CN103559496B - The extracting method of the multiple dimensioned multi-direction textural characteristics of froth images - Google Patents

Abstract

The invention discloses the extracting method of the multiple dimensioned multi-direction textural characteristics of a kind of froth images, first foam gray level image is carried out curve wave conversion, the most respectively the curve marble figure of different scale different directions is processed, extract multiple dimensioned multidirectional texture characterization information, constitute the characteristic vector of froth images.According to the textural characteristics obtained, the froth images of different operating modes can be made a distinction.The extracting method of the multiple dimensioned multi-direction textural characteristics of this froth images has good pattern separability for froth images identification, and easy to implement.

Description

Extraction method of multi-scale and multi-direction textural features of foam image

Technical Field

The invention relates to a method for extracting multi-scale and multi-direction textural features of a foam image, and belongs to the field of image processing technology and pattern recognition.

Background

In image research, texture is an important feature, which is closely related to image resolution and can only be perceived at a certain scale. According to the human visual perception psychology research on textures, the most important three dimensions of human recognition tasks on textures are directionality, periodicity and randomness, wherein direction is an especially important factor. Therefore, describing textural features must have multi-scale, multi-directional characteristics.

The flotation froth image contains abundant detail textures and singular curves, the texture change in all directions is irregular, the edge curves among bubbles are irregular, and accurate texture description of the flotation froth image is very difficult. At present, the texture feature extraction method applied to the flotation image processing mainly comprises a statistical method based on gray level co-occurrence matrix and a filtering method based on wavelet transformation. The gray level co-occurrence matrix can describe texture image structural features in the directions of 0 degrees, 45 degrees, 90 degrees and 135 degrees, but the texture image structural features are obtained under a single scale, the description of the dependency relationship among the foam texture scales is lacked, and the multi-scale characteristic of the foam texture is difficult to accurately describe.

Therefore, it is necessary to design a method for extracting multi-scale and multi-directional textural features of a foam image.

Disclosure of Invention

The technical problem to be solved by the invention is to provide the extraction method of the multi-scale and multi-direction textural features of the foam image, and the extraction method of the multi-scale and multi-direction textural features of the foam image has good pattern separability aiming at foam image identification and is easy to implement.

The technical solution of the invention is as follows:

a method for extracting multi-scale and multi-direction textural features of a foam image comprises the following steps:

the method comprises the following steps: foam gray image T obtained from copper flotation site_M×N(x, y), wherein M × N is the resolution of the foam gray image, and (x, y) represents the pixels of the gray image, and then the foam gray image is subjected to curvelet decomposition to obtain a curvelet coefficient matrix set which comprises a coarse layer, a coarse layer and a fine layer;

step two: respectively calculating average norm energy of the coarsest scale layer, namely coarse layer coefficient matrix, and the finest scale layer, namely fine layer coefficient matrix in the curvelet coefficient matrix set obtained in the step one, and taking the average norm energy as the characteristic quantity of the coarsest scale layer and the finest scale layer;

for a detail layer coefficient matrix in the curvilinear wave coefficient matrix set obtained in the step one, wherein the detail layer is a secondary coarse scale layer; reconstructing the curve wave by utilizing inverse transformation of the curve wave to obtain a detail layer reconstruction subgraph; solving a gray level co-occurrence matrix for the reconstruction subgraph of the detail layer, and calculating 3 characteristic quantities of entropy, correlation and contrast of the gray level co-occurrence matrix in different directions as the characteristic quantities of the detail layer;

step three: and D, forming a characteristic vector by using the characteristic quantities of all the scale layers obtained in the step two, and using the characteristic vector as the texture characteristic of the foam image.

Reading RGB foam images from an original foam video acquired from a copper flotation field; graying an RGB foam image: original RGB foam image K_M×N×3Changed into foam gray image T after graying_M×N(x,y)。

In the first step:

the foam gray level image uses USFFT fast discrete curvelet transform, wherein, the curvelet transform mode is set as complex value curvelet transform, and the scale layer number is J ═ log₂N]-3; the discrete curvelet transformation comprises the following steps:

1) for foam gray level image T_M×N(x, y) performing two-dimensional fast Fourier transform to a frequency domain to obtainThe formula is as follows:

$\hat{T}(m,n)=\underset{x=0}{\overset{M-1}{\Σ}}\underset{y=0}{\overset{N-1}{\Σ}}{T}_{M\×N}(x,y)e^{i2\mathrm{\π}(mx/M+ny/N)}$

wherein M and N are frequency domain variables and are horizontal and vertical coordinates of the image in a frequency domain space, M is more than or equal to M/2 and less than or equal to M/2, and N is more than or equal to N/2 and less than or equal to N/2;

2) to pairResampling at each pair of scale, direction (j, l) combinations (i.e. "wedge" windows) [ thisWhere J is obtained at each level, i.e. scale, of 1,2, …, J-1, JWhere j is a scale variable, l is a direction variable, and the resampling matrix is a wedge-shaped matrixThetal is the azimuth angle of the wedge-shaped window,l＝0,1,……,4·2[^j/2]-1，[j/2]is the smallest integer greater than or equal to j/2.

3) Will be provided withAnd parabolic window functionMultiplied so as to be at different directional angles theta of the wedge window_lSite localizationObtaining:wherein the parabolic window functionCan be obtained by the following steps:

A) calculation of satisfaction of allowance condition

$\underset{l=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}{V}^2(t-l)=1$

$\underset{l=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}{W}^2\left(2^{j}r\right)=1$

The radial window function W (r) and the angular window function V (t) are respectively:

$W\left(r\right)=\left\{\begin{array}{cc}\cos \[\frac{\mathrm{\π}}{2}v(5-6r)\]& 2/3\≤r\≤5/6\\ 1& 5/6\≤r\≤4/3\\ \cos \[\frac{\mathrm{\π}}{2}v(3r-4)\]& 4/3\≤r\≤5/3\\ 0& else\end{array}\right.$

$V\left(t\right)=\left\{\begin{array}{cc}1& \left|t\right|\≤1/3\\ cos\[\frac{\mathrm{\π}}{2}v\left(3\right|t|-1)\]& 1/3\≤\left|t\right|\≤2/3\\ 0& else\end{array}\right.$

where v is a smooth function that satisfies the following condition:

$v\left(z\right)=\left\{\begin{array}{cc}0& z\≤0\\ 1& z\≥1\end{array}\right.,v\left(z\right)+v(1-z)=1$

z, R, omega are defined in a two-dimensional space R²In the above, z is a space variable, ω and r are polar coordinates in the frequency domain,

t＝ω/2π。

B) computing a frequency domain window function of

${\tilde{U}}_j(r,{\mathrm{\θ}}_l)=2^{-3j/4}W\left(2^{-j}r\right)V\left(\frac{2^{\[j/2\]}{\mathrm{\θ}}_l}{2\mathrm{\π}}\right),j\≥j_0$

Wherein j₀Representing a coarsest scale layer; j is a function of₀＝1【j₀1 is the number representing the coarsest scale layer, which can be used from j₀1 to 6 indicate the layers from the thickest to the finest scale, and vice versa. Using j in this context₀The coarsest scale layer is denoted by 1. "C (B)

4) For each of the subdivided frequency-domain spacesPerforming two-dimensional fast Fourier inverse transformation to obtain curve wavelength resolution coefficient

$C_{k,l}^j=\underset{m,n\∈P_j}{\Σ}\hat{T}{(m,n-{\mathrm{mtan\θ}}_l)}^{\′}{\tilde{U}}_j\left(m,n\right)e^{i2\mathrm{\π}\left(x_{k}m/L_{1,j}+y_{k}n/L_{2,j}\right)}$

Wherein,denotes the l-th direction on the scale j, position k ═ x_k,y_k) The coefficient of decomposition of the curved wave of (m, n) ∈ P_j,P_j＝{(m,n):m₀≤m≤m₀+L_1,j,n₀≤n≤n₀+L_2,j}，L_1,jRepresenting window functionsLength of the supporting section of (1), L_2,jIndicates the width of the supporting section; (m)₀,n₀) The coordinates of the leftmost lower point of the supporting interval are taken as the coordinates; the length and width of the support section are not exactly 2^jOr 2^j/2，L_1,j＝₁2^jWherein₁＝1+Ο(2^-j) (ii) a O represents the higher order infinitesimal of 2j, L_2,j＝₂2^j/2Wherein₂for simplicity, all documents take the length and width of the support section to be approximately 2^jOr 2^j/2】

Obtaining a foam gray image T_M×NThe set of curvilinear wave coefficient matrices of (x, y) is as follows:

$C_{k,0}^1,C_{k,l}^2,C_{k,l}^3,...,C_{k,l}^j,...,C_{k,l}^{J-1},C_{k,0}^J,j=1,2,...,J;l=0,1,...4\·2^{\[j/2\]}-1$

wherein, when j is equal to j₀When the number is equal to 1, the alloy is put into a container,is the coarsest scale layer, i.e. coarse layer coefficient matrix, when J equals J,the method is characterized in that the method is a finest scale layer, namely a fine layer coefficient matrix, and a coarse layer and a fine layer have no direction; when J-2., J-1,is a coefficient matrix of a coarse scale layer, namely a detail layer, and the direction of the detail layer is l equal to 0,1^[j/2]-1。

In the second step:

1) to coarse layer coefficient matrixCalculating the average norm energy of the energy, wherein the calculation formula is as follows:

$E_c=\frac{1}{M_c\·N_c}\underset{x_k=1}{\overset{M_c}{\Σ}}\underset{y_k=1}{\overset{N_c}{\Σ}}\left|c_{x_k{y}_k}\right|$

wherein,is a coarse layer coefficient matrixElement of (1), M_c、N_cIs composed ofThe number of rows and columns of the matrix;

2) to fine layer coefficient matrixCalculating the average norm energy of the energy, wherein the calculation formula is as follows:

$E_f=\frac{1}{M_f\·N_f}\underset{x_k=1}{\overset{M_f}{\Σ}}\underset{y_k=1}{\overset{N_f}{\Σ}}\left|f_{x_k{y}_k}\right|$

wherein,is a fine layer coefficient matrixElement of (1), M_f、N_fIs composed ofThe number of rows and columns of the matrix,image size and original grayscale image T as described_M×NThe (x, y) are of equal size, i.e. M_f＝M,N_f＝N；

3) To detail layer coefficient matrixReconstructing by using curvelet inverse transformation to obtain reconstruction subgraph of detail layerThe reconstruction subgraph step is the prior art, and the reconstruction step of the detail layer is as follows: zeroing coefficients of a coarse layer and a fine layer in the coefficient matrix after the curvilinear wave transformation, and reserving coefficients of the detail layer; carrying out curvelet inverse transformation on the coefficient matrix, and the steps are as follows: for each pair of scale and angle combination (j, l), the pairApplying a two-dimensional fast Fourier transform to obtain Fourier samplesWherein m, n ∈ P_j(ii) a For each pair (j, l), doWill be provided withIs regarded asIn shear grid (m, n-m tan. theta.)_l) Up and resampled on a standard nyquist grid; summing the results at different scales and angles to obtainTo pairPerforming inverse fast fourier transform to obtain T (x, y), and performing gray mapping:

$G=255\·\frac{{\stackrel{\‾}{T}}_{M_d\×N_d}-\min {\stackrel{\‾}{T}}_{M_d\×N_d}}{max{\stackrel{\‾}{T}}_{M_d\×N_d}-\min {\stackrel{\‾}{T}}_{M_d\×N_d}}$

whereinAre respectively asMaximum and minimum values among all elements;

carrying out gray level quantization on the matrix G obtained after gray level mapping to obtain G_qThe quantization series q is 16;

find the gray level co-occurrence matrix, which is recorded asIt describes G_qThe pixel pairs (s, u) with intermediate gray values s and u, respectively, are at an angleThe interval distance h (angle represents the included angle between the line pointing from the pixel with the gray value s to the pixel with the gray value u and the positive horizontal direction, and the interval distance represents the length of the line between the two pixels) appears, whereinTaking any value of 0 degrees, 45 degrees, 90 degrees and 135 degrees, and taking the distance h as 1;

for different anglesGray level co-occurrence matrix ofCalculating 3 characteristic values as characteristic quantities of detail layers:

entropy:

correlation:

contrast ratio:

whereinTo representElement of (5), mu_sAnd σ_s、μ_uAnd σ_uSeparately representing gray level co-occurrence matricesThe mean value and the variance of all elements in the row and column directions of the element, wherein the row number value of the element is s, and the column number value is u.

In the third step, the characteristic quantities of all the scale layers obtained in the second step form a final characteristic vectorAs a texture feature of the foam image,respectively taking 0 degrees, 45 degrees, 90 degrees and 135 degrees, wherein F¹＝E_cThe characteristic quantity of the coarse layer subgraph obtained by decomposing the curve waves of the foam image is obtained; f²＝E_fThe characteristic quantity is the characteristic quantity of the fine layer subgraph;for different angles of detail layer subgraphThe characteristic amount of (2).

The technical idea of the invention is as follows:

wavelet transformation provides a tool for researching and analyzing texture details on different scales, an original image can be decomposed into sub-band images with different frequencies and different resolutions, a high-frequency sub-band reflects detail information such as texture and edges of the image, and a low-frequency sub-band reflects outline information of the image. However, the wavelet transform does not well describe the line singularity and curve singularity represented by the surface texture of the foam image, and also does not provide good direction selectivity. The curvelet transform is proposed to overcome the shortcomings of the conventional two-dimensional discrete wavelet transform. Unlike the isotropic wavelet base of wavelet transform, curvelet transform is anisotropic, highly sensitive to direction, and very effective for curvelet representation. The curvelet theory is developed through two generations, the curvelet transformation of the first generation is based on the ridge wave (Ridgelet) theory and is formed by combining a special filtering process and multi-scale Ridgelet transformation, parameters are multiple, redundancy is large, and a blocking effect exists. The second generation curvelet transformation and the fast discrete algorithm completely break away from the Ridgelet transformation, are directly defined in the frequency domain, are easier to understand and realize, and have less redundancy and higher speed.

Therefore, the method adopts a fast discrete curve wave transformation algorithm based on the second generation curve wave theory, combines subgraphs and gray level co-occurrence matrixes in different scales and different directions obtained by decomposing the image Curvelet, obtains texture features in multiple scales and multiple directions, jointly forms a feature vector of the image, performs texture description on the froth image, and provides a basis for identifying, analyzing and controlling the working condition of the ore dressing process based on the froth flotation image features.

Has the advantages that:

the method for extracting the multi-scale and multi-direction textural features of the foam image is essentially a method for extracting the multi-scale and multi-direction textural features of the foam image based on second-generation curvelet transformation, and the obtained characteristic vectors can well reflect the textural features of all levels and all directions of the image through multi-scale and multi-direction data processing, so that the respective limitations of a gray level co-occurrence matrix and wavelet transformation in the conventional method for extracting the textural features of the foam image are overcome, namely the gray level co-occurrence matrix can only reflect the textural structure information of the foam image on a single scale and lacks the description of the dependency relationship among the foam textural scales; the multi-scale wavelet analysis cannot depict line singularities and curve singularities represented by the surface textures of the foam image, and cannot provide good direction selectivity. Experiments prove that the extracted texture characteristic quantity has good mode separability, and can well distinguish three foams, namely normal foam, hydrated foam and viscous foam. The method can be directly realized on a computer, and has the advantages of low cost, high efficiency and easy implementation.

Drawings

FIG. 1 is an image of foam under three different conditions (FIGS. a, b, c are images of normal foam, hydrated foam, and viscous foam, respectively);

FIG. 2 is a subgraph of each scale after the curvilinear wave decomposition of the foam image; (FIGS. a-f are the coarsest scale, sub-coarse scale, finest scale, two-scale, three-scale, four-scale, and five-scale reconstructed subgraphs, respectively)

FIG. 3 is a block diagram of foam image texture feature extraction;

fig. 4 is a feature scatter diagram.

Detailed Description

The invention will be described in further detail below with reference to the following figures and specific examples:

example 1:

the foam image of a certain copper flotation site has three different working conditions, namely normal foam, hydrated foam and viscous foam, and the foam image of the three different working conditions is shown in figure 1.

Firstly, acquiring a foam image according to a foam video acquired in the current copper flotation place, and graying an RGB image. Then, carrying out curvelet decomposition on the obtained foam gray level image so as to obtain curvelet coefficient matrix sets on different scales;

step 1: reading an RGB foam image by an original foam video;

step 2: and graying the RGB foam image. Original RGB foam image K_512×512×3Changed into foam gray image T after graying_512×512；

And step 3: and (3) performing fast discrete curvelet transformation on the foam gray level image obtained in the step (2), wherein the transformation mode of the curvelet is set as a complex curvelet, and the number of scale layers is J ═ log₂N]-3. In this case, J is 6.

Thus, a gradation image T is obtained_M×NThe curvelet coefficient matrix (set) of (x, y) is as follows:

$C_{k,0}^1,C_{k,l}^2,C_{k,l}^3,C_{k,l}^4,C_{k,l}^5,C_{k,0}^6,l=0,1,...4\·2^{\[j/2\]}-1;k\∈R^2$

wherein, when j is 1,is the coarse scale layer coefficient matrix, when J equals to 6,the method is characterized in that the method is a finest scale layer, namely a fine layer coefficient matrix, and a coarse layer and a fine layer have no direction; when j is 2, 5,is a coefficient matrix of a coarse scale layer, namely a detail layer, and the direction of the detail layer is l equal to 0,1^[j/2]-1。

In the wave decomposition coefficients of the curve of each scale of the foam image, the coarse layer coefficient is a low-frequency coefficient and mainly comprises the general picture of the foam image; the fine layer coefficient is a high-frequency coefficient and reflects the detail characteristics of the image, and the coarse layer coefficient and the fine layer coefficient do not contain direction information; the detail layer coefficient mainly comprises a medium-high frequency coefficient of an image, embodies detail and edge information and has a multidirectional characteristic. Therefore, the average energy norm is calculated for the coarse layer coefficient matrix and the fine layer coefficient matrix, and the gray level co-occurrence matrix in different directions is calculated for the detail reconstruction subgraph, so as to fully extract the texture information of the detail layer.

And secondly, respectively extracting characteristic quantities of the curvilinear wave sub-graphs of the coarse layer and the fine layer.

1) To coarse layer coefficient matrixCalculating the average norm energy of the energy, wherein the calculation formula is as follows:

$E_c=\frac{1}{M_c\·N_c}\underset{x_k=1}{\overset{M_c}{\Σ}}\underset{y_k=1}{\overset{N_c}{\Σ}}\left|c_{x_k{y}_k}\right|$

wherein,is a coarse layer coefficient matrixMc, Nc areNumber of rows and columns of matrix, in this case M_c＝32，N_c＝32。

2) To fine layer coefficient matrixCalculating the average norm energy of the energy, wherein the calculation formula is as follows:

$E_f=\frac{1}{M_f\·N_f}\underset{x_k=1}{\overset{M_f}{\Σ}}\underset{y_k=1}{\overset{N_f}{\Σ}}\left|f_{x_k{y}_k}\right|$

wherein,is a fine layer coefficient matrixElement of (1), M_f、N_fIs composed ofThe number of rows and columns of the matrix,image size and original grayscale image T as described_M×NThe (x, y) are of equal size, i.e. M_f＝M,N_fN. In this case, J is 6, M_f＝M＝512，N_f＝N＝512。

Thirdly, for the detail layer coefficient matrixReconstructing by using curvelet inverse transformation to obtain reconstruction subgraph of detail layerCarrying out gray mapping on the image:

$G=255\·\frac{{\stackrel{\‾}{T}}_{M_d\×N_d}-\min {\stackrel{\‾}{T}}_{M_d\×N_d}}{max{\stackrel{\‾}{T}}_{M_d\×N_d}-\min {\stackrel{\‾}{T}}_{M_d\×N_d}}$

whereinAre respectively asMaximum and minimum values among all elements.

1) Carrying out gray level quantization on the matrix G obtained after gray level mapping to obtain G_qThe quantization level q is 16.

2) Find the gray level co-occurrence matrix, which is recorded asIt describes G_qThe pixel pairs (s, u) with intermediate gray values s and u, respectively, are at an angleNumber of times of occurrence of distance h, whereinMay be taken to be 0 °, 45 °, 90 °, 135 °, the distance h is typically taken to be 1.

3) For different directions (angles)) Gray level co-occurrence matrix ofCalculating 3 characteristic values as characteristic quantities of detail layers:

entropy:

correlation:

contrast ratio:

whereinTo representElement of (5), mu_s，μ_u，σ_s，σ_uAre respectively gray level co-occurrence matricesThe mean and variance of all elements in the row and column directions of the middle element, the row number value of the element is s, and the column number value is u.

The fourth step: combining the characteristic quantities of all the scale layers obtained in the second step and the third step into a final characteristic vector(0 °, 45 °, 90 ° and 135 °, respectively), as texture features of the foam image, wherein F¹＝E_cThe characteristic quantity of the coarse layer subgraph obtained by decomposing the curve waves of the foam image is obtained; f²＝E_fThe characteristic quantity is the characteristic quantity of the fine layer subgraph;for different directions (angles) of detail layer subgraphs) The characteristic amount of (2).

The texture feature vector of the finally obtained foam image is represented by a scatter diagram, as shown in FIG. 4The foam image texture feature scatter plot of time, wherein coarse layer energy and fine layer energy are represented by the area and color of the dots, respectively. The degree of the extracted characteristic quantity to distinguish the foams under different working conditions is inspected, and as can be seen from fig. 4, the extracted texture characteristic quantity has good mode separability, and can well distinguish three foams, namely normal foam, hydrated foam and viscous foam.

Claims (3)

1. A method for extracting multi-scale and multi-direction textural features of a foam image is characterized by comprising the following steps:

the method comprises the following steps: foam gray image T obtained from copper flotation site_M×N(x, y), wherein M × N is the resolution of the foam gray image, and (x, y) represents the pixels of the foam gray image, then the foam gray image is subjected to curvelet decomposition to obtain a curvelet coefficient matrix set which comprises a coarse layer, a coarse layer and a fine layer;

step two: respectively calculating average norm energy of the coarsest scale layer, namely coarse layer coefficient matrix, and the finest scale layer, namely fine layer coefficient matrix in the curvelet coefficient matrix set obtained in the step one, and taking the average norm energy as the characteristic quantity of the coarsest scale layer and the finest scale layer;

for a detail layer coefficient matrix in the curvilinear wave coefficient matrix set obtained in the step one, wherein the detail layer is a secondary coarse scale layer; reconstructing the curve wave by utilizing inverse transformation of the curve wave to obtain a detail layer reconstruction subgraph; solving a gray level co-occurrence matrix for the reconstruction subgraph of the detail layer, and calculating 3 characteristic quantities of entropy, correlation and contrast of the gray level co-occurrence matrix in different directions as the characteristic quantities of the detail layer;

step three: forming a characteristic vector by using the characteristic quantities of all the scale layers obtained in the step two, and using the characteristic vector as a texture characteristic of the foam image; in the first step:

the foam gray level image uses USFFT fast discrete curvelet transform, wherein, the curvelet transform mode is set as complex value curvelet transform, and the scale layer number is J ═ log₂N]-3; the discrete curvelet transformation comprises the following steps:

1) for foam gray level image T_M×N(x, y) performing two-dimensional fast Fourier transform to a frequency domain to obtainThe formula is as follows:

$\hat{T}(m,n)=\underset{x=0}{\overset{M-1}{\Σ}}\underset{y=0}{\overset{N-1}{\Σ}}{T}_{M\×N}(x,y)e^{i2\mathrm{\π}(mx/M+ny/N)}$

wherein M and N are frequency domain variables and are horizontal and vertical coordinates of the image in a frequency domain space, M is more than or equal to M/2 and less than or equal to M/2, and N is more than or equal to N/2 and less than or equal to N/2;

2) to pairResampling at each pair of scale and direction (j, l) combination to obtainWhere j is a scale variable, l is a direction variable, and the resampling matrix is a wedge-shaped matrixθ_lIs the azimuth angle of the wedge-shaped window,l＝0,1,……,4·2^[j/2]-1，[j/2]is the smallest integer greater than or equal to j/2;

3) will be provided withAnd parabolic window functionMultiplication to localize at the azimuth angle thetal of the different wedge windowsObtaining:wherein the parabolic window functionIs obtained by the following steps:

a) calculation of satisfaction of allowance condition

$\underset{l=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}{V}^2(t-l)=1$

$\underset{l=-\mathrm{\∞}}{\overset{\mathrm{\∞}}{\Σ}}{W}^2\left(2^{j}r\right)=1$

The radial window function W (r) and the angular window function V (t) are respectively:

$W\left(r\right)=\left\{\begin{array}{cc}\cos \[\frac{\mathrm{\π}}{2}v(5-6r)\]& 2/3\≤r\≤5/6\\ 1& 5/6\≤r\≤4/3\\ \cos \[\frac{\mathrm{\π}}{2}v(3r-4)\]& 4/3\≤r\≤5/3\\ 0& else\end{array}\right.$

$V\left(t\right)=\left\{\begin{array}{cc}1& \left|t\right|\≤1/3\\ cos\[\frac{\mathrm{\π}}{2}v\left(3\right|t|-1)\]& 1/3\≤\left|t\right|\≤2/3\\ 0& else\end{array}\right.$

where v is a smooth function that satisfies the following condition:

$v\left(z\right)=\left\{\begin{array}{cc}0& z\≤0\\ 1& z\≥1\end{array}\right.,v\left(z\right)+v(1-z)=1$

z, R, omega are defined in a two-dimensional space R²Z is a space variable, ω and r are polar coordinates in a frequency domain, and t is ω/2 pi;

b) computing a frequency domain window function of

${\tilde{U}}_j(r,{\mathrm{\θ}}_l)=2^{-3j/4}W\left(2^{-j}r\right)V\left(\frac{2^{\[j/2\]}{\mathrm{\θ}}_l}{2\mathrm{\π}}\right),j\≥j_0$

Wherein j₀Representing a coarsest scale layer; j is a function of₀＝1；

4) For each of the subdivided frequency-domain spacesPerforming two-dimensional fast Fourier inverse transformation to obtain curve wavelength resolution coefficient

$C_{k,l}^j=\underset{m,n\∈P_j}{\Σ}\hat{T}{(m,n-m{\mathrm{tan\θ}}_l)}^{\′}{\tilde{U}}_j(m,n)e^{i2\mathrm{\π}(x_{k}m/L_{1,j}+y_{k}n/L_{2,j})}$

Wherein,denotes a curvilinear wave decomposition coefficient at the l-th direction on the scale j at the position k ═ x, y, (m, n) ∈ P_j,P_j＝{(m,n):m₀≤m≤m₀+L_1,j,n₀≤n≤n₀+L_2,j}，L_1,jRepresenting a parabolic window functionLength of the supporting section of (1), L_2,jIndicates the width of the supporting section; (m)₀,n₀) The coordinates of the leftmost lower point of the supporting interval are taken as the coordinates;

obtaining a foam gray image T_M×NThe set of curvilinear wave coefficient matrices of (x, y) is as follows:

$C_{k,0}^1,C_{k,l}^2,C_{k,l}^3,...,C_{k,l}^j,...,C_{k,l}^{J-1},C_{k,0}^J,j=1,2,...,J;l=0,1,...4\·2^{\[j/2\]}-1$

wherein, when j is equal to j₀When the number is equal to 1, the alloy is put into a container,is the coarsest scale layer, i.e. coarse layer coefficient matrix, when J equals J,the method is characterized in that the method is a finest scale layer, namely a fine layer coefficient matrix, and a coarse layer and a fine layer have no direction; when J-2., J-1,is a coefficient matrix of a coarse scale layer, namely a detail layer, and the direction of the detail layer is l equal to 0,1^[j/2]-1。

2. The method for extracting multi-scale and multi-directional textural features of a bubble image according to claim 1,

in the second step:

1) to coarse layer coefficient matrixCalculating the average norm energy of the energy, wherein the calculation formula is as follows:

$E_c=\frac{1}{M_c\·N_c}\underset{x_k=1}{\overset{M_c}{\Σ}}\underset{y_k=1}{\overset{N_c}{\Σ}}\left|c_{x_k{y}_k}\right|$

wherein,is a coarse layer coefficient matrixElement of (1), M_c、N_cIs composed ofThe number of rows and columns of the matrix;

2) to fine layer coefficient matrixCalculating the average norm energy of the energy, wherein the calculation formula is as follows:

$E_f=\frac{1}{M_f\·N_f}\underset{x_k=1}{\overset{M_f}{\Σ}}\underset{y_k=1}{\overset{N_f}{\Σ}}\left|f_{x_k{y}_k}\right|$

wherein,is a fine layer coefficient matrixElement of (1), M_f、N_fIs composed ofThe number of rows and columns of the matrix,image size and foam grayscale image T as described_M×NThe (x, y) are of equal size, i.e. M_f＝M,N_f＝N；

3) To detail layer coefficient matrixReconstructing by using curvelet inverse transformation to obtain reconstruction subgraph of detail layerCarrying out gray mapping on the image:

$G=255\·\frac{{\stackrel{\‾}{T}}_{M_d\×N_d}-min{\stackrel{\‾}{T}}_{M_d\×N_d}}{max{\stackrel{\‾}{T}}_{M_d\×N_d}-\min {\stackrel{\‾}{T}}_{M_d\×N_d}}$

whereinAre respectively asMaximum and minimum values among all elements;

carrying out gray level quantization on the matrix G obtained after gray level mapping to obtain G_qThe quantization series q is 16;

find the gray level co-occurrence matrix, which is recorded asIt describes G_qThe pixel pairs (s, u) with intermediate gray values s and u, respectively, are at an angleNumber of times of occurrence of distance h, whereinTaking any value of 0 degrees, 45 degrees, 90 degrees and 135 degrees, and taking the distance h as 1;

for different directions, i.e. different anglesGray level co-occurrence matrix ofCalculating 3 characteristic values as characteristic quantities of detail layers:

entropy:

correlation:

contrast ratio:

whereinTo representElement of (5), mu_sAnd σ_s、μ_uAnd σ_uSeparately representing gray level co-occurrence matricesThe mean value and the variance of all elements in the row and column directions of the element, wherein the row number value of the element is s, and the column number value is u.

3. The method for extracting the multi-scale and multi-directional textural features of the foam image according to claim 2, wherein in the third step, the feature quantities of all scale layers obtained in the second step are combined into a final feature vectorAs a texture feature of the foam image,respectively taking 0 degrees, 45 degrees, 90 degrees and 135 degrees, wherein F¹＝E_cThe characteristic quantity of the coarse layer subgraph obtained by decomposing the curve waves of the foam image is obtained; f²＝E_fThe characteristic quantity is the characteristic quantity of the fine layer subgraph;for different angles of detail layer subgraphThe characteristic amount of (2).