CN102183535B - Low-dimensional nano material identification method based on SEM image - Google Patents

Abstract

The invention belongs to the crossed technical field of computer mode identification and nano material, and relates to a low-dimensional nano material identification method based on an SEM image. The method comprises the following steps of: (1) preprocessing a known nano material SEM image sample; (2) performing two-dimensional wavelet transformation on the preprocessed image to get sub-image matrixes on different frequency bands; (3) extracting characteristics of the sub-image matrixes on each frequency band, and taking a statistical value of each sub-image matrix as a characteristic value for representing surface texture of the nano material; (4) according to the characteristic value, taking a Gaussian radial basis function as a support vector machine kernel function to find an optimal hyperplane between any two classes, and creating a classification model for different classes of nano materials; (5) extracting a texture characteristic value of the known nano material SEM image sample, and identifying the unknown nano material by voting according to the classification model obtained in the step (4). The low-dimensional nano material identification method based on the SEM image represents and distinguishes different nano material structure types more accurately and effectively, and has the advantages of high accuracy, strong expansibility, high degree of automation and the like.

Description

Low-dimension nano material recognition methods based on the SEM image

Technical field

The invention belongs to the crossing domain of computer patterns identification and nano material, relate to and a kind ofly realize the low-dimension nano material recognition methods based on Computer Image Processing, can be used for appearance of nano material and characterize, synthetic and production provides guidance for nano material.

Background technology

At present, low dimension nanometer technology (generally including peacekeeping two-dimensional nano technology), especially the 1-dimention nano technology has day by day become the revolutionary force of commercial production and science and technology research, has represented nanometer technology development in future direction to a certain extent; Yet because low-dimension nano material structure, complex shape are various; Corresponding auxiliary detection means and pattern characterization technique lack relatively; Aspect pattern detection and classification discriminating, also almost be a blank at present particularly, this has become a bottleneck of the low dimension of restriction Nano-technology Development.

Traditional nano material analysis and characterizing method are confined to composition analysis mostly (like energy spectrum analysis: EDS/EDX; X-ray diffraction analysis: XRD) characterize to go up (like scanning electron microscope-SEM, transmission electron microscope-TEM, atomic force microscope-AFM) with structure and morphology.For example; The scientific research personnel who has utilizes geometric formula that the particle diameter of particulate material is calculated according to the XRD data of material, thereby obtains one of particle size distribution roughly result; Perhaps provide its corresponding theory value information through Theoretical Calculation; Though said method calculates easy, can only provide simple characteristic index such as zero-dimension nano particle diameter, size, then powerless for more complicated monodimension nanometer material.Also there are some scientific research personnel to utilize associated picture to obtain the relevant information of nano material, and its quality is assessed,, adopt the means of AFM that it is analyzed mostly, to judge the synthetic quality of film as for two-dimensional nano material (film); For quanta point material (particle), the view data that adopts TEM to provide is mostly analyzed.Said method just utilizes human eye to estimate and differentiate; Draw related conclusions with this, do not analyze from the angle of Flame Image Process, it is very big influenced by subjective factor; Be theoretically unsound, be difficult to material is carried out quantitative test; Also can't form unified standard, more be unfavorable for computer operation, be difficult to satisfy the needs of actual engineering.At present, fractal theory has been obtained certain achievement in the application of aspects such as nano film material, powder body material, CNT, nanoparticle suspension system, nano composite material, nano whisker.In document in the past, the scientific research personnel based on the image of types such as TEM, AFM, spot, through calculating the fractal and parametric texture of nano material, differentiates correlated characteristics such as nano particle and film quality mostly.Although fractal dimension and texture analysis are obtaining certain achievement aspect the material pattern sign, more deeply also do not seeing relevant report as yet in the accurate classification discriminating.Along with the develop rapidly of nanometer technology, and the continuous expansion of nano composite material kind, to the efficient processing of nano material image with analyze and just seem particularly important.The fast development of technology such as Digital Image Processing in recent years,, mathematical morphology, pattern-recognition makes the solution of the problems referred to above become possibility.

Summary of the invention

In order to solve classic method in the deficiency aspect detection of low-dimension nano material pattern and the classification discriminating; The present invention proposes a kind of new low-dimension nano material classification and recognition methods automatically based on the SEM image; Through wavelet package transforms is combined with SVM; Have higher nicety of grading, can realize the automatic classification and the identification of low-dimension nano material.Technical scheme of the present invention is following:

A kind of low-dimension nano material recognition methods based on the SEM image comprises the following steps:

(1) known nano material SEM image pattern is done pre-service;

(2) pretreated image is carried out the 2-d wavelet packet transform, obtain the subgraph matrix on the different frequency bands;

(3) each frequency band subgraph matrix is carried out feature extraction, the statistic of each subgraph matrix is as the eigenwert that characterizes the nano-material surface texture structure;

(4) according to the extraction eigenwert, adopt the radially basic kernel function of Gauss as the SVMs kernel function, between any two types, seek the optimal classification face, set up the disaggregated model of different types of nano material;

(5) nano material SEM image pattern repeating step (1), (2), (3) step of the unknown are extracted the eigenwert that characterizes the nano-material surface texture structure, the disaggregated model that obtains according to (4) step again adopts the ballot method to carry out unknown nano material identification.

As preferred implementation, the pre-service of step (1) will comprise two parts: the one, and utilize filtering method to reduce noise to the image texture effect on structure, the 2nd, divide removal and the irrelevant image block of nano-material surface texture structure through image-region.

The present invention has selected fully to reflect that the SEM image of material surface pattern analyzes on the basis of further investigation low-dimension nano material pattern, utilize the method for texture analysis to realize that the pattern of low-dimension nano material characterizes and classification automatically.The present invention's advantage compared with prior art is:

(1) aspect feature extraction; The characteristic quantity of the statistic of each frequency band subgraph matrix behind the nano material SEM image process wavelet package transforms as the sign nano material; Than traditional composition analysis, FRACTAL DIMENSION etc., more can reflect nano-material surface structure composition truly, and reduce calculated amount.

(2) proposed sorting technique, utilized structural risk minimization that classifying face can not only correctly be separated nano material, and made the class interval maximum based on SVMs, higher than traditional dependence Artificial Cognition efficient.

In a word; The present invention is used for the texture analysis correlation theory the automatic classification and the identification of low-dimension nano material; Overcome the limitation that existing manual detection method is limited by scientific research personnel's knowledge and experience; The present invention can characterize more accurately and efficiently and distinguish different nanometer material structure types, has accuracy rate height, strong, the automaticity advantages of higher of extendability, has a wide range of applications.

Description of drawings

Fig. 1 low-dimension nano material recognition methods of the present invention process flow diagram.

Fig. 2 is wavelet package transforms figure, and L is a low frequency part, and H is a HFS, and decompose the first order of subscript 1,2 presentation video and the second level.Wavelet package transforms is constantly all frequency bands to be carried out filtering and sampling processing, and it has not only kept many resolution characteristics of wavelet transformation, and has made full use of high-frequency sub-band rich details information, can form effective proper vector, thereby improves nicety of grading.

Fig. 3 is an optimal classification lineoid synoptic diagram.Zero with represent two types of nano material samples respectively, H for the classification lineoid, H ₁And H ₂Be respectively the nearest nano material sample of all kinds of middle distances classification lineoid and be parallel to the plane of the lineoid of classifying, the distance between them is designated as the class interval.

The pretreated 16 types of nano material SEM images of Fig. 4 embodiment of the invention.

Fig. 5 embodiment of the invention type nano material SEM image 64 frequency band subgraphs behind 3 layers of wavelet package transforms.

16 types of nano material classification results of Fig. 6 embodiment of the invention figure.

Embodiment

Low-dimension nano material based on the SEM image provided by the invention is classified automatically and recognition methods mainly is made up of two big steps, and the one, nano material SEM image texture features is extracted, the structure texture feature vector; The 2nd, the design of svm classifier device.Concrete steps and principle are following:

(1) texture feature extraction, the structure texture feature vector

Different nano material SEM imaging surfaces present visibly different texture and structural characteristic; According to the texture analysis correlation theory; Wavelet package transforms is as a kind of meticulous signal analysis method; Be the ideal tools of research image texture characteristic, can reflect nano material SEM imaging surface textural characteristics well.

According to the basic theories of multiresolution analysis, orthogonal wavelet decomposes and can be defined as

W wherein _jBe the wavelets Subspace of wavelet function ψ (t), V _iBe the yardstick subspace of j yardstick, then signal can be decomposed in the Hilbert space

Order

$\left\{\begin{array}{cc}{U}_j^0=V_j& j\&Element;\mathrm{<figure-callout\; id="1"\; label="Z\; U\; j"\; filenames="HDA0000049922580000013.png"\; state="\{\{state\}\}">Z</figure-callout>}& \\ U_j^{}{}_1^{}=W_j& j\&Element;Z\end{array}\right.---\left(1\right)$

$U_{j+1}^0=U_j^0\&CirclePlus;U_j^{1}j\&Element;Z---\left(2\right)$

If subspace Be function u _n(t) closure space, Be function u _2n(t) closure space, then u _n(t) satisfy following two yardstick equations

$\left\{\begin{array}{c}{u}_{2n}\left(t\right)=\sqrt{2}\underset{k\&Element;z}{\mathrm{\&Sigma;}}h\left(k\right)u_n(2t-k)\\ u_{2n+1}\left(t\right)=\sqrt{2}\underset{k\&Element;z}{\mathrm{\&Sigma;}}h\left(k\right)g_n(2t-k)\end{array}\right.---\left(3\right)$

Wherein, g (k)=(1) ^kH (1-k).When n=0, u ₀(t) and u ₁(t) deteriorate to scaling function respectively With wavelet basis function φ (t), { u of function system _n(t) } be called by basis function u ₀(t) Orthogonal Wavelet Packet of confirming.

Be exactly conjugation orthogonal filter { h (k) } and { g (k) } that utilizes one group of low pass, high pass combination on the WAVELET PACKET DECOMPOSITION process nature, constantly signal decomposition arrived in the different frequency bands, every through a bank of filters, number of data points reduces by half.Image can obtain its subgraph in each frequency band space through after the WAVELET PACKET DECOMPOSITION.Fig. 2 is the firsts and seconds WAVELET PACKET DECOMPOSITION synoptic diagram of image, and decomposed class is L, and the subgraph number of generation is 4 ^L

Nano material SEM image is through after the WAVELET PACKET DECOMPOSITION; Smooth signal in each frequency band space and detail signal can provide the configuration information of signal on time-frequency local information and the different frequency bands of original signal, and these information can be described the imaging surface textural characteristics well.Fig. 5 is the subgraph on 64 different frequency bands obtaining after through 3 layers of WAVELET PACKET DECOMPOSITION of certain nano material SEM image.

In wavelet packet was handled, the average of each frequency band subgraph and mean square deviation were two very important parameters, and they can reflect the concrete characteristics of image pattern more all sidedly, can be used for describing image texture features.If the number of greyscale levels of piece image is L, pixel size is M * N, defines its average E and mean square deviation V respectively as follows:

$E=\frac{1}{M\&times;N}\underset{x=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{N}{\mathrm{\&Sigma;}}}\left|f(x,y)\right|---\left(4\right)$

$V=\sqrt{\frac{1}{M\&times;N}\underset{x=1}{\overset{M}{\mathrm{\&Sigma;}}}\underset{y=1}{\overset{N}{\mathrm{\&Sigma;}}}{(f(x,y)-E)}^2}---\left(5\right)$

Wherein f (x, y) be the image slices vegetarian refreshments (x, gray-scale value y), 0≤f (x, y)≤(L-1).

Being provided with N class nano material, is example in the hope of the texture feature vector of k class material, and it is following that parametric texture and proper vector constitute algorithm:

1) selects wavelet basis function, respectively the SEM image that belongs to k class material is carried out 3 layers of WAVELET PACKET DECOMPOSITION.

2), calculate 64 dimension mean vector E of k class nano material SEM image respectively according to formula (4) and (5) _kWith mean square deviation vector V _k, promptly

$E_k=(e_1^k,e_2^k,...,e_{64}^k)---\left(6\right)$

$V_k=(v_1^k,v_2^k,...,V_{64}^k)---\left(7\right)$

Wherein, K=1; 2 ..., N;

and

(j=1; 2 ..., 64) represent the average and the mean square deviation of j frequency band subgraph of k class material respectively.

3) make up 128 of k class material and tie up texture feature vector F _k

F _k＝[E _k，V _k] (8)

4) proper vector that makes up is carried out normalization and handle, order

E ' after the normalization then _k=E _k/ E, in like manner V ' _k=V _k/ V, texture feature vector is F ' after the normalization _k=[E ' _k, V ' _k].

Therefore, the average of the present invention obtains nano material SEM image behind wavelet package transforms each frequency band subgraph matrix and mean square deviation be as the nano material texture characteristic amount, and classify and discern with this.

(2) svm classifier device design

SVMs (SVM) shows many distinctive advantages in solving small sample, non-linear and higher-dimension pattern recognition problem, obtained widespread use and research.According to characteristic of being extracted and known nano material sample class, select SVMs as sorter, set up the optimal classification discriminant function, realize the automatic classification and the identification of low-dimension nano material.

The nano material textural characteristics that extracts has constituted the sample of material classification pattern, is called for short the nano material sample, is designated as x _i∈ R ^dThe material classification is designated as y _i∈+1, and-1}, i=1,2, L, n, wherein n is a number of samples, d is the dimension of each sample, R ^dBe d dimension theorem in Euclid space, y _iBe class categories, its value equals+1 o'clock be one type, it is another kind of equaling at-1 o'clock.

The nano material sample belongs to the inseparable problem of two-dimensional linear, make its linear separability, just must be to x _iCarry out nonlinear transformation

To hang down the inseparable situation of dimension and be converted into higher-dimension linear separability space, and in high-dimensional feature space, construct the optimal classification lineoid, thereby realize classification.Promptly pass through Function Mapping

Utilizing characteristic x _iThe inseparable problem of two-dimensional linear be converted into and utilize z _iHigher-dimension linear separability problem, therefore define higher-dimension linear discriminant function f=w ^TZ _i+ ω ₀, in the formula: w is a weight vector, ω ₀Be biasing, if f>=1, y _i=1; F≤-1, y _i=-1, promptly

y _i[(w ^T·z _i)+ω ₀]-1≥0 (9)

Optimal classification lineoid equation expression formula is:

F＝w ^T·z+ω ₀＝0 (10)

As shown in Figure 3, represented the ultimate principle of nano material classification problem, the main thought of SVMs is to utilize kernel function that input vector x is mapped to a high-dimensional feature space z, and in this space optimal classification lineoid of structure.This shows find the solution F should be under the constraint of formula (9), can calculate the class interval is 2/||w ‖, make the class interval maximum, promptly wants || w|| ²/ 2 minimums.

Nano material is the inseparable situation of a kind of linearity, can't know mapping function

Explicit form, can utilize the Nonlinear Mapping of inner product kernel function that input vector is mapped to higher dimensional space, select suitable inner product kernel function K (x _i, x _j), construct and find the solution optimization problem:

${\min }_{\mathrm{\&alpha;}}\frac{1}{2}\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}\underset{j=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i{\mathrm{\&alpha;}}_j{y}_i{y}_{j}K(x_i,x_j)-\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{\mathrm{\&alpha;}}_i---\left(11\right)$

Its constraint condition does $\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{y}_i{\mathrm{\&alpha;}}_i=\mathrm{0,0}{\&le;\mathrm{\&alpha;}}_i\&le;C,i=\mathrm{1,2},L,n---\left(12\right)$

C is a penalty coefficient in the formula (12), and it controls the contradiction between maximum class interval and the minimum classification error.Formula (11) and (12) are the quadratic programming problems under the inequality constrain, have unique solution.Adopt method of Lagrange multipliers to solve above-mentioned each alpha _i, w, ω ₀Corresponding optimum solution α _i ^*, w ^*, ω ₀ ^*, can obtain the optimal classification decision function

$f\left(x\right)=\mathrm{sgn}(\left(w^{*T}x\right)+{{\mathrm{\&omega;}}_0}^{*})=\mathrm{sgn}(\underset{i=1}{\overset{n}{\mathrm{\&Sigma;}}}{{\mathrm{\&alpha;}}_i}^{*}{y}_{i}K(x_i,x_j)+{{\mathrm{\&omega;}}_0}^{*})---\left(13\right)$

Generally, the employing Gauss radially SVM of basic kernel function can obtain better classifying quality, and its kernel function expression formula is:

K(x _i，x _j)＝exp[-||x _i-x _j|| ²/(2σ ²)] (14)

Owing to need the nano material classification of classification to surpass two types,, design k (k-1)/2 SVM altogether for the sample of k classification therefore to all need designing a SVM between any two types of samples.A unknown nano material sample is carried out the branch time-like, last who gets the most votes's material classification is judged to be the classification of this unknown sample.

According to the texture feature vector that front (one) part calculates, the design cycle of svm classifier device is following:

1) (one) is calculated the input element of the training sample texture feature vector of gained as SVM, between any two types, seek the optimal classification face, set up disaggregated model.

2), utilize (one) to calculate its texture feature vector, again according to 1 to unknown nano material test sample book) disaggregated model that obtains, adopt the ballot method to carry out Classification and Identification, with last who gets the most votes's kind judging classification that is this unknown sample.

Idiographic flow of the present invention is following:

(1) the nano material SEM image that PSTM (STM) is obtained is done pre-service.The pre-service of SEM image mainly comprises two parts: the one, and utilize filtering method to reduce noise to the image texture effect on structure, the 2nd, divide removal and the irrelevant image block of nano-material surface texture structure through image-region.

(2) pretreated image is carried out the 2-d wavelet packet transform, obtain the subgraph matrix on the different frequency bands.

(3) each frequency band subgraph matrix is carried out feature extraction, the statistic of each subgraph matrix is as the eigenwert that characterizes the nano-material surface texture structure.

(4) according to the extraction eigenwert, utilize the method for SVMs between any two types, to seek the optimal classification face, set up the disaggregated model of variety classes nano material.

(5) nano material SEM image pattern repeating step (1), (2), (3) step of the unknown are extracted the eigenwert that characterizes the nano-material surface texture structure, the disaggregated model that obtains according to (4) step again adopts the ballot method to carry out unknown nano material classification and identification.

Process flow diagram is as shown in Figure 1.Below in conjunction with concrete instance technical scheme of the present invention is done and to be described in further detail.

Instance of the present invention utilizes PSTM equipment to obtain 16 kinds of different materials, the low-dimension nano material SEM image of different-shape, and as shown in Figure 4, class label is according to from left to right, and order from top to bottom is designated as X-1, X-2, L, X-16 successively.For every kind of nano material with identical pattern, choose 25 sample images, have 16 * 25=400 sample image and experimentize.

The present invention chooses Orthogonal Wavelets db1 function commonly used the SEM image of nano material is carried out 3 layers of WAVELET PACKET DECOMPOSITION, adopts the radially basic kernel function of Gauss as the SVM kernel function, makes up sorter.16 types of nano material SEM image section parametric textures that utilize the inventive method to extract are as shown in table 1.Can find out that from table 1 parametric texture of different classes of nano material distributes and has bigger otherness, can quantize different classes of nano material to characterize.

Table 1

When adopting the radially basic kernel function of Gauss, (C, selection σ) is a difficult problem to parameter combinations.Wherein, C is a penalty coefficient, the shape of σ control nuclear, and C and σ influence the classification performance of SVM jointly.(the present invention gets M and N value respectively to C and σ for C, combination σ), and (C, σ) different SVM is trained in combination respectively, finds out optimum combination according to the quality of promoting discrimination again, as the optimal parameter of corresponding SVM kernel function to M * N in order to find the solution the best.

According to said method, the value of establishing C is respectively [2 ^-4, 2 ^-3.5, 2 ^-3..., 2 ^3.5, 2 ⁴], the value of σ is respectively [2 ^-4, 2 ^-3.5, 2 ^-3..., 2 ^3.5, 2 ⁴], then total M * N=17 * 17=289 (C, σ) combination.Through contrast, the present invention chooses C=5.6569, and σ=16 are as best kernel function parameter.

400 sample images are divided into 2 groups at random, and the 1st group is used for training to 10 samples of every kind of material selection, and the 2nd group is used for test to 15 remaining samples of every kind of material selection.With the texture feature vector after the normalization respectively as the input of SVM; Training and testing SVM; Add up the nicety of grading (the correct number of samples of classification shared ratio in test sample book in each class testing sample) of each type nano material SEM image, the result is as shown in Figure 6.

Table 2 is the classification results of 16 types of nano materials (every type of 15 test sample books).Wherein ranks are counted i and j and are represented the true class label of SEM image and the class label of being differentiated by sorter respectively.Numerical value of N in the table _{I, j}(1≤i, j≤16) expression X-i classification is classified into the number of X-j classification, and correct number of categories partly represented in black matrix, and italicized item is represented the mis-classification number.Table 3 is that the classification results of 16 types of nano materials (10 every type and 15 test sample books) compares.

Table 2

Table 3

Can find out that by Fig. 6 and table 2 the inventive method has higher nicety of grading, can know that through calculating total classification accuracy rate reaches 93.75%, can satisfy the requirement on the common engineering fully.But also can find simultaneously; Part nano material classification accuracy rate is lower; Particularly X-2, X-11 and X-14 classification error rate are higher, and tracing it to its cause is that these several types of nano material SEM picture materials are very mixed and disorderly, and the texture structure of itself exists bigger the space parallax opposite sex and scrambling.

The content of not doing in the instructions of the present invention to describe in detail belongs to this area professional and technical personnel's known prior art.

Claims (2)

1. the low-dimension nano material recognition methods based on the SEM image is characterized in that, comprises the following steps:

(1) known nano material SEM image pattern is done pre-service;

(2) pretreated image is carried out the 2-d wavelet packet transform, obtain the subgraph matrix on the different frequency bands;

(3) with the average of each frequency band subgraph matrix and mean square deviation as the nano material texture characteristic amount, and classify and discern with this;

(4) according to the nano material texture characteristic amount that is extracted, adopt the radially basic kernel function of Gauss as the SVMs kernel function, between any two types, seek the optimal classification face, set up the disaggregated model of different types of nano material;

(5) nano material SEM image pattern repeating step (1), (2), (3) step of the unknown are extracted the eigenwert that characterizes the nano-material surface texture structure, the disaggregated model that obtains according to (4) step again adopts the ballot method to carry out unknown nano material identification.

2. the low-dimension nano material recognition methods based on the SEM image according to claim 1; It is characterized in that; The pre-service of step 1 will comprise two parts: the one, and utilize filtering method to reduce noise to the image texture effect on structure, the 2nd, divide removal and the irrelevant image block of nano-material surface texture structure through image-region.

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