CN106097430A - A kind of laser stripe center line extraction method of many gaussian signals matching - Google Patents

Abstract

The present invention is to provide the laser stripe center line extraction method of a kind of many gaussian signals matching.The inventive method has different expectation and the gaussian signal of method by using one group, get up with different positions and weighed combination, the farthest distribution of matching laser line image a line pixel value, when finding optimal matching combination, when combining according to each gaussian signal, location can make the optimal estimation to laser lines center.The inventive method can effectively solve, in the case of the pixel value of laser line image is distributed and cannot meet symmetry and homogeneity, to estimate the center of laser lines exactly, improve the precision of 3D scan rebuilding.

Description

A kind of laser stripe center line extraction method of many gaussian signals matching

Technical field

The present invention relates to the processing method of a kind of low cost 3D scanning system based on laser lines, be specifically related to one Plant laser lines center extraction method based on gaussian signal matching.

Background technology

Three-dimension object recognition technology is at numerous areas such as robot workpiece grabbing, self-navigations, automatically detection, medical analysis Have a wide range of applications.And 3D scanning system is as topmost data acquisition means, its acquisition precision will directly affect identification Success or not.

It is currently based on the contactless 3D scanning system precision height of structure light, applied range, but the cost of its costliness limits Having made the universal of it, therefore measuring system with the low cost of laser in place structure light has the most wide market and research sky Between.

In a 3D scanning system based on laser, owing to there is camera collection precision, laser stripe has necessarily Width and testee surface irregularity cause the problems such as reflective scattering, extracting laser stripe center the most exactly will be straight Connect the acquisition precision of decision systems.

At present conventional lines center extraction algorithm has: extremum method, threshold method, geometrical center method, image thinning method, based on The method of least square of Gauss distribution, Hessian matrix method etc..

Summary of the invention

It is an object of the invention to provide a kind of centrage that can accurately extract laser stripe image, make based on laser 3D scanning system there is the laser stripe center line extraction method of many gaussian signals matching of higher acquisition precision.

The object of the present invention is achieved like this:

Step one: obtained the image I comprising laser lines by image capture device, the resolution of image I is Y_max× X_max；

Step 2: set N (the N ∈ [1, X of image I_max]) row pixel value constitute sequence be initial data M_N(j),(j ∈[1,Y_max]), obtain input signal m by a cube interpolation algorithm_N(t), wherein t=nT_s, T_sIt is spaced for interpolation, N ∈ [1, X_max], j ∈ [1, Y_max]；

Step 3: for the data after the laser lines pixel value normalization of the Nth row of image I, a scope is set and exists Threshold value between 0.2 to 0.5, when pixel value data are more than described threshold value, is labeled as 1 by this pixel, less than described threshold value Time, then it is labeled as 0；Calculate the average of row sequence number belonging to all pixels being labeled as 1, using this average as initial center point u₀, calculate the difference of the pixel point range sequence number maxima and minima being labeled as 1, using this difference as initial width of fringe simultaneously w₀；

Step 4: build one group of M and there is different expectation and the substrate gaussian signal set G for matching of variance, collection The length of all substrate gaussian signals in conjunction and input signal m_NT () is identical, and set z_i=2 σ_i ², σ_iHigh for i-stage substrate The standard deviation of this signal, and by z_iThe dilatability of named i-stage substrate gaussian signal, order expectation u_i=u₀+s_i, and by u_i The symmetrical centre of named i-stage substrate gaussian signal, wherein, u₀For initial center point, s_iFor side-play amount；

Initial center point u that will obtain in step 3₀Symmetrical centre u as first order substrate gaussian signal₀, i.e. u₁= u₀, initial width of fringe w₀For determining the dilatability of first order substrate gaussian signalWherein q is constant, Thus obtain one group of M the substrate gaussian signal set G with different dilatability.

$\left\{\begin{array}{c}{z}_{i+1}=2^{-1}{z}_i,(i\∈\[1,m\])\\ u_i=u_0+s_i,(i\∈\[2,m\])\\ g_{zi,ui}\left(x\right)=\frac{1}{\sqrt{{\mathrm{\πz}}_i}}{e}^{-\frac{{(x-u_i)}^2}{z_i}}\\ G=\{g_{z1,u0}\left(t\right),g_{z2,u2}\left(t\right),g_{z3,u3}\left(t\right)...g_{zm,um}\left(t\right)\}\end{array}\right.$

In above formula, g_zi,uiX () is i-stage substrate gaussian signal, and its dilatability is z_i, symmetrical centre is u_i。

Step 5: by calculating maximum cross-correlation coefficient, tries to achieve the similarity of each substrate gaussian signal and input signal:

$\left\{\begin{array}{c}{r}_{zi}\left({\mathrm{\&tau;}}_i\right)=\max (\mathrm{cov}<m_N(t),g_{zi,ui}(t)>)=\max \left(\underset{1}{\overset{Y_{\max }}{\mathrm{\&Sigma;}}}{m}_N\right(\mathrm{\&tau;}\left)g_{zi,ui}\right(t+\mathrm{\&tau;}\left)\right)\\ i\&Element;\&lsqb;1,M\&rsqb;\end{array}\right.$

Wherein, r_zi(τ_i) it is the maximum cross-correlation value of input signal and i-stage substrate gaussian signal, τ_iIt is that two signals are mutual When pass value takes maximum, the relative alternate position spike of two signals；

Step 6: define artificial signal g_fX () is m the substrate Gaussian function with different dilatability and symmetrical centre, According to the signal after one group of fixing matching weights superposition, and setting initial m=2, matching weights are one group of fixing constant, Choosing of it should follow dilatability z_iThe biggest, matching weights this principle the biggest；

Step 7: according to following formula, calculate by substrate gaussian signal by one group of fixing matching weights be formed by stacking artificial Signal g_f(t),

$g_f\left(x\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_i{g}_{zi,ui}\left(x\right)$

Wherein φ_i(i ∈ [1, M]) is matching weights, is one group of fixed constant,

Afterbody that is i-th (i=m) the level substrate gaussian signal of this artificial signal of change composition is inclined within the specific limits Shifting amount s_i, recalculate artificial signal, be further continued for cross correlation measure r calculating artificial signal with input signal_f(τ_m):

r_f(τ_m)=max (cov < m_N(t),g_f(t) >)=max (∑ m_N(τ)g_f(t+τ))

Find and make cross correlation measure r_f(τ_m) maximum time side-play amount s_i, now adding this side-play amount is s_iSubstrate Gauss letter Number time, artificial signal is the most similar to input signal, τ_mPoor for artificial signal during cross correlation measure maximum and position input signal；

Step 8: make m=m+1, repeats step 7, until m=M, has i.e. added afterbody substrate Gaussian function；

Step 9: when the symmetrical centre side-play amount of each substrate gaussian signal is respectively s₁,s₂,s₃,…s_mTime, by these The artificial signal that substrate gaussian signal combines and input signal have the highest similarity, make r_f(τ) τ taking maximum is Integral position is poor, the calculating optimal estimation p to central point:

$\left\{\begin{array}{c}p=\mathrm{\&tau;}+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{u}_i\\ {\mathrm{\&lambda;}}_i=\frac{{\mathrm{\&eta;}}_i{r}_i\left({\mathrm{\&tau;}}_i\right)}{{\mathrm{\&Sigma;\&eta;}}_i{r}_i\left({\mathrm{\&tau;}}_i\right)}\end{array}\right.$

Wherein λ_i(i ∈ [1, M]) is the Combining weights of the symmetrical centre of i-stage substrate gaussian signal, and this Combining weights is One group of fixing constant, choosing of it should follow dilatability z_iThe biggest, Combining weights this principle the biggest, u_iFor each substrate Gauss The symmetrical centre of signal, r_ziThe substrate gaussian signal of the variant dilatability obtained for step 5 and input signal maximum mutually Pass is worth, r_ziThe highest, then comprising more dilatability in explanation input signal is z_iThe composition of substrate gaussian signal, η_iFor revising Proportionality constant, for reacting the significance level of the symmetrical centre of the Gaussian function of different dilatability；

Step 10: repetition step 2 is to step 9, until having calculated all X_maxThe central point of row, obtains laser lines The optimal estimation of picture centre line.

The method of the present invention mainly uses one group of gaussian signal approximating method to former laser line image cross section.Pass through Using the Gaussian function with different average and variance is basis function, by certain rule combination superposition, comes farthest The distribution of the laser stripe image cross section that matching collects.When finding optimal fitting result, according to each gaussian signal Symmetrical centre, extrapolates the optimal estimation to laser stripe center by certain rule.

Present invention advantage compared with prior art is: existing method major part assumes the cross section of laser line image The distribution of pixel there is the character such as symmetry and homogeneity, and during actual acquisition, due to incident angle, object being measured The problems such as refraction scattering that surface irregularity causes, image capture device noise, the pixel of the cross section of laser line image Distribution is difficult to meet general symmetry and homogeneity.The distribution that the method for the present invention does not relies on the pixel of cross section is the fullest Foot the two characteristic, is distributed by the pixel value using multiple gaussian signals of difference expectation and variance to carry out matching cross section, looks for To when making cross correlation maximum, the relative position of each different gaussian signals, so that it is determined that the center of laser lines.Carry greatly The computational accuracy of high centrage.

Accompanying drawing explanation

Fig. 1 is the inventive method flow chart.

Fig. 2 is the object being measured for test.

Fig. 3 is laser stripe image instance 1.

Fig. 4 is that certain a line pixel value of example 1 is distributed and to the input signal scattergram after its interpolation, gives simultaneously Use the calculated initial center point of threshold method.

Fig. 5 be to this row pixel value of example 1 use two-stage gaussian signal matching time, the side-play amount of second level gaussian signal with The graph of a relation of maximum cross-correlation coefficient.

Fig. 6 is the optimal result schematic diagram that this row pixel value of example 1 uses two-stage gaussian signal matching.

When Fig. 7 is that this row pixel value of example 1 is added third level gaussian signal matching, the side-play amount of third level gaussian signal Graph of a relation with maximum cross-correlation coefficient.

Fig. 8 is the optimal result schematic diagram that this row pixel value of example 1 uses three grades of gaussian signal matchings.

Fig. 9 is the central line pick-up result figure to example 1.

Figure 10 is the difference of centrage result and the ideal situation using the inventive method to extract.

Figure 11 is to use the geometrical center method central line pick-up result figure to example 1.

Figure 12 is the difference of centrage result and the ideal situation using geometrical center method to extract.

Figure 13 is to use the inventive method to extract centrage testee carries out the top view of 3D reconstruction.

Figure 14 is to use geometrical center method to extract centrage testee carries out the top view of 3D reconstruction.

Detailed description of the invention

The present invention is described in detail in citing below in conjunction with the accompanying drawings.

The inventive method does not relies on the distribution of laser line image pixel value and has the requirement of higher-symmetry, by using Multiple gaussian signals of different expectations and variance carry out the pixel value distribution of matching laser lines single file, find and make cross correlation maximum Time, the relative position of each different gaussian signals, so that it is determined that the center of these row laser lines.Calculate laser line image institute Having capable laser rays sliver transvers section central point, can try to achieve the centrage of laser line image, detailed process comprises the following steps:

(1) use 3D based on laser to measure systematic survey testee as shown in Figure 2, obtain laser line image sequence In a certain image instance 1, as shown in Figure 3.

(2) in treating excess syndrome example 1, nth row of pixels value sequence, as initial data, for the ease of calculating, is first normalized place Reason, as shown in circular hollow point in Fig. 4.Owing to initial data is the most sparse, in order to improve, step (7) calculates cross correlation measure Accuracy, carries out interpolation operation to initial data, obtains the most intensive input signal, shown in as shown in lines in Fig. 4.

(3) use threshold method i.e. to the initial data after normalization, scope threshold value between 0.2 to 0.5 be set, The pixel value that will be greater than this threshold value is labeled as 1, is labeled as 0 less than the pixel value of this threshold value, calculates pixel value and is labeled as the pixel of 1 The row coordinate average at some place, i.e. initial center point u₀, as shown in Fig. 4 stellate point, and maximum column coordinate is sat with minimum row Target difference, i.e. width w₀。

(4) central point obtained according to step (3) and width, determine one group of M substrate gaussian signal for matching altogether, It is shown below.

$\left\{\begin{array}{c}{z}_1=q\&times;w_0\\ z_{i+1}=2{\mathrm{\&sigma;}}_{i+1}^2=2^{-1}{z}_i,(i\&Element;\&lsqb;1,M-1\&rsqb;)\\ u_i=u_0+s_i,(i\&Element;\&lsqb;1,M\&rsqb;)\\ g_{zi,ui}\left(x\right)=\frac{1}{\sqrt{{\mathrm{\&pi;z}}_i}}{e}^{-\frac{{(x-u_i)}^2}{z_i}}\\ g_{z1,u0}\left(t\right),g_{z2,u2}\left(t\right),g_{z3,u3}\left(t\right)...g_{zm,um}\left(t\right)\end{array}\right.---\left(1\right)$

u_iFor the symmetrical centre of i-stage gaussian signal, s_iFor the symmetrical centre of i-stage gaussian signal relative to initial center point Side-play amount.σ_iFor the standard deviation of i-stage gaussian signal, definitionFor the dilatability of i-stage gaussian signal, and the first order The dilatability of gaussian signal is determined by the width in step (3), and q is constant.

(5) the maximum cross-correlation coefficient of this group substrate gaussian signal and input signal is calculated:

$\left\{\begin{array}{c}{r}_{zi}\left({\mathrm{\&tau;}}_i\right)=\max (\mathrm{cov}<m_N(t),g_{zi,ui}(t)>)=\max \left(\underset{1}{\overset{Y_{MAX}}{\mathrm{\&Sigma;}}}{m}_N\right(\mathrm{\&tau;}\left)g_{zi,ui}\right(t+\mathrm{\&tau;}\left)\right)\\ i\&Element;\&lsqb;1,M\&rsqb;\end{array}\right.---\left(2\right)$

(6) definition m have the Gaussian function of different dilatability and symmetrical centre according to one group fix matching weights Signal after superposition is artificial signal g_fX (), matching weights are one group of fixing constant, and it is chosen and should follow dilatability z_iIt is the biggest, Matching weights this principle the biggest.And set initial m=2, first order gaussian signal side-play amount s₁=0.

(7) according to following formula, the artificial signal being formed by stacking by substrate gaussian signal is calculated by one group of fixing matching weights g_f(t)。

$g_f\left(x\right)=\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&phi;}}_i{g}_{zi,ui}\left(x\right)---\left(3\right)$

Wherein φ_i(i ∈ [1, M]) is matching weights, is one group of fixed constant.

With 0.1 pixel wide as step-length in certain limit (being 8 pixel unit width in this example), composition is altered in steps Side-play amount s of the afterbody of this artificial signal that is i-th (i=m) level gaussian signal_i, calculate after often changing a side-play amount Artificial signal and the cross correlation measure of input signal:

r_f(τ_m)=max (cov < m_N(t),g_f(t) >)=max (∑ m_N(τ)g_f(t+τ)) (4)

Find and make cross correlation measure r_f(τ_m) maximum time side-play amount s_i, now adding this side-play amount is s_iGaussian signal time, Artificial signal is the most similar to input signal, and now τ_mPoor for artificial signal during cross correlation measure maximum and position input signal.

(8) make m=m+1, repeat step 7.Until m=M, i.e. add afterbody substrate Gaussian function.

When example 1 carrying out centrage and calculating, three grades of (i.e. M=3) different gaussian signals are used to carry out matching example 1 the The pixel value distribution of N row, when Fig. 5 is m=2, changes side-play amount s of second level gaussian signal symmetrical centre₂The artificial letter obtained Number with the relation of the cross-correlation coefficient of input signal, this example is worked as s₂When=-1.8, artificial signal and input signal have higher Similarity.Fig. 6 is the optimal fitting result using first order gaussian signal to superpose with second level gaussian signal, and thick line is artificial Signal, black thin is the input signal treating matching.When Fig. 7 is m=M=3, change the inclined of third level gaussian signal symmetrical centre Shifting amount s₃The artificial signal obtained and the relation of the cross-correlation coefficient of input signal, work as s in this example₃When=1.1, artificial signal with Input signal has higher similarity.Fig. 8 is the optimal fitting result making three grades of gaussian signal superpositions, and thick line is artificial letter Number, black thin is the input signal treating matching.

From figure 8, it is seen that artificial signal and input signal have higher similarity.

(9) optimal estimation to central point is calculated:

Believe to input signal each Gauss time the most similar according to the artificial signal that makes that step (7) obtains to step (8) Number symmetrical centre side-play amount s_i, calculate symmetrical centre u of each gaussian signal_i=u₀+s_i.Calculate artificial signal and input again The maximum cross-correlation coefficient r of signal_f(τ) take displacement τ during maximum, calculate the optimum to central point finally according to formula (5) Estimation p:

$\left\{\begin{array}{c}p=\mathrm{\&tau;}+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{u}_i\\ {\mathrm{\&lambda;}}_i=\frac{{\mathrm{\&eta;}}_i{r}_i\left({\mathrm{\&tau;}}_i\right)}{{\mathrm{\&Sigma;\&eta;}}_i{r}_i\left({\mathrm{\&tau;}}_i\right)}\end{array}\right.---\left(5\right)$

Wherein λ_iFor the weights of variant center of energy, this Combining weights is one group of fixing constant, and choosing of it should be abided by Follow dilatability z_iThe biggest, Combining weights this principle the biggest, r_iGaussian function for variant dilatability is similar to input signal Degree, r_iThe highest, then comprising more dilatability in explanation input signal is z_iThe composition of gaussian signal, η_iNormal for revising ratio Number, for reacting the significance level of the center of energy of the Gaussian function of different dilatability.

In this example to the central point result of example 1 Nth row laser line image as shown in black * shape point in Fig. 8.

(10) repetition step (2) is to step (9), has calculated all X_maxThe central point of row, i.e. can obtain laser stripe figure As the calculating of the centrage of example 1, result is as shown in Figure 9.Give the difference with ideal situation, as shown in Figure 10 simultaneously.

In order to contrast the effectiveness of the inventive method further, we use traditional geometrical center method to carry out example 1 Centrage calculates.Laser lines centrage result is as shown in figure 11.With ideal situation difference as shown in figure 12.Finally, we are right All laser line image carry out central line pick-up, according to the parameter demarcated, testee as shown in Figure 2 are carried out three Dimension is rebuild, and Figure 13 is that the inventive method calculates centrage the result rebuild.Figure 14 calculates centrage for using geometrical center method And the result rebuild, in terms of reconstructed results, reconstructed results details based on the inventive method is clear, performance is abundant, has higher Reduction degree.

Claims (1)

1. a laser stripe center line extraction method for the matching of gaussian signal more than, is characterized in that:

Step one: obtained the image I comprising laser lines by image capture device, the resolution of image I is Y_max×X_max；

Step 2: set N (the N ∈ [1, X of image I_max]) row pixel value constitute sequence be initial data M_N(j),(j∈[1, Y_max]), obtain input signal m by a cube interpolation algorithm_N(t), wherein t=nT_s, T_sIt is spaced for interpolation, N ∈ [1, X_max],j∈ [1, Y_max]；

Step 3: for the data after the laser lines pixel value normalization of the Nth row of image I, a scope is set and arrives 0.2 Threshold value between 0.5, when pixel value data are more than described threshold value, is labeled as 1 by this pixel, during less than described threshold value, then It is labeled as 0；Calculate the average of row sequence number belonging to all pixels being labeled as 1, using this average as initial center point u₀, simultaneously Calculate the difference of pixel point range sequence number maxima and minima being labeled as 1, using this difference as initial width of fringe w₀；

Step 4: build one group of M and there is different expectation and the substrate gaussian signal set G for matching of variance, in set Length and input signal m of all substrate gaussian signals_NT () is identical, and set z_i=2 σ_i ², σ_iBelieve for i-stage substrate Gauss Number standard deviation, and by z_iThe dilatability of named i-stage substrate gaussian signal, order expectation u_i=u₀+s_i, and by u_iName For the symmetrical centre of i-stage substrate gaussian signal, wherein, u₀For initial center point, s_iFor side-play amount；

Initial center point u that will obtain in step 3₀Symmetrical centre u as first order substrate gaussian signal₀, i.e. u₁=u₀, just Beginning width of fringe w₀For determining the dilatability of first order substrate gaussian signalWherein q is constant, thus To one group of M substrate gaussian signal set G with different dilatability,

$\left\{\begin{array}{c}{z}_{i+1}=2^{-1}{z}_i,\left(i\&Element;\&lsqb;1,m\&rsqb;\right)\\ u_i=u_0+s_i,\left(i\&Element;\&lsqb;2,m\&rsqb;\right)\\ g_{zi,ui}\left(x\right)=\frac{1}{\sqrt{{\mathrm{\&pi;z}}_i}}{e}^{-\frac{{\left(x-u_i\right)}^2}{z_i}}\\ G=\left\{g_{z1,u0}\left(t\right),g_{z2,u2}\left(t\right),g_{z3,u3}\left(t\right)...g_{zm,um}\left(t\right)\right\}\end{array}\right.$

In above formula, g_zi,uiX () is i-stage substrate gaussian signal, and its dilatability is z_i, symmetrical centre is u_i；

Step 5: by calculating maximum cross-correlation coefficient, tries to achieve the similarity of each substrate gaussian signal and input signal:

$\left\{\begin{array}{c}{r}_{zi}\left({\mathrm{\&tau;}}_i\right)=\max \left(\mathrm{cov}<m_N\left(t\right),g_{zi,ui}\left(t\right)>\right)=\max \left(\underset{1}{\overset{Y_{\max }}{\mathrm{\&Sigma;}}}{m}_N\left(\mathrm{\&tau;}\right)g_{zi,ui}\left(t+\mathrm{\&tau;}\right)\right)\\ i\&Element;\&lsqb;1,M\&rsqb;\end{array}\right.$

Wherein, r_zi(τ_i) it is the maximum cross-correlation value of input signal and i-stage substrate gaussian signal, τ_iIt is two signal cross correlation values When taking maximum, the relative alternate position spike of two signals；

Step 6: define artificial signal g_fX () is m the substrate Gaussian function with different dilatability and symmetrical centre, according to one Signal after the matching weights superposition that group is fixing, and set initial m=2, matching weights are one group of fixing constant, its choosing Take and should follow dilatability z_iThe biggest, matching weights this principle the biggest；

Step 7: according to following formula, calculate the artificial signal g being formed by stacking by substrate gaussian signal by one group of fixing matching weights_f (t),

$g_f\left(x\right)=\underset{i=1}{\overset{m}{\&Sigma;}}{\mathrm{\&phi;}}_i{g}_{zi,ui}\left(x\right)$

Wherein φ_i(i ∈ [1, M]) is matching weights, is one group of fixed constant,

Change side-play amount s of afterbody that is i-th (i=m) the level substrate gaussian signal forming this artificial signal_i, recalculate people Make signal, be further continued for cross correlation measure r calculating artificial signal with input signal_f(τ_m):

r_f(τ_m)=max (cov < m_N(t), g_f(t) >)=max (∑ m_N(τ)g_f(t+τ))

Find and make cross correlation measure r_f(τ_m) maximum time side-play amount s_i, now adding this side-play amount is s_iSubstrate gaussian signal time, Artificial signal is the most similar to input signal, τ_mPoor for artificial signal during cross correlation measure maximum and position input signal；

Step 8: make m=m+1, repeats step 7, until m=M, has i.e. added afterbody substrate Gaussian function；

Step 9: when the symmetrical centre side-play amount of each substrate gaussian signal is respectively s₁, s₂, s₃... s_mTime, high by these substrates The artificial signal that this signal combines and input signal have the highest similarity, make r_f(τ) τ taking maximum is overall position Put difference, the calculating optimal estimation p to central point:

$\left\{\begin{array}{c}p=\mathrm{\&tau;}+\underset{i=1}{\overset{m}{\mathrm{\&Sigma;}}}{\mathrm{\&lambda;}}_i{\mathrm{\&mu;}}_i\\ {\mathrm{\&lambda;}}_i=\frac{{\mathrm{\&eta;}}_i{r}_i\left({\mathrm{\&tau;}}_i\right)}{{\mathrm{\&Sigma;\&eta;}}_i{r}_i\left({\mathrm{\&tau;}}_i\right)}\end{array}\right.$

Wherein λ_i(i ∈ [1, M]) is the Combining weights of the symmetrical centre of i-stage substrate gaussian signal, and this Combining weights is one group and consolidates Fixed constant, choosing of it should follow dilatability z_iThe biggest, Combining weights this principle the biggest, u_iFor each substrate gaussian signal Symmetrical centre, r_ziThe substrate gaussian signal of the variant dilatability obtained for step 5 and the maximum cross-correlation value of input signal, r_ziThe highest, then comprising more dilatability in explanation input signal is z_iThe composition of substrate gaussian signal, η_iFor revising ratio Constant, for reacting the significance level of the symmetrical centre of the Gaussian function of different dilatability；

Step 10: repetition step 2 is to step 9, until having calculated all X_maxThe central point of row, obtains laser line image The optimal estimation of centrage.