatorRepresents the reconstructed vector:
step S0201: for a pixel point i in a given image V, taking a gray value feature vector fi of a square neighborhood taking the point as a center as an original feature vector, marking the size of the square neighborhood as S, and using the SRepresenting all pixel points in the image V, where f i The expression dimension is S 2 The neighborhood feature vector of the pixel is based on the principal component analysis, the basic unit of the feature extraction method of the principal component analysis is the pixel, and the same method is used for extracting the features of the pixel in the measurement of global similarity constraint and local similarity constraint;
step S0202: randomly selecting M pixel points in the image V to construct a dictionary of PCA (principal component analysis)To express the original feature vector set of the M pixel points, therefore, the original data sample set has dimension S 2 X M, preprocessing by standard deviation standardization, establishing covariance matrix, and obtaining sample eigenvalue { lambda i And the corresponding feature vectors;
step S0301:representing a slave setAccording to the feature vector f of the corresponding feature value, and then the original feature vector f i Projected into the K-dimensional PCA subspace, the constructed new feature is represented as shown in equation (5), where < f i ，λ j The projection length of the original feature vector representing the pixel point i on the jth PCA subspace basis vector is as follows:
step S0401: subspace basis vectorsThe distances between the pixel point i and the pixel point m in the PCA subspace can be simplified, the calculation process is simplified as shown in a formula (6), dist (i, m) represents the distance between the pixel point i and the pixel point m, and f is less than f m ，λ i The projection length of the original characteristic vector of the pixel point m on the ith PCA subspace basis vector is represented;
step S0402: using Dist (i, m) to replace the conventional similarity measurement method, the similarity calculation method between the target pixel point i and the auxiliary pixel point m can be represented as shown in formula (7), where the exp () function represents an exponential function with e as the base, h is a weight attenuation coefficient, and is related to the noise level:
step S0403: given pixel point i, a global auxiliary similar point set can be obtained through a layering orthogonal matching tracking algorithmFor auxiliary pixel pointThe global similarity constraint is defined as shown in equation (8):
wherein, f i Representing the domain feature vector of the pixel point i, | · | | luminance 2 Representing the euclidean distance between the feature vectors, when z = n,if not, then,
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