CN103345636A - Method for identifying foam working condition on copper flotation site based on wavelet multi-scale binaryzation - Google Patents

Abstract

The invention discloses a method for identifying the foam working condition on a copper flotation site based on wavelet multi-scale binaryzation. The method comprises the steps of carrying out wavelet transformation on a foam grey image; carrying out binaryzation on wavelet approaching subgraphs with different scales; carrying out statistical calculation on white areas of all binary images according to the space-frequency relation of two-dimensional wavelet transformation to obtain a novel multi-scale statistical characteristic, namely an equivalent dimension characteristic directly related to the apparent form of foam. A foam image equivalent dimension distribution diagram can be obtained according to the obtained equivalent dimension characteristic, and foam images with different working conditions can be distinguished directly through the distribution diagram. The method for identifying the foam working condition on the copper flotation site based on the wavelet multi-scale binaryzation is simple and efficient, and has great guiding significance for foam working condition identification on the copper flotation site.

Description

Based on the on-the-spot bubble condition recognition methods of the copper flotation of multi-scale wavelet binaryzation

Technical field

The present invention relates to the on-the-spot bubble condition recognition methods of a kind of copper flotation based on the multi-scale wavelet binaryzation, belong to fields such as image processing techniques and pattern-recognition.

Background technology

The flotation operating mode is the working condition in the flotation production run, and it is most important to instructing flotation to produce to identify operating mode timely and accurately.The mode of traditional apparent variation of dependence operating worker visual inspection foam can't satisfy current flotation and produce the needs of quick and precisely identifying operating mode.Along with the develop rapidly of technology such as machine vision and image processing, the work of carrying out the Intelligent Recognition operating mode in conjunction with the on-the-spot foam characteristics of flotation has obtained remarkable progress.By identifying the operating mode classification at flotation scene fast and accurately, the flotation production control system can in time be adjusted manufacturing parameter, makes the flotation production run remain at optimum state.

Studies show that foam surface visual signature (hereinafter to be referred as the foam appearance features) such as the foam size that is directly observed by naked eyes, color is the concentrated expression of flotation operating mode.How accurately extracting in the floatation process and the closely-related foam appearance features of crucial production target, is the key that realizes the identification of flotation operating mode.The traditional characteristic that is applied to the identification of copper flotation operating mode mainly obtains by dividing method, comprises foam color, size, load-carry duty, speed and degree of stability etc., but these directly do not possess multiple dimensioned characteristic by the feature of cutting apart the original image acquisition.Bianry image is the simple form that characterizes piece image.With foam gray level image binaryzation, can obtain form statistical natures such as foam number, area.The same with image partition method, the foam characteristics of utilizing binarization method to obtain does not possess multiple dimensioned characteristic yet.Wavelet analysis has multiple dimensioned characteristic, and energy anthropomorphic dummy's vision system carries out the analysis of hyperchannel time-frequency domain to signal, thereby can access the statistical nature of more abundant information.Though the conventional statistics feature of utilizing wavelet analysis to extract has multiple dimensioned characteristic, is difficult to describe to meet the foam mode of appearance of operating worker visual custom, thereby directly influences the accurate judgement of operating mode.

Therefore, be necessary to design the on-the-spot bubble condition recognition methods of a kind of copper flotation based on the multi-scale wavelet binaryzation.

Summary of the invention

Technical matters to be solved by this invention provides the on-the-spot bubble condition recognition methods of a kind of copper flotation based on the multi-scale wavelet binaryzation, should be easy to implement based on the on-the-spot bubble condition recognition methods of the copper flotation of multi-scale wavelet binaryzation, implementation cost is low, and recognition effect is good.

The technical solution of invention is as follows:

A kind of froth images equivalent dimension Feature Extraction method is characterized in that, may further comprise the steps:

Step 1: the foam video that obtains according to copper flotation scene obtains the three-dimensional foam image, the three-dimensional foam image is carried out gray processing, two dimensional gray image to gained carries out wavelet decomposition then, thereby obtain the small echo subgraph on the different scale, the feature of ignoring each rank details subgraph, only each rank ll channel is carried out single reconstruct, obtain the reconstruct ll channel;

Step 2: according to uncertainty principle and discrete wavelet frequency domain relation, extrapolate the foam diameter variation range of different order subgraphs;

Step 3: utilize maximum variance between clusters with each reconstruct ll channel binaryzation, obtain bianry image, count the foam total area of each bianry image, and then try to achieve foam equivalent dimension feature; The foam diameter variation range that last integrating step two is extrapolated calculates equivalent foam number, and then obtains foam equivalent dimension distribution plan; [width of cloth froth images can obtain a plurality of ll channels behind wavelet transformation, the back is further processed these ll channels (a plurality of image) again, just obtains corresponding equivalent dimension distribution plan.】

Step 4: foam equivalent dimension distribution plan and benchmark distribution plan are compared, determine the copper flotation field working conditions of current froth images correspondence.

Described step 1 comprises following substep:

Step 1: original froth images gray processing;

Original three-dimensional RGB froth images K _{(X * Y * 3)}Become the two dimensional gray image I behind the gray processing _{(X * Y)}

Step 2: select the sym4 small echo that the two dimensional gray image is carried out five rank and decompose, decompose order at each, two-dimensional wavelet transformation will produce the details subgraph of a ll channel and level, vertical, three different directions of diagonal line;

At each wavelet transformation formula that decomposes order be:

Decompose the matrix of coefficients that approaches in order at each

With 3 detail coefficients matrixes Can be obtained by the Mallat algorithm that 2-d wavelet decomposes:

$\left\{\begin{array}{c}{c}_{k,m}^j=\underset{l,n}{\mathrm{\Σ}}{\stackrel{\‾}{h}}_{2k-l}{\stackrel{\‾}{h}}_{2m-n}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,1}=\underset{l,n}{\mathrm{\Σ}}{\stackrel{\‾}{h}}_{2k-l}{\stackrel{\‾}{g}}_{2m-n}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,2}=\underset{l,n}{\mathrm{\Σ}}{\stackrel{\‾}{g}}_{2k-l}{\stackrel{\‾}{h}}_{2m-n}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,3}=\underset{l,n}{\mathrm{\Σ}}{\stackrel{\‾}{g}}_{2k-l}{\stackrel{\‾}{g}}_{2m-n}{c}_{l,n}^{j+1}\end{array}\right.$ Formula 2

Formula mesoscale function is: 3 wavelet functions are respectively: ψ ¹(x, y)=φ (x) ψ (y), ψ ²(x, y)=ψ (x) φ (y), ψ ³(x, y)=ψ (x) ψ (y), wherein With

Two yardstick equations and the little wave equation of representing an orthogonal dimension multiresolution analysis respectively; J carries out five rank wavelet decomposition for decomposing the number of plies in this example, then get j=5,4,3,2,1; K, m ∈ Z is the system of representatives matrix number respectively Row and column, l, n ∈ Z be the system of representatives matrix number respectively

Row and column; [when carrying out the first rank wavelet transformation, l=600, n=800, k=300, m=400] coefficient sequence h={h _iBe a low-pass filter, and h={-0.076 is arranged ,-0.030,0.498,0.804,0.298 ,-0.100 ,-0.013,0.032},

Sequential counter-rotating for h

Coefficient sequence g={g _iBe a Hi-pass filter and g _i=(1) ⁱh _1-i, Sequential counter-rotating for g

At first application of formula 1 is carried out the two-dimensional wavelet transformation on first rank, obtains 1 ll channel and 3 details subgraphs, and its coefficient is calculated by formula 2; Then, utilize 1 pair of single order ll channel of formula (low frequency part)

Proceed the two-dimensional wavelet transformation on second rank, obtain 1 ll channel and 3 details subgraphs again; The rest may be inferred, can obtain Five wavelet transformations that decompose orders; Correspondingly, just obtain gray level image I _{(X * Y)}Multiple dimensioned expression;

Step 3: ignore the feature of each rank details subgraph, only each rank ll channel is carried out single reconstruct, obtain the reconstruct ll channel:

Approaching the reconstruct subgraph with five remembers respectively and makes S ^v, v=1,2 ..., 5, they have represented the outline portion of foam subgraph under the different scale, and its matrix of coefficients is tried to achieve by following reconstruction formula:

$c_{k,m}^{j+1}=\underset{l,n}{\mathrm{\Σ}}{h}_{k-2l}{h}_{m-2n}{c}_{l,n}^j+\underset{l,n}{\mathrm{\Σ}}{h}_{k-2l}{g}_{m-2n}{d}_{l,n}^{j,1}+\underset{l,n}{\mathrm{\Σ}}{g}_{k-2l}{h}_{m-2n}{d}_{l,n}^{j,2}+\underset{l,n}{\mathrm{\Σ}}{g}_{k-2l}{g}_{m-2n}{d}_{l,n}^{j,3}$ Formula 3.

In the described step 2,

Frequency domain between the discrete wavelet different scale signal closes: approximation signal f _j(t) band width only is f _J+1(t) half of band width; f _J+1(t) second half of band width is by detail signal d _j(t) performance;

Table 1

Ll channel	Frequency range	Spatial dimension
			A1	0～0.5π	0～1
A2	0～0.25π	0～2
			A3	0～0.125π	0～4
A4	0～0.0625π	0～8
			A5	0～0.03125π	0～16

[by uncertainty principle as can be known, the spatial frequency window area of wavelet multi-scale analysis has unchangeability.Therefore, the corresponding different spaces width of the band width of each reconstruct subgraph difference.] spatial frequency that obtains five ll channels according to the frequency domain between discrete wavelet different scale signal relation and uncertainty principle concerns as shown in table 1.[spatial dimension in the table is exactly the equivalent diameter scope among Fig. 6]

Described step 3 comprises following substep:

Step 1: calculate the optimal threshold of each reconstruct subgraph according to maximum variance between clusters, each reconstruct subgraph is carried out binaryzation, and count the foam total area of each bianry image:

If S ^vL gray level arranged, and gray-scale value is that the pixel count of i is n _i, then total pixel count is

The probability that each gray-scale value occurs is

If with gray scale L _ThFor thresholding is divided into 2 zones with image, gray level is 1～L _ThPixel region A, gray level is L _ThThe probability that pixel region B:A, the B of+1～L-1 occurs is respectively:

$p_A=\underset{i=0}{\overset{L_{\mathrm{th}}}{\mathrm{\Σ}}}{p}_i,$ $p_B=\underset{i=L_{\mathrm{th}}+1}{\overset{L-1}{\mathrm{\Σ}}}{p}_i=1-p_A;$

The gray average of A and B two classes is respectively:

${\mathrm{\ω}}_A=\frac{\underset{i=0}{\overset{L_{\mathrm{th}}}{\mathrm{\Σ}}}{\mathrm{ip}}_i}{p_A},$ ${\mathrm{\ω}}_B=\frac{\underset{i=L_{\mathrm{th}}+1}{\overset{L-1}{\mathrm{\Σ}}}{\mathrm{ip}}_i}{p_B};$

Thereby can obtain the total gray average of image:

${\mathrm{\ω}}_0=p_A{\mathrm{\ω}}_A+p_B{\mathrm{\ω}}_B=\underset{i=L_{\mathrm{th}}=1}{\overset{L-1}{\mathrm{\Σ}}}{\mathrm{ip}}_i;$

Can obtain the inter-class variance in A, B two zones thus:

σ ²＝p _A(ω _A-ω ₀) ²+p _B(ω _B-ω ₀) ²；

For obtaining the optimum segmentation threshold value, as criterion, make σ with the inter-class variance of two classes ²The value maximum

Be the optimal threshold of asking:

$L_{\mathrm{th},v}^{*}=\mathrm{Arg}\underset{0\≤L_{\mathrm{th}}\≤L-1}{\mathrm{Max}}[p_A{({\mathrm{\ω}}_A-{\mathrm{\ω}}_0)}^2+p_B{({\mathrm{\ω}}_B-{\mathrm{\ω}}_0)}^2],V=\mathrm{1,2,3,4,5},$

Calculate the optimal threshold that respectively approaches the reconstruct subgraph

Basis again

Respectively to S ^vCarry out binaryzation, obtain five bianry images, add up the white portion area of each bianry image, namely obtain the foam total area, be designated as A _v

Step 2: adjacent binary image foam total area is subtracted each other, and obtains foam equivalent dimension feature;

The foam total area of adjacent binary image is subtracted each other, obtain foam subgraph equivalent area, be designated as E _q

E is arranged _q=A _Q+1-A _q, q=1,2,3,4;

E _qBe the foam equivalent dimension feature of trying to achieve by multiple dimensioned binaryzation, subscript q is the number of equivalent dimension feature, and q+1 is for decomposing order; Because decomposing order is 5, then 4 equivalent dimension features are distinguished corresponding 4 continuous foam diameter variation ranges: 1～2,2～4,4～8,8～16; [this scope is that the space-frequency relation between the analysis wavelet subgraph directly obtains, rather than is obtained by area.The diameter here is equivalent diameter, does not therefore give unit.】

Step 3: according to the foam diameter variation range of extrapolating, calculate equivalent foam number, and then obtain foam equivalent dimension distribution plan;

With D _qBe the mean value of foam diameter variation range, the D of 4 foam diameter variation range correspondences _qBe respectively 1.5,3,6,12, obtain the equivalent foam number of each order according to following formula:

[this number is exactly the frequency among Fig. 6]

Finally obtain the equivalent dimension distribution plan of current working froth images.

In the described step 4, the acquisition methods of benchmark distribution plan is: the image by several known operating modes obtains a plurality of foam equivalent dimension distribution plans through step 1 to three earlier, a plurality of foam equivalent dimension distribution plans of gained is added up, thereby obtained the benchmark distribution plan; Described statistics refers to count the foam frequency of each the froth images equivalent diameter under different operating modes, and the benchmark distribution plan is that off-line obtains.

Beneficial effect:

The on-the-spot bubble condition recognition methods of copper flotation based on the multi-scale wavelet binaryzation of the present invention, wavelet multi-scale analysis is combined with image binaryzation, utilize the multi-scale wavelet binaryzation to extract a kind of new multiple dimensioned statistical nature directly related with the foam mode of appearance---equivalent dimension feature.Identify copper flotation production status according to this feature, for stabilized copper flotation operating mode, realize that the optimal control of copper floatation process has important meaning.

The feature that the present invention extracts is the expression of original image on different scale, has multiple dimensioned characteristic; This feature is directly related with the foam mode of appearance simultaneously, and the corresponding different equivalent dimension of different froth images distributes.Can be directly the froth images of different operating modes be made a distinction by equivalent dimension distribution plan relatively, therefore effectively simple, significant to instructing copper flotation operating mode to identify.

Description of drawings

The froth images of three kinds of different operating modes of Fig. 1;

The dendrogram of Fig. 2 froth images five rank wavelet decomposition;

Fig. 3 froth images reconstruct ll channel;

Frequency domain relation between Fig. 4 discrete wavelet different scale signal;

The spatial frequency relation of five ll channels of Fig. 5;

The equivalent dimension of three kinds of different operating mode froth images of Fig. 6 distributes.

Embodiment

Below with reference to the drawings and specific embodiments the present invention is described in further details:

Embodiment 1:

Below in conjunction with accompanying drawing the specific embodiment of the present invention is described, there is the foam of three kinds of different operating modes at certain copper flotation scene, is respectively normal foam, aquation foam and viscous foam, and the froth images of these three kinds of different operating modes as shown in Figure 1.

The first step, the foam video according to copper flotation scene obtains obtains froth images, and 3-D view is carried out gray processing.Then the two dimensional gray image is carried out wavelet decomposition, obtain the small echo subgraph on the different scale.The feature of ignoring each rank details subgraph is only carried out single reconstruct to each rank ll channel, obtains the reconstruct ll channel.

Step 1: original froth images gray processing;

Original three-dimensional RGB froth images K _{(X * Y * 3)}Become the two dimensional gray image I behind the gray processing _{(X * Y)}

Step 2: select the sym4 small echo that gray level image is carried out five rank and decompose, decompose order at each, two-dimensional wavelet transformation will produce the details subgraph of a ll channel and level, vertical, three different directions of diagonal line, and Fig. 2 is froth images five rank wavelet decomposition dendrograms;

At each wavelet transformation formula that decomposes order be:

Decompose the matrix of coefficients that approaches in order at each

With 3 detail coefficients matrixes

Can be obtained by the Mallat algorithm that 2-d wavelet decomposes:

$\left\{\begin{array}{c}{c}_{k,m}^j=\underset{l,n}{\mathrm{\Σ}}{\stackrel{\‾}{h}}_{2k-l}{\stackrel{\‾}{h}}_{2m-n}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,1}=\underset{l,n}{\mathrm{\Σ}}{\stackrel{\‾}{h}}_{2k-l}{\stackrel{\‾}{g}}_{2m-n}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,2}=\underset{l,n}{\mathrm{\Σ}}{\stackrel{\‾}{g}}_{2k-l}{\stackrel{\‾}{h}}_{2m-n}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,3}=\underset{l,n}{\mathrm{\Σ}}{\stackrel{\‾}{g}}_{2k-l}{\stackrel{\‾}{g}}_{2m-n}{c}_{l,n}^{j+1}\end{array}\right.---\left(2\right)$

Formula mesoscale function is:

3 wavelet functions are respectively: ψ ¹(x, y)=φ (x) ψ (y), ψ ²(x, y)=ψ (x) φ (y), ψ ³(x, y)=ψ (x) ψ (y), wherein With

Two yardstick equations and the little wave equation of representing an orthogonal dimension multiresolution analysis respectively; J carries out five rank wavelet decomposition for decomposing the number of plies in this example, then get j=5,4,3,2,1; K, m ∈ Z is the system of representatives matrix number respectively

Row and column, l, n ∈ Z be the system of representatives matrix number respectively

Row and column; [when carrying out the first rank wavelet transformation, l=600, n=800, k=300, m=400] coefficient sequence h={h _iBe a low-pass filter, and h={-0.076 is arranged ,-0.030,0.498,0.804,0.298 ,-0.100 ,-0.013,0.032}, Sequential counter-rotating for h

Coefficient sequence g={g _iBe a Hi-pass filter and g _i=(1) ⁱh _1-i,

Sequential counter-rotating for g

At first application of formula (1) is carried out the two-dimensional wavelet transformation of ground floor, and (get j=5, k=300, m=400, l=600, n=800) obtain 1 ll channel

With 3 details subgraphs (

), its coefficient is calculated by formula (2), at this moment

Be the two dimensional gray image array I that step 1 obtains _{(X * Y)}(

Calculation procedure be: to arbitrary fixing columns n=800, use earlier

With

Each column vector make convolution, carry out downward two the sampling obtain

And then use

With

Each the row vector make convolution, carry out downward two the sampling obtain

); Then, recycling formula (1) is to single order ll channel (low frequency part)

Proceed the second layer two-dimensional wavelet transformation (this moment j=4, k=150, m=200, l=300 n=400), obtains 1 ll channel again $(c_{k,m}^j=c_{\mathrm{150,200}}^4)$ With 3 details subgraphs ( $d_{k,m}^{j,1}=d_{\mathrm{150,200}}^{\mathrm{4,1}},$ $d_{k,m}^{j,2}=d_{\mathrm{150,200}}^{\mathrm{4,2}},$ ); The rest may be inferred, namely obtains

Five wavelet transformations that decompose orders, correspondingly, just obtain gray level image I _{(X * Y)}Multiple dimensioned expression;

Step 3: ignore the feature of each rank details subgraph, only each rank ll channel is carried out single reconstruct, obtain the reconstruct ll channel, as shown in Figure 3;

Along with the increase of decomposing order, the small echo subgraph diminishes gradually.Be the acquisition subgraph consistent with original image size, and keep the frequency component of each subgraph, need carry out single reconstruct.When carrying out single reconstruct, only utilize the wavelet coefficient of single subgraph to carry out signal reconstruction, the wavelet coefficient of other subgraph is set to zero.Since the profile of ll channel reflection froth images, and therefore the variations in detail of details subgraph reflection froth images, when obtaining the foam size feature, can ignore each rank details subgraph, only ll channel is reconstructed.Approaching the reconstruct subgraph with five remembers respectively and makes S ^v(v=1,2 ..., 5), they have represented the outline portion of foam subgraph under the different scale, and its matrix of coefficients can be tried to achieve by reconstruction formula:

$c_{k,m}^{j+1}=\underset{l,n}{\mathrm{\Σ}}{h}_{k-2l}{h}_{m-2n}{c}_{l,n}^j+\underset{l,n}{\mathrm{\Σ}}{h}_{k-2l}{g}_{m-2n}{d}_{l,n}^{j,1}+\underset{l,n}{\mathrm{\Σ}}{g}_{k-2l}{h}_{m-2n}{d}_{l,n}^{j,2}+\underset{l,n}{\mathrm{\Σ}}{g}_{k-2l}{g}_{m-2n}{d}_{l,n}^{j,3}---\left(3\right)$

In second step, according to uncertainty principle and discrete wavelet frequency domain relation, extrapolate the foam diameter variation range of different order subgraphs.

Frequency domain relation between the discrete wavelet different scale signal as shown in Figure 4.Wherein, f _j, f _J-1, f _J-2Represent the approximation signal of different scale, d _J-1, d _J-2Represent the detail signal of different scale.

By uncertainty principle as can be known, the spatial frequency window area of wavelet multi-scale analysis has unchangeability.Therefore, the corresponding different spaces width of the band width of each reconstruct subgraph difference.Can get the spatial frequency relation of five ll channels according to Fig. 4 and uncertainty principle, as shown in Figure 5.

The 3rd step, utilize maximum variance between clusters with each reconstruct subgraph binaryzation, count the foam total area of each bianry image.Try to achieve foam equivalent dimension feature by calculating again.The foam diameter variation range of extrapolating in conjunction with second step calculates equivalent foam number, and then obtains foam equivalent dimension distribution plan at last.

Step 1: calculate the optimal threshold of each reconstruct subgraph according to maximum variance between clusters, it is carried out binaryzation, and count the foam total area of each bianry image;

If S ^vL gray level arranged, and gray-scale value is that the pixel count of i is n _i, then total pixel count is

The probability that each gray-scale value occurs is

Obvious p _i〉=0,

If be that thresholding is divided into 2 zones with image with gray scale t, gray level is 1～L _ThPixel region A, gray level is L _ThThe pixel region B of+1～L-1.The probability that A, B occur is respectively:

$p_A=\underset{i=0}{\overset{L_{\mathrm{th}}}{\mathrm{\Σ}}}{p}_i,$ $p_B=\underset{i=L_{\mathrm{th}}+1}{\overset{L-1}{\mathrm{\Σ}}}{p}_i=1-p_A---\left(4\right)$

The gray average of A and B two classes is respectively:

${\mathrm{\ω}}_A=\frac{\underset{i=0}{\overset{L_{\mathrm{th}}}{\mathrm{\Σ}}}{\mathrm{ip}}_i}{p_A},$ ${\mathrm{\ω}}_B=\frac{\underset{i=L_{\mathrm{th}}+1}{\overset{L-1}{\mathrm{\Σ}}}{\mathrm{ip}}_i}{p_B}---\left(5\right)$

Thereby can obtain the total gray average of image:

${\mathrm{\ω}}_0=p_A{\mathrm{\ω}}_A+p_B{\mathrm{\ω}}_B=\underset{i=L_{\mathrm{th}}=1}{\overset{L-1}{\mathrm{\Σ}}}{\mathrm{ip}}_i---\left(6\right)$

Can obtain the inter-class variance in A, B two zones thus:

σ ²＝p _A(ω _A-ω ₀) ²+p _B(ω _B-ω ₀) ² (7)

For obtaining the optimum segmentation threshold value, as criterion, make σ with the inter-class variance of two classes ²The value maximum

Be the optimal threshold of asking:

$L_{\mathrm{th},v}^{*}=\mathrm{<figure-callout\; id="0"\; label="Arg\; Max"\; filenames="HDA00003394837700022.png,HDA00003394837700023.png"\; state="\{\{state\}\}">Arg</figure-callout>}\underset{}{\mathrm{Max}}\underset{0\&le;L_{\mathrm{th}}\&le;L-1}{}[p_A{({\mathrm{\&omega;}}_A-{\mathrm{\&omega;}}_0)}^2+p_B{({\mathrm{\&omega;}}_B-{\mathrm{\&omega;}}_0)}^2],V=\mathrm{1,2,3,4,5}---\left(8\right)$

Calculate the optimal threshold that respectively approaches the reconstruct subgraph

Basis again

Respectively to S ^vCarry out binaryzation, obtain five bianry images.Add up the white portion area of each bianry image, thereby obtain the foam total area, be designated as A _v

Step 2: adjacent binary image foam total area is subtracted each other, and obtains foam equivalent dimension feature;

The foam total area of adjacent binary image is subtracted each other, obtain foam subgraph equivalent area, be designated as E _qE _qBe the foam equivalent dimension feature of trying to achieve by multiple dimensioned binaryzation, q is the number of equivalent dimension feature, and q+1 is for decomposing order.Because decomposing order is 5, then 4 equivalent dimension features are distinguished corresponding 4 continuous foam diameter variation ranges: 1～2,2～4,4～8,8～16.

E _q＝A _q+1-A _q，q＝1，2，3，4 (9)

Step 3: according to the foam diameter variation range of extrapolating, calculate equivalent foam number, and then obtain foam equivalent dimension distribution plan;

Because foam shape is approximately round, its area can be by π (D _q/ 2) ²Calculate, get D _qBe the mean value of foam diameter variation range, be respectively 1.5,3,6,12, can obtain the equivalent foam number of each order according to following formula.

$N_q=\frac{E_q}{\mathrm{\&pi;}{(D_q/2)}^2}---\left(10\right)$

Finally obtain the equivalent dimension distribution plan of current working froth images.

The 4th step compared foam equivalent dimension distribution plan and the benchmark distribution plan that obtains in real time, determined the on-the-spot bubble condition of copper flotation of current froth images correspondence.

The acquisition methods of benchmark distribution plan is: at first the on-the-spot historical foam video of the copper flotation of gathering is carried out the manual sort, thereby obtain several froth images of three kinds of different operating modes, respectively these three kinds of froth images are handled through step 1 to three then, obtain a plurality of foam equivalent dimension distribution plans, at last a plurality of foam equivalent dimension distribution plans of gained are added up, obtain the benchmark distribution plan, as shown in Figure 6.

As shown in Figure 6, normal foam size dimension distributes more even, mainly concentrates on 2～10; The little foam of aquation foam is in the majority, and Size Distribution mainly concentrates on 1～4; The Size Distribution of viscous foam is close with normal foam, but its vesicle foam many than normal foam, macrofoam lacks than normal foam.The foam equivalent dimension distribution plan and the benchmark distribution plan that obtain are in real time compared, observe the foam equivalent dimension distribution situation of (as adopting manual observation) this moment, thereby just can identify the on-the-spot bubble condition of current copper flotation.

The result shows that feature that the present invention carries had both comprised multi-scale information, and is directly related with the foam mode of appearance again, and the corresponding different equivalent dimensions of different froth images distribute, and can be directly the froth images of different operating modes be made a distinction by distribution plan relatively.This method is simply effective, to instructing the on-the-spot bubble condition identification of copper flotation significant.

Claims (5)

1. a froth images equivalent dimension Feature Extraction method is characterized in that, may further comprise the steps:

Step 1: the foam video that obtains according to copper flotation scene obtains the three-dimensional foam image, the three-dimensional foam image is carried out gray processing, two dimensional gray image to gained carries out wavelet decomposition then, thereby obtain the small echo subgraph on the different scale, the feature of ignoring each rank details subgraph, only each rank ll channel is carried out single reconstruct, obtain the reconstruct ll channel;

Step 2: according to uncertainty principle and discrete wavelet frequency domain relation, extrapolate the foam diameter variation range of different order subgraphs;

Step 3: utilize maximum variance between clusters with each reconstruct ll channel binaryzation, obtain bianry image, count the foam total area of each bianry image, and then try to achieve foam equivalent dimension feature; The foam diameter variation range that last integrating step two is extrapolated calculates equivalent foam number, and then obtains foam equivalent dimension distribution plan;

Step 4: foam equivalent dimension distribution plan and benchmark distribution plan are compared, determine the copper flotation field working conditions of current froth images correspondence.

2. froth images equivalent dimension Feature Extraction method according to claim 1 is characterized in that the described step

Rapid one comprises following substep:

Step 1: original froth images gray processing;

Original three-dimensional RGB froth images K _{(X * Y * 3)}Become the two dimensional gray image I behind the gray processing _{(X * Y)}

Step 2: select the sym4 small echo that the two dimensional gray image is carried out five rank and decompose, decompose order at each, two-dimensional wavelet transformation will produce the details subgraph of a ll channel and level, vertical, three different directions of diagonal line;

At each wavelet transformation formula that decomposes order be:

Formula 1

Decompose the matrix of coefficients that approaches in order at each

With 3 detail coefficients matrixes

Can be obtained by the Mallat algorithm that 2-d wavelet decomposes:

$\left\{\begin{array}{c}{c}_{k,m}^j=\underset{l,n}{\mathrm{\&Sigma;}}{\stackrel{\&OverBar;}{h}}_{2k-l}{\stackrel{\&OverBar;}{h}}_{2m-n}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,1}=\underset{l,n}{\mathrm{\&Sigma;}}{\stackrel{\&OverBar;}{h}}_{2k-l}{\stackrel{\&OverBar;}{g}}_{2m-n}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,2}=\underset{l,n}{\mathrm{\&Sigma;}}{\stackrel{\&OverBar;}{g}}_{2k-l}{\stackrel{\&OverBar;}{h}}_{2m-n}{c}_{l,n}^{j+1}\\ d_{k,m}^{j,3}=\underset{l,n}{\mathrm{\&Sigma;}}{\stackrel{\&OverBar;}{g}}_{2k-l}{\stackrel{\&OverBar;}{g}}_{2m-n}{c}_{l,n}^{j+1}\end{array}\right.$ Formula 2

Formula mesoscale function is: 3 wavelet functions are respectively: ψ ¹(x, y)=φ (x) ψ (y), ψ ²(x, y)=ψ (x) φ (y), ψ ³(x, y)=ψ (x) ψ (y), wherein

With

Two yardstick equations and the little wave equation of representing an orthogonal dimension multiresolution analysis respectively; J carries out five rank wavelet decomposition for decomposing the number of plies in this example, then get j=5,4,3,2,1; K, m ∈ Z is the system of representatives matrix number respectively

Row and column, l, n ∈ Z be the system of representatives matrix number respectively

Row and column; Coefficient sequence h=(h _iBe a low-pass filter, and h={-0.076 is arranged ,-0.030,0.498,0.804,0.298 ,-0.100 ,-0.013,0.032},

Sequential counter-rotating for h

Coefficient sequence g={g _iBe a Hi-pass filter and g _i=(1) ⁱh _1-i,

Sequential counter-rotating for g

At first application of formula 1 is carried out the two-dimensional wavelet transformation on first rank, obtains 1 ll channel and 3 details subgraphs, and its coefficient is calculated by formula 2; Then, utilize 1 pair of single order ll channel of formula (low frequency part)

Proceed the two-dimensional wavelet transformation on second rank, obtain 1 ll channel and 3 details subgraphs again; The rest may be inferred, can obtain Five wavelet transformations that decompose orders; Correspondingly, just obtain gray level image I _{(X * Y)}Multiple dimensioned expression;

Step 3: ignore the feature of each rank details subgraph, only each rank ll channel is carried out single reconstruct, obtain the reconstruct ll channel:

Approaching the reconstruct subgraph with five remembers respectively and makes S ^v, v=1,2 ..., 5, they have represented the outline portion of foam subgraph under the different scale, and its matrix of coefficients is tried to achieve by following reconstruction formula:

$c_{k,m}^{j+1}=\underset{l,n}{\mathrm{\&Sigma;}}{h}_{k-2l}{h}_{m-2n}{c}_{l,n}^j+\underset{l,n}{\mathrm{\&Sigma;}}{h}_{k-2l}{g}_{m-2n}{d}_{l,n}^{j,1}+\underset{l,n}{\mathrm{\&Sigma;}}{g}_{k-2l}{h}_{m-2n}{d}_{l,n}^{j,2}+\underset{l,n}{\mathrm{\&Sigma;}}{g}_{k-2l}{g}_{m-2n}{d}_{l,n}^{j,3}$ Formula 3.

3. froth images equivalent dimension Feature Extraction method according to claim 1 is characterized in that, in the described step 2,

Frequency domain between the discrete wavelet different scale signal closes: approximation signal f _j(t) band width only is f _J+1(t) half of band width; f _J+1(t) second half of band width is by detail signal d _j(t) performance;

Table 1

Ll channel Frequency range Spatial dimension A1 0～0.5π 0～1 A2 0～0.25π 0～2

A3 0～0.125π 0～4 A4 0～0.0625π 0～8 A5 0～0.03125π 0～16

The spatial frequency that obtains five ll channels according to the frequency domain between discrete wavelet different scale signal relation and uncertainty principle concerns as shown in table 1.

4. froth images equivalent dimension Feature Extraction method according to claim 1 is characterized in that described step 3 comprises following substep:

Step 1: calculate the optimal threshold of each reconstruct subgraph according to maximum variance between clusters, each reconstruct subgraph is carried out binaryzation, and count the foam total area of each bianry image:

If S ^vL gray level arranged, and gray-scale value is that the pixel count of i is n _i, then total pixel count is

The probability that each gray-scale value occurs is

If with gray scale L _ThFor thresholding is divided into 2 zones with image, gray level is 1～L _ThPixel region A, gray level is L _ThThe probability that pixel region B:A, the B of+1～L-1 occurs is respectively:

$p_A=\underset{i=0}{\overset{L_{\mathrm{th}}}{\mathrm{\&Sigma;}}}{p}_i,$ $p_B=\underset{i=L_{\mathrm{th}}+1}{\overset{L-1}{\mathrm{\&Sigma;}}}{p}_i=1-p_A;$

The gray average of A and B two classes is respectively:

${\mathrm{\&omega;}}_A=\frac{\underset{i=0}{\overset{L_{\mathrm{th}}}{\mathrm{\&Sigma;}}}{\mathrm{ip}}_i}{p_A},$ ${\mathrm{\&omega;}}_B=\frac{\underset{i=L_{\mathrm{th}}+1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{ip}}_i}{p_B};$

Thereby can obtain the total gray average of image:

${\mathrm{\&omega;}}_0=p_A{\mathrm{\&omega;}}_A+p_B{\mathrm{\&omega;}}_B=\underset{i=L_{\mathrm{th}}=1}{\overset{L-1}{\mathrm{\&Sigma;}}}{\mathrm{ip}}_i;$

Can obtain the inter-class variance in A, B two zones thus:

σ ²＝p _A(ω _A-ω ₀) ²+p _B(ω _B-ω ₀) ²；

For obtaining the optimum segmentation threshold value, as criterion, make σ with the inter-class variance of two classes ²The value maximum

Be the optimal threshold of asking:

$L_{\mathrm{th},v}^{*}=\mathrm{Arg}\underset{0\&le;L_{\mathrm{th}}\&le;L-1}{\mathrm{Max}}[p_A{({\mathrm{\&omega;}}_A-{\mathrm{\&omega;}}_0)}^2+p_B{({\mathrm{\&omega;}}_B-{\mathrm{\&omega;}}_0)}^2],V=\mathrm{1,2,3,4,5},$

Calculate the optimal threshold that respectively approaches the reconstruct subgraph Basis again Respectively to S ^vCarry out binaryzation, obtain five bianry images, add up the white portion area of each bianry image, namely obtain the foam total area, be designated as A _v

Step 2: adjacent binary image foam total area is subtracted each other, and obtains foam equivalent dimension feature;

The foam total area of adjacent binary image is subtracted each other, obtain foam subgraph equivalent area, be designated as E _qHave,

E _q＝A _q+1-A _q，q＝1，2，3，4；

E _qBe the foam equivalent dimension feature of trying to achieve by multiple dimensioned binaryzation, subscript q is the number of equivalent dimension feature, and q+1 is for decomposing order; Because decomposing order is 5, then 4 equivalent dimension features are distinguished corresponding 4 continuous foam diameter variation ranges: 1～2,2～4,4～8,8～16; [this scope is that the space-frequency relation between the analysis wavelet subgraph directly obtains, rather than is obtained by area.The diameter here is equivalent diameter, does not therefore give unit.】

Step 3: according to the foam diameter variation range of extrapolating, calculate equivalent foam number, and then obtain foam equivalent dimension distribution plan;

With D _qBe the mean value of foam diameter variation range, the D of 4 foam diameter variation range correspondences _qBe respectively 1.5,3,6,12, obtain the equivalent foam number of each order according to following formula:

Finally obtain the equivalent dimension distribution plan of current working froth images.

5. froth images equivalent dimension Feature Extraction method according to claim 1, it is characterized in that, in the described step 4, the acquisition methods of benchmark distribution plan is: the image by several known operating modes obtains a plurality of foam equivalent dimension distribution plans through step 1 to three earlier, a plurality of foam equivalent dimension distribution plans to gained are added up, thereby obtain the benchmark distribution plan; Described statistics refers to count the foam frequency of each the froth images equivalent diameter under different operating modes, and the benchmark distribution plan is that off-line obtains.

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