CN107133565A - Laser incising molded line feature extracting method based on line laser - Google Patents

Laser incising molded line feature extracting method based on line laser Download PDF

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CN107133565A
CN107133565A CN201710203364.3A CN201710203364A CN107133565A CN 107133565 A CN107133565 A CN 107133565A CN 201710203364 A CN201710203364 A CN 201710203364A CN 107133565 A CN107133565 A CN 107133565A
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mrow
msub
munderover
mtd
mtr
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CN107133565B (en
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刘巍
张致远
张洋
赵海洋
叶帆
兰志广
马建伟
贾振元
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Dalian University of Technology
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    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02Preprocessing
    • G06F2218/04Denoising
    • BPERFORMING OPERATIONS; TRANSPORTING
    • B23MACHINE TOOLS; METAL-WORKING NOT OTHERWISE PROVIDED FOR
    • B23KSOLDERING OR UNSOLDERING; WELDING; CLADDING OR PLATING BY SOLDERING OR WELDING; CUTTING BY APPLYING HEAT LOCALLY, e.g. FLAME CUTTING; WORKING BY LASER BEAM
    • B23K26/00Working by laser beam, e.g. welding, cutting or boring
    • B23K26/36Removing material
    • B23K26/361Removing material for deburring or mechanical trimming
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T11/002D [Two Dimensional] image generation
    • G06T11/20Drawing from basic elements, e.g. lines or circles
    • G06T11/203Drawing of straight lines or curves
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T7/00Image analysis
    • G06T7/10Segmentation; Edge detection
    • G06T7/13Edge detection
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06FELECTRIC DIGITAL DATA PROCESSING
    • G06F2218/00Aspects of pattern recognition specially adapted for signal processing
    • G06F2218/02Preprocessing
    • G06F2218/04Denoising
    • G06F2218/06Denoising by applying a scale-space analysis, e.g. using wavelet analysis
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/20Special algorithmic details
    • G06T2207/20024Filtering details
    • G06T2207/20032Median filtering
    • GPHYSICS
    • G06COMPUTING; CALCULATING OR COUNTING
    • G06TIMAGE DATA PROCESSING OR GENERATION, IN GENERAL
    • G06T2207/00Indexing scheme for image analysis or image enhancement
    • G06T2207/30Subject of image; Context of image processing
    • G06T2207/30108Industrial image inspection

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  • Length Measuring Devices By Optical Means (AREA)

Abstract

Laser incising molded line feature extracting method of the invention based on line laser belongs to laser measuring technique field, is related to a kind of laser incising molded line feature extracting method based on line laser.This method is detected for the line laser of large aerospace wallboard class part milling area laser incising type Working position, is carried out data prediction to the primary signal of acquisition based on medium filtering and wavelet threshold denoising, is obtained smooth steady signal.The line laser profile-followed curve of position workpiece and quarter type groove curve precise shapes are reduced using adaptive curve matching;Pass through the profile-followed curve of obtained workpiece and quarter type groove curvilinear equation is determined on groove along edge feature point, groove accurate feature points are obtained by the way of centering is averaging.This method has very high robustness, and the characteristic point position for extracting quarter molded line is accurate, and the quarter molded line contour curve finally fitted also meets the requirement contrasted with digital-to-analogue, to instructing work pieces process and assembling to have great significance.

Description

Laser incising molded line feature extracting method based on line laser
Technical field
The invention belongs to laser measuring technique field, it is related to a kind of laser incising molded line feature extraction side based on line laser Method.
Background technology
, it is necessary to which the chemical milling area progress laser incising type to large aerospace wallboard type component adds in aircraft manufacturing process Work, then reaches defined technology and required precision, meets its high-quality demand being linked and packed.Pass through laser simultaneously Sensor, based on line laser, extracts the characteristic point of laser incising molded line, the reduction line laser profile-followed curve of position workpiece and quarter type groove Curve precise shapes;Pass through the profile-followed curve of obtained workpiece and quarter type groove curvilinear equation is determined on groove along boundary characteristic Point, obtains groove accurate feature points by the way of centering is averaging, and us can be helped accurately to measure laser incising type machining position Put and whether meet digital-to-analogue requirement, instruct work pieces process and assembling.
Zhang Guoliang, respects refined, and the Patent No. CN103777192A's that Xu Jun etc. is delivered is " a kind of based on the straight of laser sensor Line feature extraction method " proposes a kind of extraction of straight line method based on laser sensor.In segmentation and merging method On the basis of, raising method efficiency is detected by adaptive neighbouring point set, line segment segmentation is carried out using fuzzy partition and merging method Ameliorative way is finally fitted in environment under each straightway polar coordinate system to the sensitivity of parameter using least square method Parameter.Method result of implementation shows that when the point that straightway is included is more as a result very accurate, most straight line errors are all very Small, polar diameter error is both less than 1mm, and angular error is less than 0.01rad, and fitting effect is preferable.But it is limited to carrying for linear feature Take, it is impossible to which a pair laser incising molded line with curve and straight line carries out the higher feature extraction of versatility.
The content of the invention
The invention solves the problems that technical barrier be for the part chemical milling region laser incising type such as the component of large aerospace zero The feature extraction reduction of line position, has invented the laser incising molded line feature extracting method based on line laser.To passing through laser sensing The primary signal that device is obtained is carried out after noise suppression preprocessing, and the shape for carrying out quarter type groove curve confirms and Boundary characteristic extraction, makes Obtaining can be in part production process, and whether accurate measurement laser incising type Working position meets digital-to-analogue requirement, and work is instructed to realize Part processes the purpose with assembling, it is possible to automatic that classification is identified to carving molded line type, and curve is entered with straight line situation respectively Row processing, with very high robustness, the characteristic point position for extracting quarter molded line is accurate, can meet what is contrasted with digital-to-analogue It is required that, to instructing work pieces process with assembling with great significance.
The technical solution adopted by the present invention is a kind of laser incising molded line feature extracting method based on line laser, its feature It is that this method is detected for the line laser of large aerospace wallboard class part milling area laser incising type Working position, based on intermediate value filter Ripple and wavelet threshold denoising carry out data prediction to the primary signal of acquisition, obtain smooth steady signal;Using adaptive song The line fitting reduction line laser profile-followed curve of position workpiece and quarter type groove curve precise shapes;Pass through obtained workpiece profile-followed Curve and quarter type groove curvilinear equation are determined on groove along edge feature point, and groove essence is obtained by the way of centering is averaging True characteristic point.Method is comprised the following steps that:
The first step is based on medium filtering and wavelet threshold denoising carries out Signal Pretreatment
Due to the original two dimensional data that laser sensor is gathered, comprising influence of noise, abscissa is represented with x respectively, with z tables Show ordinate;For the robustness and stability that improve the identification of subsequent characteristics position with extract, discrete signal is carried out first and is located in advance Reason, including medium filtering and Wavelet Transform Threshold denoising, to obtain the data-signal of smooth steady;
1) medium filtering
Assuming that original noisy data-signal is x (k), k=1,2 ..., n, wherein, n is the data length of collection, and x (k) is Corresponding original data signal value z under k length;When carrying out median filter process to it, the L that a length is odd number is defined first Long sliding window, L=2N+1, N ∈ Z, Z are an integer, and 2N+1 represents an odd number;Therefore, if at a time in window Sample of signal value be { x (i-N) ..., x (i), x (i+N) }, wherein x (i) be the window in center signal sample value;It is right L signal value in the window is sorted from small to large, then takes its intermediate value as filtering output value, replace the x (i) of original signal Sample value, its mathematical expression is as follows:
Y (i)=med x (i-N) ..., x (i) ..., x (i+N) } (1)
Wherein, med { } represents to calculate the intermediate value in braces in data sequence, and y (i) represents the intermediate value in x (i) window;
2) wavelet threshold denoising
The noise in original data signal is suppressed by medium filtering, to the spike noise in initial data Suppressed with isolated noise point;In order to obtain the data and curves of more smooth steady, using the method for wavelet threshold denoising Carry out further denoising smooth processing;
For the noiselike signal y (k), k=1,2 ..., n after above-mentioned medium filtering, discrete wavelet transformer is carried out to it Get in return to one group of wavelet conversion coefficient wy(s, j), j=1,2 ..., s, s be wavelet decomposition the number of plies, j be the corresponding frequencies of s; Then to wy(s, j) carries out threshold process, selects suitable threshold value λ, and the wavelet coefficient that will be less than the threshold value is suppressed, and retains Higher than the useful signal of the threshold value, wavelet coefficient is estimatedIt is as follows:
Wherein, λ is the threshold value chosen,For the data-signal wavelet coefficient after threshold denoising;UtilizeCarry out wavelet reconstruction and obtain signal z (k), k=1,2 after denoising ..., n, handled by above formula threshold value, be It is effective to remove noise, useful signal is retained to the full extent;
Second step is based on adaptive curve matching reduction line laser position workpiece shapes
1) the profile-followed curve matching of workpiece surface
Practical work piece surface is usually small curvature surface variations or plane, therefore the profile-followed curve matching of workpiece surface is divided into Two kinds:Fitting a straight line and conic fitting;
First according to the valid data (x after denoisingi,zi), i=1,2 ..., n carries out fitting a straight line, if fitting a straight line is z (x)=a0+a1X, then be fitted mean square error W (a0,a1) be:
xiFor i-th of signal, ziFor the corresponding original signal value of i-th of signal, z (xi) represent xiAfter corresponding denoising Signal value;N is valid data sum;
Fitting a straight line is carried out with mean square error minimalization to obtain:
The mean square error of digital simulation straight lineWherein diFor measurement data each point to fitting a straight line away from From;Certain threshold value R is set, if Re≤R, then it is assumed that workpiece surface is plane, fitting a straight line is reasonable;If otherwise Re>R, then it is assumed that Fitting a straight line is overproof, and workpiece surface is small curvature surface, using conic fitting;If fitting quadratic curve equation be z (x)= a0+a1x+a2x2, then being fitted mean square error is:
By the extremum principle of the function of many variables, W (a0,a1,a2) minimum meet
Arrange and obtain the equation group of conic fitting and be
By solving above equation group, that is, obtain the minimum fitting conic section function z (x) of mean square error;
Above by the profile-followed curve fitting algorithm of adaptive workpiece surface of straight line to conic section, work can be calculated exactly Part surface configuration, conveniently determines the groove location of laser scribing processing;
2) quarter type groove curve matching
Using second step 1) curve that fits, as accurate workpiece surface curve, utilizes the measurement data (x after denoisingi, zi), i=1,2 ..., n calculate matched curve apart from di, it is believed that the corresponding position x of ultimate range0For groove position, Each m measurement data points composition recess region data in its left and right are taken, and carry out groove curve matching, according to measurement data in groove The form of expression at place, is fitted from conic section;So that the iunction for curve for drawing groove is
Z (x)=b0+b1x+b2x2
3) molded line feature locations are carved to extract
The groove curve of acquisition is analyzed, the feature locations for carving molded line are extracted;
3rd step laser incising molded line feature point extraction
Pass through the workpiece surface curve 1), 2) fitted respectively and groove curvilinear equation of second step, simultaneous solution two The intersection point of curve is as follows
If workpiece surface is plane, corresponding coefficient a2Automatic is 0;Solve above equation group and can obtain two sides of groove Boundary's point coordinates is a (x1,z1),b(x2,z2);Therefore groove position feature point coordinates c (xc,zc) be
So as to be extracted the coordinate value of laser incising molded line characteristic point, accurate measurement laser incising type Working position exactly.
Carry out after noise suppression preprocessing, carved the beneficial effects of the invention are as follows the primary signal obtained by laser sensor The shape of type groove curve confirms and Boundary characteristic extraction so that can be in part production process, accurate measurement laser incising type Whether Working position meets digital-to-analogue requirement, and work pieces process and the purpose of assembling are instructed to realize, it is possible to automatic to carving molded line class Classification is identified in type, and curve is handled with straight line situation respectively, with very high robustness, is extracted and is carved molded line Characteristic point position is accurate, and the quarter molded line contour curve finally fitted also meets the requirement contrasted with digital-to-analogue, to instructing work Part is processed has great significance with assembling.
Brief description of the drawings
Fig. 1 is the flow chart of the laser incising molded line feature extracting method based on line laser.
Fig. 2 is the original signals and associated noises obtained by laser sensor, and transverse axis represents signal sequence number, and the longitudinal axis represents signal value.
Fig. 3 is the result after medium filtering and wavelet threshold denoising, and transverse axis represents signal sequence number, and the longitudinal axis represents signal Value.
Fig. 4 carves molded line feature locations for one that the present invention is finally extracted, and transverse axis represents signal sequence number, and the longitudinal axis represents letter Number value.A, b point represent two boundary position point coordinates points of quarter type groove or so respectively, and the jut of point-to-point transmission is quarter molded line Produced feature.
Embodiment
Describe the embodiment of the present invention in detail with technical scheme below in conjunction with the accompanying drawings.
Embodiment 1, measured object of the invention is the aluminum panels that one piece of 600*800mm flatness is 0.01mm.Have thereon The quarter molded line border left after milling cutting, by laser projection in piece surface.Pass through KEYNECE laser sensors and its blueness Laser, obtains original signal data, is handled as original signals and associated noises.The original signals and associated noises obtained are as shown in Figure 2. Then proceeded as follows according to the flow chart shown in accompanying drawing 1.
The first step is based on medium filtering and wavelet threshold denoising carries out Signal Pretreatment.Original noisy data-signal is carried out Median filter process.A long sliding window is defined first.If the sample of signal value at a time in window is { x (i- N),...,x(i),...,x(i+N)}.Signal value in the window is sorted from small to large, takes its intermediate value defeated as filtering Go out value, replace x (i) sample values of original signal, draw the expression formula of formula (1).
Then, data are carried out with further small value threshold denoising.Can be in original data signal by medium filtering Noise carry out preliminary suppression, mainly the spike noise and isolated noise point in initial data have been carried out largely Suppression;In order to obtain the data and curves of more smooth steady, further denoising is carried out using the method for wavelet threshold denoising Smoothing processing;
Wavelet transform, which is carried out, for the noiselike signal after above-mentioned medium filtering obtains one group of wavelet conversion coefficient wy(s, j), j=1,2 ..., s, s be wavelet decomposition the number of plies;Then to wy(s, j) carries out threshold process, selects suitable threshold Value λ, the wavelet coefficient that will be less than the threshold value is suppressed, and retains the useful signal higher than the threshold value, recycles formula (2) estimation Go out wavelet coefficient.
Wavelet reconstruction is carried out using wavelet coefficient and obtains signal z (k), k=1,2 after denoising ..., n, passes through above formula threshold Value is handled, can be with more efficiently removal noise, and retains useful signal to the full extent.As a result as shown in Figure 3.
Second step, based on adaptive curve matching reduction line laser position workpiece shapes.
The profile-followed curve matching of workpiece surface is first carried out, practical work piece surface is usually small curvature surface variations or plane, because The profile-followed curve matching of this workpiece surface is broadly divided into two kinds:Fitting a straight line and conic fitting;
First according to the valid data (x after denoisingi,zi), i=1,2 ..., n carries out fitting a straight line, if fitting a straight line is z (x)=a0+a1X, then be fitted mean square error W (a using formula (3)0,a1)。
Fitting a straight line is carried out with mean square error minimalization, i.e., a can be obtained using formula (4)0And a1
The mean square error of digital simulation straight lineCertain threshold value R is set, if Re≤R, then it is assumed that workpiece Surface is plane, and fitting a straight line is reasonable;If otherwise Re>R, then it is assumed that fitting a straight line is overproof, workpiece surface is small curvature surface, is adopted Use conic fitting;If fitting quadratic curve equation is z (x)=a0+a1x+a2x2, then it is fitted mean square error such as formula (5) institute Show.
By the extremum principle of the function of many variables, W (a0,a1,a2) minimum meet the conditions of formula (6), arrangement obtains secondary The equation group (7) of curve matching.
By solving above equation group, you can obtain the minimum fitting conic section function z (x) of mean square error;Above by Straight line can calculate workpiece surface shape exactly to the profile-followed curve fitting algorithm of adaptive workpiece surface of conic section, side Just the groove location of laser scribing processing is determined.
Then the curve matching of quarter type groove is carried out.
The curve fitted using previous step utilizes the measurement data (x after denoising as accurate workpiece surface curvei,zi),i =1,2 ..., n calculate matched curve apart from di, it is believed that the corresponding position x of ultimate range0For groove position, it is taken Each m measurement data points composition recess region data in left and right, and groove curve matching is carried out, according to measurement data in groove The form of expression, is fitted from conic section;Fitting theory and method are consistent with workpiece surface curve-fitting method, so that The iunction for curve for going out groove is z (x)=b0+b1x+b2x2
Finally the groove curve of acquisition is analyzed, the feature locations for carving molded line are extracted.
3rd step, carries out laser incising molded line feature point extraction.
The workpiece surface curve and groove curvilinear equation fitted respectively by second step, passes through at formula (8) solution two The intersection point of bar curve.
If workpiece surface is plane, corresponding coefficient a2Automatic is 0;Solve above equation group and can obtain two sides of groove Boundary's point coordinates is a (x1,z1),b(x2,z2);Therefore groove position feature point coordinates c (x are solved using formula (9)c, zc)。
Fig. 4 carves molded line feature locations for one that the present embodiment is finally extracted, and a, b points represent quarter type groove or so respectively Two boundary position point coordinates points.The jut of point-to-point transmission is to carve the feature produced by molded line.
Extracting method can automatically to carve molded line type classification is identified, respectively to curve with straight line situation Reason, with very high robustness, the characteristic point position extracted is accurate, very careless to instructing work pieces process and assembling to have Justice.

Claims (1)

1. a kind of laser incising molded line feature extracting method based on line laser, it is characterized in that, this method is directed to large aerospace wallboard The line laser detection of class part milling area laser incising type Working position, based on the original of medium filtering and wavelet threshold denoising to acquisition Beginning signal carries out data prediction, obtains smooth steady signal;Using adaptive curve matching reduction line laser position workpiece with Shape curve and quarter type groove curve precise shapes;Pass through the profile-followed curve of obtained workpiece and quarter type groove curvilinear equation it is true Determine on groove along edge feature point, groove accurate feature points are obtained by the way of centering is averaging;Method is comprised the following steps that:
The first step is based on medium filtering and wavelet threshold denoising carries out Signal Pretreatment
Due to the original two dimensional data that laser sensor is gathered, comprising influence of noise, abscissa is represented with x respectively, represents vertical with z Coordinate;For the robustness and stability that improve the identification of subsequent characteristics position with extract, discrete signal pretreatment, bag are carried out first Medium filtering and Wavelet Transform Threshold denoising are included, to obtain the data-signal of smooth steady;
1) medium filtering
Assuming that original noisy data-signal is x (k), k=1,2 ..., n, wherein, n is the data length of collection, and x (k) is k length Corresponding original data signal value z under degree;When carrying out median filter process to it, the L length that a length is odd number is defined first Sliding window, L=2N+1, N ∈ Z, Z are an integer, and 2N+1 represents an odd number;Therefore, if at a time in window Sample of signal value is { x (i-N) ..., x (i), x (i+N) }, and wherein x (i) is the center signal sample value in the window;To this L signal value in window is sorted from small to large, then takes its intermediate value as filtering output value, replace x (i) samples of original signal This value, its mathematical expression is as follows:
Y (i)=med x (i-N) ..., x (i) ..., x (i+N) } (1)
Wherein, med { } represents to calculate the intermediate value in braces in data sequence, and y (i) represents the intermediate value in x (i) window;
2) wavelet threshold denoising
The noise in original data signal is suppressed by medium filtering, to the spike noise in initial data and orphan Vertical noise spot is suppressed;In order to obtain the data and curves of more smooth steady, carried out using the method for wavelet threshold denoising Further denoising smooth processing;
For the noiselike signal y (k), k=1,2 ..., n after above-mentioned medium filtering, discrete wavelet transformer is carried out to it and got in return To one group of wavelet conversion coefficient wy(s, j), j=1,2 ..., s, s be wavelet decomposition the number of plies, j be the corresponding frequencies of s;Then To wy(s, j) carries out threshold process, selects suitable threshold value λ, and the wavelet coefficient that will be less than the threshold value is suppressed, and reservation is higher than The useful signal of the threshold value, estimates wavelet coefficientIt is as follows:
<mrow> <msub> <mover> <mi>w</mi> <mo>^</mo> </mover> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>=</mo> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>s</mi> <mi>i</mi> <mi>g</mi> <mi>n</mi> <mo>&amp;lsqb;</mo> <msub> <mi>w</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>&amp;rsqb;</mo> <msqrt> <mrow> <mo>|</mo> <msub> <mi>w</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <msup> <mo>|</mo> <mn>2</mn> </msup> <mo>-</mo> <msup> <mi>&amp;lambda;</mi> <mn>2</mn> </msup> </mrow> </msqrt> </mrow> </mtd> <mtd> <mrow> <mo>|</mo> <msub> <mi>w</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>&amp;GreaterEqual;</mo> <mi>&amp;lambda;</mi> </mrow> </mtd> </mtr> <mtr> <mtd> <mn>0</mn> </mtd> <mtd> <mrow> <mo>|</mo> <msub> <mi>w</mi> <mi>y</mi> </msub> <mrow> <mo>(</mo> <mi>s</mi> <mo>,</mo> <mi>j</mi> <mo>)</mo> </mrow> <mo>|</mo> <mo>&lt;</mo> <mi>&amp;lambda;</mi> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>2</mn> <mo>)</mo> </mrow> </mrow>
Wherein, λ is the threshold value chosen,For the data-signal wavelet coefficient after threshold denoising;UtilizeCarry out Wavelet reconstruction obtains signal z (k), k=1,2 after denoising ..., n, is handled by above formula threshold value, and effective remove is made an uproar Sound, and retain useful signal to the full extent;
Second step is based on adaptive curve matching reduction line laser position workpiece shapes
1) the profile-followed curve matching of workpiece surface
Practical work piece surface is usually small curvature surface variations or plane, therefore the profile-followed curve matching of workpiece surface is divided into two Kind:Fitting a straight line and conic fitting;
First according to the valid data (x after denoisingi,zi), i=1,2 ..., n carries out fitting a straight line, if fitting a straight line is z (x) =a0+a1X, then be fitted mean square error W (a0,a1) be:
<mrow> <mi>W</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <mi>z</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>3</mn> <mo>)</mo> </mrow> </mrow>
xiFor i-th of signal, ziFor the corresponding original signal value of i-th of signal, z (xi) represent xiSignal after corresponding denoising Value;N is valid data sum;
Fitting a straight line is carried out with mean square error minimalization to obtain:
<mrow> <mtable> <mtr> <mtd> <mrow> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>z</mi> <mi>i</mi> </msub> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <msub> <mi>x</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <mi>n</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <msub> <mi>x</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>=</mo> <mrow> <mo>(</mo> <mi>n</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>-</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>/</mo> <mrow> <mo>(</mo> <mi>n</mi> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <msub> <mi>x</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <msup> <mrow> <mo>(</mo> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>)</mo> </mrow> </mrow> </mtd> </mtr> </mtable> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>4</mn> <mo>)</mo> </mrow> </mrow>
The mean square error of digital simulation straight lineWherein diFor the distance of measurement data each point to fitting a straight line; Certain threshold value R is set, if Re≤R, then it is assumed that workpiece surface is plane, fitting a straight line is reasonable;If otherwise Re>R, then it is assumed that straight line Fitting is overproof, and workpiece surface is small curvature surface, using conic fitting;If fitting quadratic curve equation is z (x)=a0+ a1x+a2x2, then being fitted mean square error is:
<mrow> <mi>W</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <mi>z</mi> <mo>(</mo> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>)</mo> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>=</mo> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msup> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msup> <msub> <mi>x</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mn>2</mn> </msup> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>5</mn> <mo>)</mo> </mrow> </mrow>
By the extremum principle of the function of many variables, W (a0,a1,a2) minimum meet
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msup> <msub> <mi>x</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msup> <msub> <mi>x</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mfrac> <mrow> <mo>&amp;part;</mo> <mi>W</mi> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mo>,</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <mo>)</mo> </mrow> </mrow> <mrow> <mo>&amp;part;</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> </mrow> </mfrac> <mo>=</mo> <mn>2</mn> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <mrow> <mo>(</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mi>i</mi> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msup> <msub> <mi>x</mi> <mi>i</mi> </msub> <mn>2</mn> </msup> <mo>-</mo> <msub> <mi>z</mi> <mi>i</mi> </msub> <mo>)</mo> </mrow> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>6</mn> <mo>)</mo> </mrow> </mrow>
Arrange and obtain the equation group of conic fitting and be
<mrow> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mi>n</mi> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>x</mi> <mi>i</mi> <mn>3</mn> </msubsup> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>x</mi> <mi>i</mi> <mn>3</mn> </msubsup> </mrow> </mtd> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>x</mi> <mi>i</mi> <mn>4</mn> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <msub> <mi>a</mi> <mn>0</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>1</mn> </msub> </mtd> </mtr> <mtr> <mtd> <msub> <mi>a</mi> <mn>2</mn> </msub> </mtd> </mtr> </mtable> </mfenced> <mo>=</mo> <mfenced open = "(" close = ")"> <mtable> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msub> <mi>x</mi> <mi>i</mi> </msub> <msub> <mi>z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <munderover> <mo>&amp;Sigma;</mo> <mrow> <mi>i</mi> <mo>=</mo> <mn>1</mn> </mrow> <mi>n</mi> </munderover> <msubsup> <mi>x</mi> <mi>i</mi> <mn>2</mn> </msubsup> <msub> <mi>z</mi> <mi>i</mi> </msub> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>7</mn> <mo>)</mo> </mrow> </mrow>
By solving above equation group, that is, obtain the minimum fitting conic section function z (x) of mean square error;
Above by the profile-followed curve fitting algorithm of adaptive workpiece surface of straight line to conic section, workpiece surface shape is calculated exactly Shape, conveniently determines the groove location of laser scribing processing;
2) quarter type groove curve matching
Using second step 1) curve that fits, as accurate workpiece surface curve, utilizes the measurement data (x after denoisingi,zi), i= 1,2 ..., n calculate matched curve apart from di, it is believed that the corresponding position x of ultimate range0For groove position, take it left Right each m measurement data points constitute recess region data, and carry out groove curve matching, according to measurement data groove table Existing form, is fitted from conic section;So that the iunction for curve for drawing groove is
Z (x)=b0+b1x+b2x2
3) molded line feature locations are carved to extract
The groove curve of acquisition is analyzed, the feature locations for carving molded line are extracted;
3rd step laser incising molded line feature point extraction
Pass through the workpiece surface curve 1), 2) fitted respectively and groove curvilinear equation of second step, two curves of simultaneous solution Intersection point it is as follows
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>a</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>a</mi> <mn>1</mn> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>a</mi> <mn>2</mn> </msub> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <mi>y</mi> <mrow> <mo>(</mo> <mi>x</mi> <mo>)</mo> </mrow> <mo>=</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <mi>x</mi> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <msup> <mi>x</mi> <mn>2</mn> </msup> <mo>=</mo> <mn>0</mn> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>8</mn> <mo>)</mo> </mrow> </mrow>
If workpiece surface is plane, corresponding coefficient a2Automatic is 0;Solve above equation group and can obtain two boundary points of groove Coordinate is a (x1,z1),b(x2,z2);Therefore groove position feature point coordinates c (xc,zc) be
<mrow> <mfenced open = "{" close = ""> <mtable> <mtr> <mtd> <mrow> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>=</mo> <mfrac> <mrow> <msub> <mi>x</mi> <mn>1</mn> </msub> <mo>+</mo> <msub> <mi>x</mi> <mn>2</mn> </msub> </mrow> <mn>2</mn> </mfrac> </mrow> </mtd> </mtr> <mtr> <mtd> <mrow> <msub> <mi>z</mi> <mi>c</mi> </msub> <mo>=</mo> <msub> <mi>b</mi> <mn>0</mn> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>1</mn> </msub> <msub> <mi>x</mi> <mi>c</mi> </msub> <mo>+</mo> <msub> <mi>b</mi> <mn>2</mn> </msub> <msubsup> <mi>x</mi> <mi>c</mi> <mn>2</mn> </msubsup> </mrow> </mtd> </mtr> </mtable> </mfenced> <mo>-</mo> <mo>-</mo> <mo>-</mo> <mrow> <mo>(</mo> <mn>9</mn> <mo>)</mo> </mrow> </mrow>
So as to be extracted the coordinate value of laser incising molded line characteristic point exactly, laser incising type Working position is accurately measured.
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CN114518116A (en) * 2022-02-17 2022-05-20 广州大学 Visual navigation method based on tracking guide line

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