CN104637060B - A kind of image partition method based on neighborhood principal component analysis-Laplce - Google Patents
A kind of image partition method based on neighborhood principal component analysis-Laplce Download PDFInfo
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Abstract
The invention discloses a kind of image partition method based on neighborhood principal component analysis-Laplce, this method carries out principal component analysis to original image, obtains the feature vector of each pixel, extract the main component of image, effectively inhibit noise；Then, edge detection is carried out to image with Laplace operator, to realize the segmentation to image.Compared with traditional Sobel operators and LOG operator partitioning algorithms, this method to image pixel by carrying out principal component analysis, to estimate the parameter value during denoising, and independent of empirical value, the interference that noise on image can be effectively reduced, simplifies computation complexity.The experimental results showed that this method can effectively improve the segmentation effect of image, there is stronger superiority in accuracy and robustness.
Description
Technical field
The present invention relates to technical field of image processing more particularly to a kind of based on neighborhood principal component analysis-Laplce's
Image partition method.
Background technology
Image Segmentation Technology has penetrated into the every aspect of life, such as in biology, medical image analysis, need by
Cell, histoorgan are split from image measures its shape, cross sectional images etc., to determine pathological tissues
Measure qualitative analysis, assessment and prediction.As the capture of the visual informations such as video camera, camera, infrared ray and various sensors is set
The acquisition of the standby development with technology, visual information has become simple question, but how to go and obtain in numerous visual information
Interested part becomes important research direction.It is especially noise-containing in the image of acquisition, how to obtain more
Accurate detailed information becomes the main problem of image studies.Image segmentation is the basic problem of computer vision field, especially
The critical issue in image procossing, analysis and understanding, the quality of image segmentation quality directly influence the performance of vision system,
The accuracy of target detection and target identification.In past research, researcher proposes many dividing methods, but still
So without a kind of general algorithm, these algorithms are often to be proposed for certain specific images.We divide the image into point
For traditional dividing method and based on the dividing method of study.For the noise for how reducing image, the segmentation matter of image is improved
The problem of amount, image Segmentation Technology first to Noise imagery exploitation principal component analysis denoising, to image carry out edge extracting and
Segmentation, obtains the segmentation image of high quality, and be widely used.
Traditional dividing method includes edge detection dividing method [1] [2] [3] based on differential operator, based on region
Dividing method [4] [5] and the dividing method etc. based on threshold value.Edge detection dividing method based on differential operator uses single order
Or the marginal point of Second Order Differential Operator detection image, point is then connected into forming region profile according to certain strategy.
Edge can be accurately positioned in this method, and arithmetic speed is fast, and still, the edge of detection is often discontinuous, detection it is accurate
There are contradictions between property and noise immunity.Dividing method based on region mainly finds suitable seed or suitable
Growth criterion carrys out forming region, to realize image segmentation.This dividing method can preferably form cut zone, but count
Calculation amount is larger, is easy to cause over-segmentation to image.It is obtained most preferably by rational object function based on the dividing method of threshold value
Segmentation threshold distinguishes the target and background of image, realizes the segmentation of image.This method calculating is simple, efficient, and can
It is connected to the region that closed boundary definition does not overlap.But the selection of threshold value determines the quality of image segmentation.Traditional segmentation
Algorithm is often directly split image, is not pre-processed to image, cannot effectively inhibit noise on image
Interference, reduce the segmentation quality of image.
Invention content
The technical problem to be solved in the present invention is for the defects in the prior art, to provide a kind of based on neighborhood principal component
The image partition method of analysis-Laplce, this method solve edge in the existing similar partitioning algorithm based on edge extracting and carry
The problem of taking to noise-sensitive carries out denoising to image using neighborhood principal component analysis, then utilizes Laplace operator
Edge extracting is carried out to image and improves the segmentation quality of image to realize image segmentation.
The technical solution adopted by the present invention to solve the technical problems is：One kind being based on neighborhood principal component analysis-La Pula
This image partition method, includes the following steps：
S1 appoints take a pixel P in the picture, and point centered on it carries out figure according to the size of the piecemeal of preset image
As the selection of block, then centered on pixel P, piecemeal is carried out to the original image of input, image graph is square block, in this way may be used
Each pixel of original image is expressed as the image block being made of its neighborhood territory pixel；
S2 chooses the identical similar block of size, the sample as image to pixel P, in the window put centered on pixel P
Training set；The window is the square window for including multiple images block；
S3 carries out PCA transformation to above-mentioned sample training collection, reaches input pixel P with the main composition expression base table of training sample
Neighborhood territory pixel block, adjust the contribution rate of main composition, the pixel value P ' after the denoising of pixel P can be obtained；
S4 seeks the master of the neighborhood block of each pixel to each pixel of the original image of input with step S1, S2, S3
Composition is expressed；And the estimated value after the denoising of each pixel is calculated according to the characteristic value in main composition domain, last split is whole to go
Pixel after making an uproar acquires the image after denoising；
S5 carries out Laplce's edge extracting to the denoising image of acquisition, obtains a breadths edge characteristic image；
S6 is split the edge feature image of acquisition according to edge, obtains edge segmentation image.
By said program, the step S2) in, the basis for selecting of similar block is：If the image block meets σ<T, T are a certain
The threshold value of setting just chooses its central point pixel x (i, j), and feature can be indicated by formula (1), the input picture block of acquisition
Pixel characteristic domain similitude as the similarity criterion for weighing alternatively training sample；
X (i, j)=X0(i,j)+n(i,j) (1)
σ is the inequality of sample block to be selected and input picture block；M is the number for the block chosen from sample database；X(xi) it is choosing
I-th of the neighborhood block vector taken；To input the image block vector centered on pixel；
Sample set in window indicates with matrix X, X=[X1,X2,…,Xm] T, whereinIt indicates
Centered on pixel central point pixel x (i, j)The image block of size be unfolded from row (or row) to
Amount.
By said program, the step S3) in PCA transformation carried out to sample training collection include the following steps：
Centralization matrix can be acquired by carrying out centralization to sample set XIt indicates to calculate each figure
As the sample average of block, it is assumed that the Mean Matrix of each sample block corresponding to sample set X is
WhereinThe mean value device matrix of so each block of pixels isWherein n is indicated in image block
The number of element；Centralization matrix in this wayIt can be indicated by formula (3)：
Wherein, rightIts sample covariance matrix C (X) is asked to be by formula (4)：
SVD decomposition is carried out to covariance C (X), since noise is white Gaussian noise, covariance matrix can be by formula (5) table
Show：
C (X)=EtET+C0 (5)
E is the orthogonal matrix of m × m, is made of feature vector, and t is diagonal matrix, and diagonal element is the spy of pixel P
Value indicative, and arranged according to descending, that wherein E is indicated is the percentage contribution that various elements synthesize image in sample space, row
Components contribution in front is bigger, also referred to as main composition, C0Indicate noise matrix.
By said program, the step S4) in calculate the estimated value of each pixel according to principal component analysis and use following step
Suddenly：
S4.1) to eigenvalue matrix t, diagonal element is λ i, characteristic value λ1≥λ2≥…≥λp, (i=1,2 ..., p),
The contribution rate of accumulative total of r characteristic value before being calculated by formula (6)：
S4.2) assume C0=σ2I, σ indicate the intensity of Gaussian noise, then the C (X) in formula (5) can be calculated by formula (7)：
C (X)=EtET+σ2I=E (t+ σ2)ET(7)；
In this way it can be found that the feature vector of C (X) is E, illustrates contaminated pixel and do not have contaminated pixel
Feature vector having the same, and ET=E-1；It is E to obtain PCA transformation matrixsT, also referred to as main composition expresses base, by ETEffect
InY can be obtained by formula (8)：
Wherein Y is the expression sparse matrix on the main composition expression base corresponding to sample X, then for the image block of input
X0, corresponding expression coefficient is Y0=ETX0；
S4.3 the number of feature vector in main composition expression base) is controlled, so that it may divide noise and picture material to realize
From, the larger expression picture material of main composition expression characteristic vector characteristics value, characteristic value it is smaller illustrate noise contribution, in this way
The separation between picture material and noise is realized, can be obtained by formula (9)：
Wherein,Indicate that the noiseless estimated value of input picture block, E indicate that main composition expresses base, Y0Indicate input picture
The main composition of block expresses coefficient.
S4.4) due to having subtracted mean value, X during variation0Estimated valueIt can be obtained by formula (10)：
Wherein, μ indicates the mean value of training sample image block.
S4.5) to each pixel of the noise-containing image of input, its estimated value for not having contaminated pixel is found out,
Obtain the image after denoising.
The beneficial effect comprise that：The present invention carries out principal component denoising by the sample set to selection, distinguishes
The internal characteristics and noise of input image pixels, influence when can effectively inhibit edge extracting to noise-sensitive, to carry
The segmentation quality of hi-vision.This paper algorithms and the comparison carried out based on traditional Sobel and LOG methods, to the image energy of input
Enough preferably extraction edges, to realize the segmentation of image.
Description of the drawings
Present invention will be further explained below with reference to the attached drawings and examples, in attached drawing：
Fig. 1 is the method flow diagram of the embodiment of the present invention；
Fig. 2 is that the image block of the embodiment of the present invention divides schematic diagram；
Fig. 3 carries out image for algorithms of different in the table 1 of the embodiment of the present invention result of edge detection.
Specific implementation mode
In order to make the purpose , technical scheme and advantage of the present invention be clearer, with reference to embodiments, to the present invention
It is further elaborated.It should be appreciated that described herein, specific examples are only used to explain the present invention, is not used to limit
The fixed present invention.
The present invention implement the image partition method based on neighborhood principal component analysis-Laplce to original image carry out it is main at
Analysis, extracts the main component of image；Then, edge detection is carried out to image with Laplace operator, to realize to figure
The segmentation of picture.Main two images in Fig. 1, the left side is input picture, with blackening arrow direction calculation part.The lower right corner is defeated
Go out image, after methods herein is handled, which is directed toward by thin arrow.The portion being framed in Fig. 1 with dotted line frame
Point.It is two major parts of algorithm：Image denoising and image segmentation.It is image denoising in first dotted line frame, it is main to wrap
Include four steps：The selection of image block, the selection of neighborhood block, four parts of principal component decomposition and principal component noise reduction；It uses respectively
Broad arrow is directed toward next step.It is image segmentation, including Laplce's edge extracting and image segmentation in second dotted line frame
Two parts；Black broad arrow is used to be directed toward next step respectively.
The specific steps are：
S1 appoints take a pixel P in the picture, and point centered on it carries out figure according to the size of the piecemeal of preset image
As the selection of block, then centered on pixel P, piecemeal is carried out to the original image of input, image graph is square block, in this way may be used
Each pixel of original image is expressed as the image block being made of its neighborhood territory pixel；
The noise-containing original image of input, that is, image to be split.To the image of input, a certain pixel P is chosen,
Centered on it, image block is chosen.In embodiment, to a certain pixel x (i, j), centered on it, its 8 neighborhood is chosen as figure
As block, as shown in Figure 2.Brightness, single order transverse gradients and the single order longitudinal direction Grad of selected pixels point x (i, j).I.e. with x (i, j)
Centered on formwork.Formwork is indicated with column vector, for each pixel x (i, j), can be indicated by formula (1):
X (i, j)=X0(i,j)+n(i,j) (1)
X (i, j) indicates noise-containing variate-value, X0(i, j) indicates that the variate-value of not Noise, n (i, j) indicate noise
Value.
S2 chooses the identical similar block of size, the sample as image to pixel P, in the window put centered on pixel P
Training set；The window is the square window for including multiple images block；
Pixel centered on selected pixels point x (i, j) is chosen from the window that the size centered on point x (i, j) is L × L
N most like sample block is n × m matrixes as training sample set X, X.Because this paper noises use white Gaussian noise,
Noise and signal are independent from each other.Its variance can be indicated by formula (2)：
σ is the inequality of sample block to be selected and input picture block；M is the number for the block chosen from sample database；X(xi) it is choosing
I-th of the neighborhood block vector taken；To input the image block vector centered on pixel；
If meeting σ<T, T are the value of a certain setting, and sample is used as with regard to selected point pixel x (i, j).
Sample set in window indicates with matrix X, X=[X1,X2,…,Xm]T, whereinIndicate with
Centered on pixel central point pixel x (i, j)The vector that the image block of size is unfolded from row (or row).
S3 carries out PCA transformation to above-mentioned sample training collection, reaches input pixel P with the main composition expression base table of training sample
Neighborhood territory pixel block, adjust the contribution rate of main composition, the pixel value P ' after the denoising of pixel P can be obtained；
Centralization matrix can be acquired by carrying out centralization to sample set XIt indicates to calculate each figure
As the sample average of block, it is assumed that the Mean Matrix of each sample block corresponding to sample set X is
WhereinThe mean value device matrix of so each block of pixels isWherein n is indicated in image block
The number of element；Centralization matrix in this wayIt can be indicated by formula (3)：
It is rightIts sample covariance matrix can be asked to be by formula (4)：
SVD decomposition is carried out to covariance C (X), since noise is white Gaussian noise, is obtained
C (X)=EtET+C0 (5)
E is the orthogonal matrix of m × m, is made of feature vector, and t is diagonal matrix, and diagonal element is the spy of pixel P
Value indicative, and arranged according to descending, that wherein E is indicated is the percentage contribution that various elements synthesize image in sample space, row
Components contribution in front is bigger, also referred to as main composition, C0Indicate noise matrix.
S4 seeks the master of the neighborhood block of each pixel to each pixel of the original image of input with step S1, S2, S3
Composition is expressed；And the estimated value after the denoising of each pixel is calculated according to the characteristic value in main composition domain, last split is whole to go
Pixel after making an uproar acquires the image after denoising；
S4.1) to eigenvalue matrix t, diagonal element is λ i, characteristic value λ1≥λ2≥…≥λp, (i=1,2 ..., p),
The contribution rate of accumulative total of r characteristic value before being calculated by formula (6)：
S4.2) assume C0=σ2I, σ indicate the intensity of Gaussian noise, then formula (5) C (X) can be calculated by formula (7)：
C (X)=EtET+σ2I=E (t+ σ2)ET (7)
In this way it can be found that the feature vector of C (X) is E, illustrates contaminated pixel and do not have contaminated pixel
Feature vector having the same, and ET=E-1；It is E to obtain PCA transformation matrixsT, by ETIt acts onY can be obtained by formula (8)：
Wherein Y is the expression sparse matrix on the main composition expression base corresponding to sample X, then for the image block of input
X0, corresponding expression coefficient is Y0=ETX0；
S4.3 the number of feature vector in main composition expression base) is controlled, so that it may divide noise and picture material to realize
From, the larger expression picture material of main composition expression characteristic vector characteristics value, characteristic value it is smaller illustrate noise contribution, in this way
The separation between picture material and noise is realized, can be obtained by formula (9)：
Wherein,Indicate that the noiseless estimated value of input picture block, E indicate that main composition expresses base, Y0Indicate input picture
The main composition of block expresses coefficient.
S4.3) due to having subtracted mean value during variation, estimated value can be obtained by formula (10)：
Wherein, μ indicates the mean value of training sample image block.
S4.3) to each pixel of the noise-containing image of input, its estimated value for not having contaminated pixel is found out,
Obtain the image after denoising.
S5 carries out Laplce's edge extracting to the denoising image of acquisition, obtains a breadths edge characteristic image；
Edge extracting is carried out to the image Y after removal noise, carrying out edge to image there is used herein Laplace operators carries
It takes.Convolution is carried out to image Y using 3 × 3 template, its zero crossing is found, as its marginal point.Since the edge of extraction has
Breakpoint exist it is necessary to connect together originally the breakpoint generated due to edge extracting the case where repair.It needs to breakpoint
Place carry out marginal growth method, the direction of growth along the deflection of the line segment at the place of the breakpoint some neighborhood,
If occurring a plurality of candidate line sections in some direction of growth, priority algorithm is just used, considers length and the side of candidate line sections
To angle, select length is longer, deflection close to the deflection at breakpoint as growth object.It can be obtained by complete side in this way
Edge image.
S6 is split the edge feature image of acquisition according to edge, obtains edge segmentation image.
Specific testing example：Use Berkeley database (document 13：P.Arbelaez；M.Maire；
C.Fowlkes；J.Malik,"Contour Detection and Hierarchical Image Segmentation",
Pattern Analysis and Machine Intelligence,IEEE Transactions on,2011,vol.33,
no.5,pp:898-916.).The original image that 100 pixel sizes are 481 × 321 is had chosen as test image.To original
It is 0 that image, which adds mean value, the white Gaussian noise of standard deviation 0.2,0.4,0.6,0.8.Such as be 0 for containing addition mean value,
The image for the goose that standard deviation is 0.2 chooses 8 neighborhoods of its a certain pixel x (i, j) as image block, then should according to fig. 2
Brightness, single order transverse gradients and the single order longitudinal direction Grad of neighborhood block are indicated with column vector.Then centered on x (i, j)
Size is according to formula (2), to choose its similar block in the window of L × L, form sample set, sample set is indicated with matrix X.So
PCA transformation is carried out to sample set X according to formula (3) (4) (5) afterwards, obtains its characteristic value, and arrange according to descending.According to formula
(6) its characteristic value is selected, so that it may obtain the estimated value of eigenmatrix t.It then can according to formula (7) (8) (9) (10)
It obtains pixel x (i, j) and does not have contaminated estimated valueThen all pixels of the goose image to input all carry out pixel x
The processing step of (i, j), just obtain whole image not by the image of noise pollution, i.e. image after denoising.Then according to step
Rapid 5, Laplace edge extractings are carried out to the image after denoising, edge feature image are obtained, according to edge feature image to image
It is split, obtains segmentation image.
Experimental comparison presented below illustrates the validity of this method.
Herein, using the average value of wherein goose, aircraft and all images as displaying result.To noise-containing image profit
Image segmentation is carried out with context of methods, and records experimental result.Since the key of the image segmentation algorithm based on edge extracting is
Edge extracting, therefore only show the effect after edge extracting.And by the algorithm of this paper and traditional Sobel edge detection algorithms,
The artificial extraction edge of LOG edge detection algorithms and Berkeley is compared.Image is evaluated, Y-PSNR is chosen
(Peak Signal Noise Ratio, PSNR) and picture structure similar mass index (Structure Similarity,
SSIM) carry out the segmentation quality of evaluation image.It is 0 to addition mean value, the noise image of standard deviation 0.2,0.4,0.6,0.8 carries out
After edge extracting, divides and measure its PSNR value and SSIM values, and record experimental result.It is 0 that Fig. 3, which gives mean value, standard deviation 0.2
The edge that is extracted under Sobel edge detection algorithms, LOG edge detection algorithms and this paper algorithms of noise image, and give
The effect of the artificial edge extracting of Berkeley.Table 1 gives PSNR value of the different noise levels under different Boundary extracting algorithms.
Table 2 gives SSIM value of the different noise levels under different Boundary extracting algorithms.
The image Y-PSNR (PSNR/db) of 1 several edge detection algorithms of table
The picture structure similarity index (SSIM/db) of 2 several edge detection algorithms of table
It should be understood that for those of ordinary skills, it can be modified or changed according to the above description,
And all these modifications and variations should all belong to the protection domain of appended claims of the present invention.
Claims (4)
1. a kind of image partition method based on neighborhood principal component analysis-Laplce, which is characterized in that include the following steps：
S1 appoints take a pixel P in the picture, point centered on it, and image block is carried out according to the size of the piecemeal of preset image
Selection piecemeal is carried out to the original image of input, image block is square block, original image then centered on pixel P
Each pixel be expressed as the image block being made of its neighborhood territory pixel；Image block corresponding to a certain pixel x (i, j) is chosen
Brightness, single order transverse gradients and the single order longitudinal direction Grad of image block are indicated with column vector；In being formed and being with pixel x (i, j)
The image block of the heart, described image block are indicated with column vector；
S2 chooses the identical multiple similar neighborhood block of pixels of size to pixel P, in the window put centered on pixel P, as figure
The sample training collection of picture；The window is the square window for including multiple images block；
S3 carries out PCA transformation to above-mentioned sample training collection, and the phase of input pixel P is reached with the main composition expression base table of training sample
Like neighborhood territory pixel block, the contribution rate of main composition is adjusted, obtains the pixel value P ' after the denoising of pixel P；
S4 seeks the main composition of the neighborhood block of each pixel to each pixel of the original image of input with step S1, S2, S3
Expression；And the estimated value after the denoising of each pixel is calculated according to the characteristic value in main composition domain, after the denoising of last split whole
Pixel acquire the image after denoising；
S5 carries out Laplce's edge extracting to the denoising image of acquisition, obtains a breadths edge characteristic image；
S6 is split the edge feature image of acquisition according to edge, obtains edge segmentation image.
2. image partition method according to claim 1, which is characterized in that in the step S2, similar neighborhood block of pixels
Basis for selecting be：If the image block meets σ<T, T are the threshold value of a certain setting, just choose its central point pixel x (i, j),
Its feature indicates by formula (1), and the similitude of the input picture block of acquisition in pixel characteristic domain is alternatively trained as weighing
The similarity criterion of sample；
X (i, j)=X0(i,j)+n(i,j) (1)
X0(i, j) indicates that the variate-value of not Noise, n (i, j) indicate noise figure；σ is the equal of sample block to be selected and input picture block
Difference；M is the number for the block chosen from sample database；X(xi) it is i-th of the neighborhood block vector chosen；To input with pixel
Centered on image block vector；
Sample set in window indicates with matrix X, X=[X1,X2,…,Xm]T, whereinIt indicates with pixel
Centered on dot center point pixel x (i, j)The vector that the image block of size is unfolded from row or column.
3. image partition method according to claim 2, which is characterized in that carried out to sample training collection in the step S3
PCA transformation includes the following steps：
Centralization is carried out to sample set X and acquires centralization matrixIt indicates to calculate each image block
Sample average, it is assumed that the Mean Matrix of each sample block corresponding to sample set X isWhereinThe mean value transposed matrix of so each image block isWherein n indicates pixel in image block
Number；Centralization matrix in this wayIt is indicated by formula (3)：
Wherein, rightIts sample covariance matrix C (X) is asked to be by formula (4)：
SVD decomposition is carried out to sample covariance matrix C (X), since noise is white Gaussian noise, covariance matrix is by formula (5)
It indicates：
C (X)=EtET+C0 (5)
E is the orthogonal matrix of m × m, is made of feature vector, and t is diagonal matrix, and diagonal element is the characteristic value of pixel P,
And it is arranged according to descending, what wherein E was indicated is the percentage contribution that various elements synthesize image in sample space, comes front
Components contribution it is bigger, also referred to as main composition, C0Indicate noise matrix.
4. image partition method according to claim 3, which is characterized in that according to principal component analysis meter in the step S4
The estimated value for calculating each pixel uses following steps：
S4.1) to eigenvalue matrix t, diagonal element λi, eigenvalue λ1≥λ2≥…≥λp, (i=1,2 ..., p), by formula
(6) contribution rate of accumulative total of r characteristic value before calculating：
S4.2) assume C0=α2I, α indicate the intensity of Gaussian noise, then the C (X) in formula (5) is calculated by formula (7)：
C (X)=EtET+α2I=E (t+ α2)ET(7)；
The feature vector of C in this way (X) is E, illustrates contaminated pixel and does not have contaminated pixel spy having the same
Sign vector, and ET=E-1；It is E to obtain PCA transformation matrixsT, also referred to as main composition expresses base, by ETIt acts onY is by formula
(8) it obtains：
Wherein, Y is the expression sparse matrix on the main composition expression base corresponding to sample X, then for the image block X of input0,
Its corresponding expression coefficient is Y0=ETX0；
S4.3 the number for) controlling feature vector in main composition expression base, realizes the separation to noise and picture material, main composition table
The expression picture material larger up to feature vector characteristic value, characteristic value it is smaller illustrate noise contribution, image has been achieved
Separation between content and noise is obtained by formula (9)：
Wherein,Indicate that the noiseless estimated value of input picture block, E indicate that main composition expresses base, Y0Indicate input picture block
Main composition expresses coefficient；
S4.4) due to having subtracted mean value, X during variation0Estimated valueIt is obtained by formula (10)：
Wherein, μ indicates the mean value of training sample image block；
S4.5) to each pixel of the noise-containing image of input, its estimated value for not having contaminated pixel is found out, is obtained
Image after denoising.
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