CN103559496B

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

Info

Publication number: CN103559496B
Application number: CN201310574723.8A
Authority: CN
Inventors: 彭涛; 赵璐; 曹威; 彭小奇; 宋彦坡; 赵林; 黄易
Original assignee: Central South University
Current assignee: Central South University
Priority date: 2013-11-15
Filing date: 2013-11-15
Publication date: 2016-08-17
Anticipated expiration: 2033-11-15
Also published as: CN103559496A

Abstract

The invention discloses a method for extracting multi-scale and multi-directional texture features of a foam image. First, the foam grayscale image is subjected to curve wave transformation, and then the curve wave subgraphs of different scales and directions are respectively processed to extract multi-scale and multi-directional textures. Representation information, constituting the feature vector of the bubble image. According to the obtained texture features, the foam images of different working conditions can be distinguished. The foam image multi-scale and multi-directional texture feature extraction method has good pattern separability for foam image recognition and is easy to implement.

Description

Extraction method of multi-scale and multi-directional texture features of foam images

技术领域technical field

本发明涉及一种泡沫图像多尺度多方向纹理特征的提取方法，属于图像处理技术和模式识别领域。The invention relates to a method for extracting multi-scale and multi-directional texture features of foam images, which belongs to the fields of image processing technology and pattern recognition.

背景技术Background technique

在图像研究中，纹理是一个重要特征，它与图像分辨率密切相关，只有在一定尺度下才能感知到。根据人类对纹理的视觉感知心理学研究，人类在对纹理的识别任务中，最重要的三个维度是方向性、周期性和随机性，其中方向是尤为重要的因素。因此，描述纹理特征必须具备多尺度、多方向特性。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 psychological research on human visual perception of texture, the three most important dimensions in human texture recognition tasks are directionality, periodicity and randomness, among which direction is a particularly important factor. Therefore, the description of texture features must have multi-scale and multi-directional characteristics.

浮选泡沫图像包含丰富的细节纹理和奇异曲线，各个方向纹理变化不规则，气泡间边缘曲线不规则，对其进行准确的纹理描述非常困难。目前，应用于浮选图像处理的纹理特征提取方法主要有基于灰度共生矩阵的统计方法和基于小波变换的滤波方法。灰度共生矩阵可以描述0°、45°、90°和135°方向上的纹理图像结构特征，但都是在单一尺度下获得的，缺乏对泡沫纹理尺度间依赖关系的描述，很难准确地刻画泡沫纹理多尺度特性。The flotation foam image contains rich detailed textures and singular curves. The texture changes irregularly in all directions, and the edge curves between bubbles are irregular. It is very difficult to accurately describe the texture. At present, the texture feature extraction methods used in flotation image processing mainly include the statistical method based on gray level co-occurrence matrix and the filtering method based on wavelet transform. The gray level co-occurrence matrix can describe the structural features of the texture image in the directions of 0°, 45°, 90° and 135°, but they are all obtained at a single scale. It lacks the description of the inter-scale dependence of the foam texture, and it is difficult to accurately Characterize the multiscale properties of foam textures.

因此，有必要设计一种泡沫图像多尺度多方向纹理特征的提取方法。Therefore, it is necessary to design a method for extracting multi-scale and multi-directional texture features of foam images.

发明内容Contents of the invention

本发明所要解决的技术问题是提供一种泡沫图像多尺度多方向纹理特征的提取方法，该泡沫图像多尺度多方向纹理特征的提取方法针对泡沫图像识别具有良好的模式可分性，且易于实施。The technical problem to be solved by the present invention is to provide a method for extracting multi-scale and multi-directional texture features of foam images. The method for extracting multi-scale and multi-directional texture features of foam images has good pattern separability for foam image recognition and is easy to implement .

发明的技术解决方案如下：The technical solution of the invention is as follows:

一种泡沫图像多尺度多方向纹理特征的提取方法，包括以下步骤：A method for extracting multi-scale and multi-directional texture features of foam images, comprising the following steps:

步骤一：从铜浮选现场所获取的泡沫灰度图像T_M×N(x,y)，其中M×N为泡沫灰度图像的分辨率，(x,y)表示灰度图像的像素；然后对泡沫灰度图像进行曲线波分解，得到曲线波系数矩阵集合，包括最粗尺度层即coarse层、次粗尺度层即detail层以及最细尺度层即fine层；Step 1: the foam grayscale image T _{M * N} (x, y) obtained from the copper flotation site, where M * N is the resolution of the foam grayscale image, and (x, y) represents the pixel of the grayscale image; Then, the curve wave decomposition is performed on the foam grayscale image to obtain a set of curve wave coefficient matrices, including the coarsest layer, the coarse layer, the second-coarse layer, the detail layer, and the thinnest layer, the fine layer;

步骤二：对步骤一得到的曲线波系数矩阵集合中的最粗尺度层即coarse层系数矩阵和最细尺度层即fine层系数矩阵，分别计算平均范数能量，作为最粗尺度层和最细尺度层的特征量；Step 2: Calculate the average norm energy for the coarsest scale layer, namely the coarse layer coefficient matrix, and the finest scale layer, namely the fine layer coefficient matrix, in the curvilinear wave coefficient matrix set obtained in step 1, as the coarsest scale layer and the finest The feature quantity of the scale layer;

对步骤一得到的曲线波系数矩阵集合中的detail层系数矩阵，所述的detail层即次粗尺度层；利用曲线波逆变换对其进行重构，得到detail层重构子图；对detail层重构子图求取灰度共生矩阵，计算不同方向上灰度共生矩阵的熵、相关性和对比度3个特征量，作为detail层的特征量；For the detail layer coefficient matrix in the curve wave coefficient matrix set obtained in step 1, the detail layer is the sub-coarse scale layer; utilize the curve wave inverse transform to reconstruct it to obtain the detail layer reconstruction subgraph; for the detail layer Reconstruct the subgraph to obtain the gray level co-occurrence matrix, and calculate the three feature quantities of the gray level co-occurrence matrix in different directions, entropy, correlation and contrast, as the feature quantity of the detail layer;

步骤三：将步骤二得到的各个尺度层的特征量组成特征向量，作为泡沫图像的纹理特征。Step 3: Combining the feature quantities of each scale layer obtained in Step 2 into a feature vector, which is used as the texture feature of the foam image.

从铜浮选现场获取的原始泡沫视频读取RGB泡沫图像；对RGB泡沫图像灰度化：原始RGB泡沫图像K_M×N×3灰度化后变为泡沫灰度图像T_M×N(x,y)。Read the RGB foam image from the original foam video obtained from the copper flotation site; grayscale the RGB foam image: the original RGB foam image K _M×N×3 grayscale becomes the foam grayscale image T _M×N (x ,y).

所述步骤一中：In said step one:

泡沫灰度图像使用USFFT快速离散曲线波变换，其中，曲线波变换方式设置为复值曲线波变换，尺度层数为J＝[log₂ N]-3；离散曲线波变换的步骤为：The foam grayscale image uses USFFT fast discrete curvelet transform, wherein the curvelet transform mode is set to complex valued curvelet transform, and the number of scale layers is J=[log ₂ N]-3; the steps of discrete curvelet transform are:

1)对泡沫灰度图像T_M×N(x,y)进行二维快速傅里叶变换至频域，得到公式为：1) Carry out two-dimensional fast Fourier transform to the frequency domain of the foam grayscale image T _M×N (x, y), and obtain The formula is:

$\overset{^^}{T T} ((m m,, n no)) = = {Σ Σ}_{x x = = 00}^{M m - - 11} {Σ Σ}_{y the y = = 00}^{N N - - 11} {T T}_{M m \times \times N N} ((x x,, y the y)) {e e}^{i i 22 π π ((m m x x / / M m + + n no y the y / / N N))}$

其中m、n为频域变量，是图像在频域空间里的横纵坐标，且-M/2≤m≤M/2，-N/2≤n≤N/2；Among them, m and n are frequency domain variables, which are the horizontal and vertical coordinates of the image in the frequency domain space, and -M/2≤m≤M/2, -N/2≤n≤N/2;

2)对在每一对尺度、方向(j,l)组合处(即“楔形”窗)进行重采样，【这里指在j＝1,2，…，J-1，J,的每个层次即尺度上】得到其中j是尺度变量，l是方向变量，重采样矩阵为楔形阵θl为楔形窗的方位角，l＝0,1,……,4·2[^j/2]-1，[j/2]是大于或等于j/2的最小整数。2 pairs Resampling is performed at each pair of scale and direction (j,l) combinations (ie "wedge" window), [here refers to each level of j=1,2,...,J-1,J, that is, the scale 】get where j is the scale variable, l is the direction variable, and the resampling matrix is a wedge matrix θl is the azimuth angle of the wedge window, l=0,1,...,4·2[ ^j/2 ]-1, [j/2] is the smallest integer greater than or equal to j/2.

3)将与抛物窗函数相乘，从而在不同的楔形窗的方向角θ_l处局部化得到：其中抛物窗函数可以通过如下步骤得到：3) Will with parabolic window function multiplied by , thus localizing at different orientation angles θ _l of the wedge window get: where the parabolic window function It can be obtained by the following steps:

A)计算满足容许条件A) Calculation meets the allowable conditions

${Σ Σ}_{l l = = - - ∞ ∞}^{∞ ∞} {V V}^{22} ((t t - - l l)) = = 11$

${Σ Σ}_{l l = = - - ∞ ∞}^{∞ ∞} {W W}^{22} ((22^{j j} r r)) = = 11$

的径向窗函数W(r)和角度窗函数V(t)分别为:The radial window function W(r) and the angular window function V(t) of are respectively:

$W W ((r r)) = = \{\begin{matrix} cos cos [[\frac{π π}{22} v v ((55 - - 66 r r))]] & 22 / / 33 \leq \leq r r \leq \leq 55 / / 66 \\ 11 & 55 / / 66 \leq \leq r r \leq \leq 44 / / 33 \\ cos cos [[\frac{π π}{22} v v ((33 r r - - 44))]] & 44 / / 33 \leq \leq r r \leq \leq 55 / / 33 \\ 00 & e e l l s the s e e \end{matrix}$

$V V ((t t)) = = \{\begin{matrix} 11 & | | t t | | \leq \leq 11 / / 33 \\ c c o o s the s [[\frac{π π}{22} v v ((33 | | t t | | - - 11))]] & 11 / / 33 \leq \leq | | t t | | \leq \leq 22 / / 33 \\ 00 & e e l l s the s e e \end{matrix}$

其中，v是满足以下条件的光滑函数：where v is a smooth function satisfying the following conditions:

$v v ((z z)) = = \{\begin{matrix} 00 & z z \leq \leq 00 \\ 11 & z z &GreaterEqual; &Greater Equal; 11 \end{matrix},, v v ((z z)) + + v v ((11 - - z z)) = = 11$

z、r、ω定义在二维空间R²上，z为空间变量，ω、r为频域内的极坐标，z, r, ω are defined on the ^two -dimensional space R2, z is the space variable, ω, r are the polar coordinates in the frequency domain,

t＝ω/2π。t=ω/2π.

B)计算频域窗函数为B) Calculate the frequency domain window function as

${\overset{~ ~}{U u}}_{j j} ((r r,, {θ θ}_{l l})) = = 22^{- - 33 j j / / 44} W W ((22^{- - j j} r r)) V V ((\frac{22^{[[j j / / 22]]} {θ θ}_{l l}}{22 π π})),, j j &GreaterEqual; &Greater Equal; {j j}_{00}$

其中j₀表示最粗尺度层；j₀＝1【j₀＝1是表示最粗尺度层的序号，可以用从j₀＝1至6表示从最粗到最细尺度层，也可以反过来。本文中用j₀＝1表示最粗尺度层。】Among them, j ₀ represents the coarsest scale layer; j ₀ = 1 [j ₀ = 1 is the serial number representing the coarsest scale layer, and j ₀ = 1 to 6 can be used to represent the scale layer from the coarsest to the finest, or vice versa . In this paper, j ₀ =1 is used to represent the coarsest scale layer. 】

4)对每一个重新划分频域空间的作二维快速傅里叶逆变换，得到曲线波分解系数 4) For each re-divided frequency domain space Do two-dimensional fast Fourier inverse transform to get the curve wave decomposition coefficient

${C C}_{k k,, l l}^{j j} = = \underset{m m,, n no &Element; &Element; {P P}_{j j}}{Σ Σ} \overset{^^}{T T} {((m m,, n no - - {mtanθ mtanθ}_{l l}))}^{' '} {\overset{~ ~}{U u}}_{j j} ((m m,, n no)) {e e}^{i i 22 π π (({x x}_{k k} m m / / {L L}_{11,, j j} + + {y the y}_{k k} n no / / {L L}_{22,, j j}))}$

其中，表示尺度j上第l个方向、位置k＝(x_k,y_k)处的曲线波分解系数，(m,n)∈P_j,P_j＝{(m,n):m₀≤m≤m₀+L_1,j,n₀≤n≤n₀+L_2,j}，L_1,j表示窗函数的支撑区间的长，L_2,j表示其支撑区间的宽；(m₀,n₀)为其支撑区间最左下点的坐标；【支撑区间的长、宽并不是精确地等于2^j或2^j/2，L_1,j＝δ₁2^j，其中，δ₁＝1+Ο(2^-j)；O表示2j的高阶无穷小，L_2,j＝δ₂2^j/2，其中，δ₂＝π/3，为简单起见，所有文献都将支撑区间的长、宽近似取为2^j或2^j/2】in, Indicates the curve wave decomposition coefficient at the lth direction on scale j at position k=(x _k ,y _k ), (m,n)∈P _j ,P _j ＝{(m,n):m ₀ ≤m≤ m ₀ +L _1,j ,n ₀ ≤n≤n ₀ +L _2,j }, L _1,j represents the window function (m ₀ , ⁿ ₀ ) is the coordinate of the lower left point of the support interval; [the length and width of the support interval are not exactly equal to 2 _j or 2 ^j/2 , L _1,j =δ ₁ 2 ^j , where, δ ₁ =1+Ο(2 ^-j ); O represents the higher-order infinitesimal of 2j, L _2,j =δ ₂ 2 ^j/2 , where, δ ₂ = π/3, for the sake of simplicity, all literatures take the length and width of the support interval as approximately 2 ^j or 2 ^j/2 ]

得到泡沫灰度图像T_M×N(x,y)的曲线波系数矩阵集合如下：The curvilinear wave coefficient matrix set of the foam grayscale image T _{M × N} (x, y) is obtained as follows:

${C C}_{k k,, 00}^{11},, {C C}_{k k,, l l}^{22},, {C C}_{k k,, l l}^{33},, ... ...,, {C C}_{k k,, l l}^{j j},, ... ...,, {C C}_{k k,, l l}^{J J - - 11},, {C C}_{k k,, 00}^{J J},, j j = = 11,, 22,, ... ...,, J J;; l l = = 00,, 11,, ... ... 44 \cdot \cdot 22^{[[j j / / 22]]} - - 11$

其中，当j＝j₀＝1时，为最粗尺度层即coarse层系数矩阵，当j＝J时，为最细尺度层即fine层系数矩阵，coarse层和fine层没有方向；当j＝2,...,J-1时，为次粗尺度层即detail层系数矩阵，detail层方向为l＝0,1,...4·2^[j/2]-1。Wherein, when j=j ₀ =1, is the coefficient matrix of the coarsest layer, that is, the coarse layer, when j=J, It is the coefficient matrix of the thinnest scale layer, that is, the fine layer, and the coarse layer and the fine layer have no direction; when j=2,...,J-1, is the second-coarse scale layer, that is, the coefficient matrix of the detail layer, and the direction of the detail layer is l=0,1,...4·2 ^[j/2] -1.

所述的步骤二中：In said step two:

1)对coarse层系数矩阵计算其平均范数能量，计算公式为：1) For the coarse layer coefficient matrix Calculate its average norm energy, the calculation formula is:

${E E.}_{c c} = = \frac{11}{{M m}_{c c} \cdot \cdot {N N}_{c c}} {Σ Σ}_{{x x}_{k k} = = 11}^{{M m}_{c c}} {Σ Σ}_{{y the y}_{k k} = = 11}^{{N N}_{c c}} | | {c c}_{{x x}_{k k} {y the y}_{k k}} | |$

其中，为coarse层系数矩阵的元素，M_c、N_c为矩阵的行列数；in, is the coefficient matrix of the coarse layer The elements of M _c , N _c are the number of rows and columns of the matrix;

2)对fine层系数矩阵计算其平均范数能量，计算公式为：2) For the fine layer coefficient matrix Calculate its average norm energy, the calculation formula is:

${E E.}_{f f} = = \frac{11}{{M m}_{f f} \cdot \cdot {N N}_{f f}} {Σ Σ}_{{x x}_{k k} = = 11}^{{M m}_{f f}} {Σ Σ}_{{y the y}_{k k} = = 11}^{{N N}_{f f}} | | {f f}_{{x x}_{k k} {y the y}_{k k}} | |$

其中，为fine层系数矩阵的元素，M_f、N_f为矩阵的行列数，所描述的图像大小与原灰度图像T_M×N(x,y)的大小相等，即M_f＝M,N_f＝N；in, is the fine layer coefficient matrix The elements of M _f , N _f are the number of rows and columns of the matrix, The size of the described image is equal to the size of the original grayscale image T _M×N (x, y), that is, M _f =M, N _f =N;

3)对detail层系数矩阵使用curvelet逆变换进行重构，得到detail层重构子图【重构子图步骤为现有技术，对detail层进行重构步骤如下：将曲线波变换后系数矩阵中coarse层和fine层系数置零，保留detail层系数；对系数矩阵进行curvelet逆变换，步骤为：对每一对尺度、角度组合处(j,l)，对应用二维快速傅里叶变换，得到傅里叶采样其中m，n∈P_j；对每一对(j,l)，作将看成在剪切网格(m,n-m tanθ_l)上的采样，并对其在标准奈奎斯特网格上重采样；对不同尺度和角度上的结果求和，得到对进行快速傅里叶逆变换，得到T(x,y)】，对其进行灰度映射：3) For the detail layer coefficient matrix Use the curvelet inverse transformation to reconstruct, and get the reconstructed subgraph of the detail layer [The step of reconstructing the subgraph is the existing technology, and the steps of reconstructing the detail layer are as follows: set the coefficients of the coarse layer and fine layer in the coefficient matrix after the curvelet transformation to zero, and retain the coefficients of the detail layer; perform curvelet inverse transformation on the coefficient matrix, The steps are: for each pair of scale and angle combinations (j,l), for Apply the 2D Fast Fourier Transform to get the Fourier samples where m, n∈P _j ; for each pair (j,l), make Will regarded as Sampling on a sheared grid (m,nm tanθ _l ) and resampling it on a standard Nyquist grid; summing the results at different scales and angles gives right Perform inverse fast Fourier transform to get T(x,y)], and perform grayscale mapping on it:

$G G = = 255255 \cdot &Center Dot; \frac{{\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}} - - min min {\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}}}{m m a a x x {\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}} - - min min {\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}}}$

其中分别为所有元素中的最大值和最小值；in respectively the maximum and minimum values among all elements;

对灰度映射后得到的矩阵G进行灰度级量化，得到G_q，量化级数q＝16；Perform grayscale quantization on the matrix G obtained after grayscale mapping to obtain G _q , and the number of quantization levels q=16;

求取灰度共生矩阵，记为其描述了G_q中灰度值分别为s和u的像素对(s,u)以角度相隔距离h【角度表示从灰度值为s的像素点指向灰度值为u的像素点的连线与水平正方向之间的夹角，相隔距离表示两个像素点连线的长度】出现的次数，其中取为0°、45°、90°、135°中任一值，距离h取为1；Find the gray level co-occurrence matrix, denoted as It describes the pixel pair (s, u) with the gray value s and u in G _q and the angle The distance h [the angle represents the angle between the line from the pixel with the gray value s to the pixel with the gray value u and the horizontal positive direction, and the distance represents the length of the line connecting two pixels] appears times, of which Take any value of 0°, 45°, 90°, 135°, and take the distance h as 1;

对不同角度的灰度共生矩阵计算3个特征值，作为detail层的特征量：to different angles The gray level co-occurrence matrix of Calculate 3 eigenvalues as the feature quantity of the detail layer:

熵： entropy:

相关性： Correlation:

对比度： Contrast:

其中表示中的元素，μ_s和σ_s、μ_u和σ_u分别表示灰度共生矩阵中元素所在的行和列方向上所有元素的均值和方差，其中元素所在的行号数值为s，列号数值为u。in express The elements in , μ _s and σ _s , μ _u and σ _u respectively represent the gray level co-occurrence matrix The mean and variance of all elements in the direction of the row and column where the element is located, where the value of the row number of the element is s, and the value of the column number is u.

所述的步骤三中，将步骤二得到的各个尺度层特征量组成最终的特征向量作为泡沫图像的纹理特征，分别取0°、45°、90°和135°，其中F¹＝E_c，为泡沫图像曲线波分解得到的coarse层子图的特征量；F²＝E_f，为fine层子图的特征量；为detail层子图不同角度的特征量。In Step 3, the feature quantities of each scale layer obtained in Step 2 are combined to form the final feature vector As the texture features of the foam image, Take 0°, 45°, 90° and 135° respectively, where F ¹ =E _c is the feature quantity of the coarse layer sub-graph obtained from the foam image curve wave decomposition; F ² =E _f is the feature of the fine layer sub-graph quantity; Different angles for detail layer submaps feature quantity.

本发明的技术构思：Technical concept of the present invention:

小波变换提供了一种在不同尺度上研究分析纹理细节的工具，可以将原始图像分解成不同频率不同分辨率的子带图像，高频子带反映图像的纹理、边缘等细节信息，低频子带反映图像的轮廓信息。但小波变换并不能很好地刻画泡沫图像表面纹理所表现出来的线奇异和曲线奇异，也不能提供很好的方向选择性。曲线波变换就是为了克服传统二维离散小波变换的缺点而提出来的。不同于小波变换的各向同性小波基，曲线波变换是各向异性的，对方向高度敏感，对于曲线奇异表示非常有效。曲线波理论经过两代的发展，第一代曲线波变换以脊波(Ridgelet)理论为基础，由一种特殊的滤波过程和多尺度Ridgelet变换组合而成，参数多，冗余大，并且存在分块效应。第二代curvelet变换及其快速离散算法则完全脱离了Ridgelet变换，直接在频域定义，更容易理解和实现，算法冗余少而速度更快。Wavelet transform provides a tool for studying and analyzing texture details at different scales. It can decompose the original image into sub-band images of different frequencies and resolutions. The high-frequency sub-band reflects the texture, edge and other details of the image. Reflect the contour information of the image. But the wavelet transform can't describe the line singularity and curve singularity shown by the surface texture of the foam image well, nor can it provide a good direction selectivity. The curvelet transform is proposed to overcome the shortcomings of the traditional two-dimensional discrete wavelet transform. Unlike the isotropic wavelet base of the wavelet transform, the curvelet transform is anisotropic, highly sensitive to direction, and very effective for singular representations of curves. After two generations of development of the curve wave theory, the first generation of curve wave transform is based on the Ridgelet theory, which is composed of a special filtering process and multi-scale Ridgelet transform, with many parameters, large redundancy, and existence of Blocking effect. The second-generation curvelet transform and its fast discrete algorithm are completely separated from the Ridgelet transform, and are defined directly in the frequency domain, which is easier to understand and implement, and the algorithm is less redundant and faster.

因此，本发明采用基于第二代曲线波理论的快速离散曲线波变换算法，将图像Curvelet分解得到的不同尺度和不同方向上的子图与灰度共生矩阵相结合，获取多尺度多方向上的纹理特征，共同组成图像的特征向量，对泡沫图像进行纹理描述，为基于泡沫浮选图像特征的选矿过程工况识别、分析与控制提供依据。Therefore, the present invention adopts the fast discrete curvelet transform algorithm based on the second-generation curvelet theory, and combines the subimages of different scales and directions obtained by the Curvelet decomposition of the image with the gray level co-occurrence matrix to obtain multi-scale and multi-directional Texture features, which together form the feature vector of the image, describe the texture of the foam image and provide a basis for the identification, analysis and control of the mineral processing process based on the image features of the froth flotation.

有益效果：Beneficial effect:

本发明的泡沫图像多尺度多方向纹理特征的提取方法，其本质是基于第二代曲线波变换的泡沫图像多尺度多方向纹理特征提取方法，通过多尺度多方向的数据处理，得到的特征向量能很好的反映图像各层次和各方向的纹理特征，克服目前泡沫图像纹理特征提取方法中灰度共生矩阵和小波变换各自的局限，即灰度共生矩阵只能反映泡沫图像单一尺度上的纹理结构信息，缺乏对泡沫纹理尺度间依赖关系的描述；多尺度小波分析不能刻画泡沫图像表面纹理所表现出来的线奇异和曲线奇异，也不能提供很好的方向选择性。实验证明，本发明所提取的纹理特征量具有良好的模式可分性，可以很好地将正常、水化、粘性三种泡沫区分开来。且这种方法可以直接在计算机上实现，成本低，效率高，易于实施。The method for extracting multi-scale and multi-directional texture features of foam images of the present invention is essentially a method for extracting multi-scale and multi-directional texture features of foam images based on second-generation curve wave transform, and the feature vector obtained is obtained through multi-scale and multi-directional data processing It can well reflect the texture features of each level and direction of the image, and overcome the respective limitations of the gray level co-occurrence matrix and wavelet transform in the current foam image texture feature extraction method, that is, the gray level co-occurrence matrix can only reflect the texture of the foam image on a single scale Structural information lacks the description of the inter-scale dependence of foam texture; multi-scale wavelet analysis cannot describe the line singularity and curve singularity shown in the surface texture of foam image, nor can it provide good direction selectivity. Experiments have proved that the texture feature quantity extracted by the present invention has good mode separability, and can well distinguish three types of foams: normal, hydrated and viscous. Moreover, this method can be directly implemented on a computer, has low cost, high efficiency and is easy to implement.

附图说明Description of drawings

图1为三种不同工况的泡沫图像(图a，b，c分别为正常泡沫、水化泡沫和粘性泡沫的图像)；Figure 1 is the foam images of three different working conditions (picture a, b, c are the images of normal foam, hydration foam and viscous foam respectively);

图2为泡沫图像曲线波分解后各尺度子图；(图a-f分别为最粗尺度、次粗尺度、最细尺度、二尺度、三尺度、四尺度和五尺度的重构子图)Fig. 2 is the sub-graphs of each scale after the curve wave decomposition of the foam image; (Fig.

图3为泡沫图像纹理特征提取框图；Fig. 3 is a block diagram of foam image texture feature extraction;

图4为特征散布图。Figure 4 is a feature scatter diagram.

具体实施方式detailed description

以下将结合附图和具体实施例对本发明做进一步详细说明：The present invention will be described in further detail below in conjunction with accompanying drawing and specific embodiment:

实施例1：Example 1:

某铜浮选现场有三种不同工况的泡沫，分别为正常泡沫、水化泡沫和粘性泡沫，这三种不同工况的泡沫图像如图1所示。There are three different working conditions of foam in a copper flotation site, which are normal foam, hydration foam and viscous foam. The foam images of these three different working conditions are shown in Figure 1.

第一步，根据铜浮选现场所获得的泡沫视频，获取泡沫图像，并将RGB图像进行灰度化。然后对所得的泡沫灰度图像进行曲线波分解，从而得到不同尺度上的曲线波系数矩阵集合；The first step is to obtain the foam image according to the foam video obtained at the copper flotation site, and grayscale the RGB image. Then, the curve wave decomposition is performed on the obtained foam gray image, so as to obtain the set of curve wave coefficient matrices on different scales;

步骤1：原始泡沫视频读取RGB泡沫图像；Step 1: Read the RGB foam image from the original foam video;

步骤2：RGB泡沫图像灰度化。原始RGB泡沫图像K_512×512×3灰度化后变为泡沫灰度图像T_512×512；Step 2: Grayscale the RGB foam image. The original RGB foam image K _512×512×3 becomes gray-scaled into a foam grayscale image T _512×512 ;

步骤3：对步骤2得到的泡沫灰度图像做快速离散曲线波变换，曲线波的变换方式设置为复值曲线波，尺度层数为J＝[log₂ N]-3。此时，J＝6。Step 3: Perform fast discrete curve wave transformation on the foam grayscale image obtained in step 2. The transformation mode of the curve wave is set to complex-valued curve wave, and the number of scale layers is J=[log ₂ N]-3. At this time, J=6.

于是，得到灰度图像T_M×N(x,y)的曲线波系数矩阵(集合)如下：Then, the curvilinear wave coefficient matrix (set) of the grayscale image T _M×N (x, y) is obtained as follows:

${C C}_{k k,, 00}^{11},, {C C}_{k k,, l l}^{22},, {C C}_{k k,, l l}^{33},, {C C}_{k k,, l l}^{44},, {C C}_{k k,, l l}^{55},, {C C}_{k k,, 00}^{66},, l l = = 00,, 11,, ... ... 44 \cdot &Center Dot; 22^{[[j j / / 22]]} - - 11;; k k &Element; &Element; {R R}^{22}$

其中，当j＝1时，为最粗尺度层即coarse层系数矩阵，当j＝J＝6时，为最细尺度层即fine层系数矩阵，coarse层和fine层没有方向；当j＝2,...,5时，为次粗尺度层即detail层系数矩阵，detail层方向为l＝0,1,...4·2^[j/2]-1。Among them, when j=1, is the coarsest scale layer, that is, the coefficient matrix of the coarse layer, when j=J=6, It is the coefficient matrix of the finest layer, that is, the fine layer, and the coarse layer and the fine layer have no direction; when j=2,...,5, is the second-coarse scale layer, that is, the coefficient matrix of the detail layer, and the direction of the detail layer is l=0,1,...4·2 ^[j/2] -1.

泡沫图像的各尺度曲线波分解系数中，coarse层系数是低频系数，主要包含泡沫图像的概貌；fine层系数是高频系数，体现图像的细节特征，coarse层和fine层系数不包含方向信息；detail层系数主要包含图像的中高频系数，体现细节和边缘信息，具备多方向特征。因此，对coarse层和fine层系数矩阵计算平均能量范数，对detail重构子图计算不同方向上的灰度共生矩阵，以充分提取detail层的纹理信息。Among the curve wave decomposition coefficients of each scale of the foam image, the coefficients of the coarse layer are low-frequency coefficients, which mainly contain the general appearance of the foam image; the coefficients of the fine layer are high-frequency coefficients, which reflect the detailed characteristics of the image, and the coefficients of the coarse layer and the fine layer do not contain direction information; The detail layer coefficients mainly include mid-to-high frequency coefficients of the image, which reflect details and edge information, and have multi-directional features. Therefore, the average energy norm is calculated for the coefficient matrices of the coarse layer and the fine layer, and the gray level co-occurrence matrix in different directions is calculated for the detail reconstruction sub-image to fully extract the texture information of the detail layer.

第二步，对coarse层和fine层的曲线波子图分别进行特征量提取。In the second step, feature extraction is performed on the curve wave subgraphs of the coarse layer and the fine layer respectively.

${E E.}_{c c} = = \frac{11}{{M m}_{c c} \cdot &Center Dot; {N N}_{c c}} {Σ Σ}_{{x x}_{k k} = = 11}^{{M m}_{c c}} {Σ Σ}_{{y the y}_{k k} = = 11}^{{N N}_{c c}} | | {c c}_{{x x}_{k k} {y the y}_{k k}} | |$

其中，为coarse层系数矩阵的元素，Mc、Nc为矩阵的行列数，此时M_c＝32，N_c＝32。in, is the coefficient matrix of the coarse layer elements, Mc and Nc are The number of rows and columns of the matrix, at this time M _c =32, N _c =32.

${E E.}_{f f} = = \frac{11}{{M m}_{f f} \cdot &Center Dot; {N N}_{f f}} {Σ Σ}_{{x x}_{k k} = = 11}^{{M m}_{f f}} {Σ Σ}_{{y the y}_{k k} = = 11}^{{N N}_{f f}} | | {f f}_{{x x}_{k k} {y the y}_{k k}} | |$

其中，为fine层系数矩阵的元素，M_f、N_f为矩阵的行列数，所描述的图像大小与原灰度图像T_M×N(x,y)的大小相等，即M_f＝M,N_f＝N。此时，J＝6，M_f＝M＝512，N_f＝N＝512。in, is the fine layer coefficient matrix The elements of M _f , N _f are the number of rows and columns of the matrix, The size of the described image is equal to the size of the original grayscale image T _M×N (x, y), that is, M _f =M, N _f =N. At this time, J=6, M _f =M=512, N _f =N=512.

第三步，对detail层系数矩阵使用curvelet逆变换进行重构，得到detail层重构子图对其进行灰度映射：The third step, the coefficient matrix of the detail layer Use the curvelet inverse transformation to reconstruct, and get the reconstructed subgraph of the detail layer Grayscale map it:

$G G = = 255255 \cdot \cdot \frac{{\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}} - - min min {\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}}}{m m a a x x {\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}} - - min min {\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}}}$

其中分别为所有元素中的最大值和最小值。in respectively The maximum and minimum value among all elements.

1)对灰度映射后得到的矩阵G进行灰度级量化，得到G_q，量化级数q＝16。1) Gray scale quantization is performed on the matrix G obtained after gray scale mapping to obtain G _q , and the number of quantization levels q=16.

2)求取灰度共生矩阵，记为其描述了G_q中灰度值分别为s和u的像素对(s,u)以角度相隔距离h出现的次数，其中可以取为0°、45°、90°、135°，距离h一般取为1。2) Obtain the gray level co-occurrence matrix, denoted as It describes the pixel pair (s, u) with the gray value s and u in G _q and the angle The number of occurrences separated by a distance h, where It can be taken as 0°, 45°, 90°, and 135°, and the distance h is generally taken as 1.

3)对不同方向(角度)的灰度共生矩阵计算3个特征值，作为detail层的特征量：3) For different directions (angle ) gray level co-occurrence matrix Calculate 3 eigenvalues as the feature quantity of the detail layer:

熵： entropy:

Claims

1. an extraction method of multi-scale and multi-directional texture features of foam images, characterized in that, comprising the following steps:

Step 1: Foam grayscale image T _M×N (x,y) obtained from the copper flotation site, where M×N is the resolution of the foam grayscale image, and (x,y) represents the pixel of the foam grayscale image ; Then, the curve wave decomposition is performed on the foam grayscale image to obtain a set of curve wave coefficient matrices, including the coarsest scale layer, namely the coarse layer, the second coarse scale layer, namely the detail layer, and the thinnest scale layer, namely the fine layer;

Step 2: Calculate the average norm energy respectively for the coarsest scale layer, namely the coarse layer coefficient matrix, and the finest scale layer, namely the fine layer coefficient matrix, in the curvilinear wave coefficient matrix set obtained in step 1, as the coarsest scale layer and the finest The feature quantity of the scale layer;

For the detail layer coefficient matrix in the curve wave coefficient matrix set obtained in step 1, the detail layer is the sub-coarse scale layer; it is reconstructed by using the curve wave inverse transform to obtain the detail layer reconstruction subgraph; for the detail layer Reconstruct the subgraph to obtain the gray level co-occurrence matrix, and calculate the three feature quantities of the gray level co-occurrence matrix in different directions, entropy, correlation and contrast, as the feature quantity of the detail layer;

Step 3: The feature quantities of each scale layer obtained in step 2 are used to form a feature vector as the texture feature of the foam image; in the step 1:

The foam grayscale image uses USFFT fast discrete curvelet transform, wherein the curvelet transform mode is set to complex valued curvelet transform, and the number of scale layers is J=[log ₂ N]-3; the steps of discrete curvelet transform are:

1) Carry out two-dimensional fast Fourier transform to the frequency domain of the foam grayscale image T _M×N (x, y), and obtain The formula is:

\overset{^^}{T T} ((m m,, n no)) = = {Σ Σ}_{x x = = 00}^{M m - - 11} {Σ Σ}_{y the y = = 00}^{N N - - 11} {T T}_{M m \times \times N N} ((x x,, y the y)) {e e}^{i i 22 π π ((m m x x / / M m + + n no y the y / / N N))}

Among them, m and n are frequency domain variables, which are the horizontal and vertical coordinates of the image in the frequency domain space, and -M/2≤m≤M/2, -N/2≤n≤N/2;

2 pairs Resampling is performed at each pair of scale and direction (j,l) combinations to obtain where j is the scale variable, l is the direction variable, and the resampling matrix is a wedge matrix θ _l is the azimuth angle of the wedge window, l=0,1,...,4.2 ^[j/2] -1, [j/2] is the smallest integer greater than or equal to j/2;

3) Will with parabolic window function multiplied by , thus localizing at different azimuths θl of the wedge window get: where the parabolic window function Obtained by the following steps:

a) Calculation meets the allowable conditions

{Σ Σ}_{l l = = - - ∞ ∞}^{∞ ∞} {V V}^{22} ((t t - - l l)) = = 11

{Σ Σ}_{l l = = - - ∞ ∞}^{∞ ∞} {W W}^{22} ((22^{j j} r r)) = = 11

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

W W ((r r)) = = \{\begin{matrix} cos cos [[\frac{π π}{22} v v ((55 - - 66 r r))]] & 22 / / 33 \leq \leq r r \leq \leq 55 / / 66 \\ 11 & 55 / / 66 \leq \leq r r \leq \leq 44 / / 33 \\ cos cos [[\frac{π π}{22} v v ((33 r r - - 44))]] & 44 / / 33 \leq \leq r r \leq \leq 55 / / 33 \\ 00 & e e l l s the s e e \end{matrix}

V V ((t t)) = = \{\begin{matrix} 11 & | | t t | | \leq \leq 11 / / 33 \\ c c o o s the s [[\frac{π π}{22} v v ((33 | | t t | | - - 11))]] & 11 / / 33 \leq \leq | | t t | | \leq \leq 22 / / 33 \\ 00 & e e l l s the s e e \end{matrix}

where v is a smooth function satisfying the following conditions:

v v ((z z)) = = \{\begin{matrix} 00 & z z \leq \leq 00 \\ 11 & z z &GreaterEqual; &Greater Equal; 11 \end{matrix},, v v ((z z)) + + v v ((11 - - z z)) = = 11

z, r, ω are defined on the two-dimensional space R ² , z is a space variable, ω, r are polar coordinates in the frequency domain, t=ω/2π;

b) Calculate the frequency domain window function as

{\overset{~ ~}{U u}}_{j j} ((r r,, {θ θ}_{l l})) = = 22^{- - 33 j j / / 44} W W ((22^{- - j j} r r)) V V ((\frac{22^{[[j j / / 22]]} {θ θ}_{l l}}{22 π π})),, j j &GreaterEqual; &Greater Equal; {j j}_{00}

Where j ₀ represents the coarsest scale layer; j ₀ =1;

4) For each re-divided frequency domain space Do two-dimensional fast Fourier inverse transform to get the curve wave decomposition coefficient

{C C}_{k k,, l l}^{j j} = = \underset{m m,, n no &Element; &Element; {P P}_{j j}}{Σ Σ} \overset{^^}{T T} {((m m,, n no - - m m {tanθ tanθ}_{l l}))}^{' '} {\overset{~ ~}{U u}}_{j j} ((m m,, n no)) {e e}^{i i 22 π π (({x x}_{k k} m m / / {L L}_{11,, j j} + + {y the y}_{k k} n no / / {L L}_{22,, j j}))}

in, Indicates the curve wave decomposition coefficient at the lth direction and position k=(xk,yk) on the scale j, (m,n)∈P _j ,P _j ＝{(m,n):m ₀ ≤m≤m ₀ +L _1,j ,n ₀ ≤n≤n ₀ +L _2,j }, L _1,j represents the parabolic window function The length of the support interval, L _{2, j} represents the width of the support interval; (m ₀ , n ₀ ) is the coordinate of the bottom left point of the support interval;

The curvilinear wave coefficient matrix set of the foam grayscale image T _{M × N} (x, y) is obtained as follows:

{C C}_{k k,, 00}^{11},, {C C}_{k k,, l l}^{22},, {C C}_{k k,, l l}^{33},, ... ...,, {C C}_{k k,, l l}^{j j},, ... ...,, {C C}_{k k,, l l}^{J J - - 11},, {C C}_{k k,, 00}^{J J},, j j = = 11,, 22,, ... ...,, J J;; l l = = 00,, 11,, ... ... 44 \cdot &Center Dot; 22^{[[j j / / 22]]} - - 11

Wherein, when j=j ₀ =1, is the coefficient matrix of the coarsest layer, that is, the coarse layer, when j=J, It is the coefficient matrix of the thinnest scale layer, that is, the fine layer, and the coarse layer and the fine layer have no direction; when j=2,...,J-1, is the second-coarse scale layer, that is, the coefficient matrix of the detail layer, and the direction of the detail layer is l=0,1,...4·2 ^[j/2] -1.

2. the method for extracting the multi-scale and multi-directional texture feature of foam image according to claim 1, is characterized in that,

In said step two:

1) For the coarse layer coefficient matrix Calculate its average norm energy, the calculation formula is:

{E E.}_{c c} = = \frac{11}{{M m}_{c c} \cdot &Center Dot; {N N}_{c c}} {Σ Σ}_{{x x}_{k k} = = 11}^{{M m}_{c c}} {Σ Σ}_{{y the y}_{k k} = = 11}^{{N N}_{c c}} | | {c c}_{{x x}_{k k} {y the y}_{k k}} | |

in, is the coefficient matrix of the coarse layer The elements of M _c , N _c are the number of rows and columns of the matrix;

2) For the fine layer coefficient matrix Calculate its average norm energy, the calculation formula is:

{E E.}_{f f} = = \frac{11}{{M m}_{f f} \cdot &Center Dot; {N N}_{f f}} {Σ Σ}_{{x x}_{k k} = = 11}^{{M m}_{f f}} {Σ Σ}_{{y the y}_{k k} = = 11}^{{N N}_{f f}} | | {f f}_{{x x}_{k k} {y the y}_{k k}} | |

in, is the fine layer coefficient matrix The elements of M _f , N _f are the number of rows and columns of the matrix, The size of the described image is equal to the size of the foam grayscale image T _M×N (x, y), that is, M _f =M, N _f =N;

3) For the detail layer coefficient matrix Use the curvelet inverse transformation to reconstruct, and get the reconstructed subgraph of the detail layer Grayscale map it:

G G = = 255255 \cdot &Center Dot; \frac{{\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}} - - m m i i n no {\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}}}{m m a a x x {\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}} - - min min {\overset{&OverBar; &OverBar;}{T T}}_{{M m}_{d d} \times \times {N N}_{d d}}}

in respectively the maximum and minimum values among all elements;

Perform grayscale quantization on the matrix G obtained after grayscale mapping to obtain G _q , and the number of quantization levels q=16;

Find the gray level co-occurrence matrix, denoted as It describes the pixel pair (s, u) with the gray value s and u in G _q and the angle The number of occurrences separated by a distance h, where Take any value of 0°, 45°, 90°, 135°, and take the distance h as 1;

different angles The gray level co-occurrence matrix of Calculate 3 eigenvalues as the feature quantity of the detail layer:

entropy:

Correlation:

Contrast:

in express The elements in , μ _s and σ _s , μ _u and σ _u respectively represent the gray level co-occurrence matrix The mean and variance of all elements in the direction of the row and column where the element is located, where the value of the row number of the element is s, and the value of the column number is u.

3. the method for extracting the multi-scale and multi-directional texture features of the foam image according to claim 2, characterized in that, in the step 3, the feature quantities of each scale layer obtained in the step 2 are formed into the final feature vector As the texture features of the foam image, Take 0°, 45°, 90° and 135° respectively, where F ¹ =E _c is the feature quantity of the coarse layer sub-image obtained from the foam image curve wave decomposition; F ² =E _f is the feature of the fine layer sub-image quantity; Different angles for detail layer submaps feature quantity.