CN107133565B - Line laser-based laser engraving line feature extraction method - Google Patents

Line laser-based laser engraving line feature extraction method Download PDF

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CN107133565B
CN107133565B CN201710203364.3A CN201710203364A CN107133565B CN 107133565 B CN107133565 B CN 107133565B CN 201710203364 A CN201710203364 A CN 201710203364A CN 107133565 B CN107133565 B CN 107133565B
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curve
groove
fitting
signal
laser
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CN107133565A (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

Abstract

The invention discloses a line laser-based laser engraving line feature extraction method, belongs to the technical field of laser measurement, and relates to a line laser-based laser engraving line feature extraction method. The method aims at the line laser detection of the laser engraving processing position of the chemical milling area of large-scale aviation wallboard parts, and performs data preprocessing on the acquired original signal based on median filtering and wavelet threshold denoising to obtain a smooth and stable signal. Fitting a reduction line laser position workpiece conformal curve and an accurate shape of a carving groove curve by adopting a self-adaptive curve; and determining the boundary characteristic points of the upper edge of the groove according to the obtained workpiece conformal curve and the curve equation of the notch groove, and obtaining the accurate characteristic points of the groove by adopting a centering and averaging mode. The method has high robustness, the position of the characteristic point of the extracted carving line is accurate, the finally fitted carving line profile curve also meets the requirement of comparison with a digital model, and the method has great significance for guiding the processing and assembly of a workpiece.

Description

Line laser-based laser engraving line feature extraction method
Technical Field
The invention belongs to the technical field of laser measurement, and relates to a line laser-based laser engraving line feature extraction method.
Background
In the aircraft manufacturing process, laser lithography type processing needs to be carried out on a chemical milling area of a large-scale aviation wall plate type part, and then the chemical milling area meets the specified technical and precision requirements, so that the requirement of high-quality connection assembly is met. Meanwhile, extracting characteristic points of laser-etched molded lines through a laser sensor based on line laser, and restoring accurate shapes of a line laser position workpiece conformal curve and a carved groove curve; the boundary characteristic points on the upper edge of the groove are determined through the obtained workpiece conformal curve and the curve equation of the notch groove, and the accurate characteristic points of the groove are obtained by adopting a centering averaging mode, so that the method can help people to accurately measure whether the laser-etching machining position meets the digital-analog requirement, and guide the workpiece machining and assembly.
The patent No. CN103777192A issued by zhuang, jing, xujun et al, "a method for extracting linear features based on a laser sensor" proposes a method for extracting linear features based on a laser sensor. On the basis of a segmentation and combination method, the efficiency of the method is improved through self-adaptive adjacent point set detection, the sensitivity of the method for improving the line segment segmentation to parameters is improved by using a fuzzy segmentation and combination method, and finally the parameters under each linear segment polar coordinate system in the environment are fitted by using a least square method. The implementation result of the method shows that when the straight line segment contains more points, the result is very accurate, most straight line errors are very small, the diameter error is less than 1mm, the angle error is less than 0.01rad, and the fitting effect is good. However, the method is limited to the extraction of linear features, and the feature extraction with high universality cannot be performed on a laser engraving line having both a curve and a straight line.
Disclosure of Invention
The invention aims to solve the technical problem of extracting and reducing the characteristics of the laser engraving line position in the chemical milling area of parts such as large aviation components and the like, and provides a line laser-based laser engraving line characteristic extraction method. The method comprises the steps of carrying out denoising pretreatment on an original signal acquired by a laser sensor, then carrying out shape confirmation and boundary feature extraction on an engraving groove curve, accurately measuring whether the laser engraving machining position meets the digital-analog requirement or not in the part production process, achieving the purpose of guiding workpiece machining and assembly, automatically identifying and classifying engraving line types, respectively processing curve and straight line conditions, having high robustness, accurately extracting the feature point position of an engraving line, meeting the requirement of comparing the engraving line with the digital-analog, and having great significance for guiding workpiece machining and assembly.
The technical scheme adopted by the invention is a line laser-based laser engraving line feature extraction method, which is characterized in that the method is used for carrying out data preprocessing on an obtained original signal based on median filtering and wavelet threshold denoising aiming at line laser detection of a laser engraving machining position of a large aviation wallboard part milling area to obtain a smooth and stable signal; fitting the accurate shapes of a reduction line laser position workpiece conformal curve and an engraving groove curve by adopting a self-adaptive curve; and determining the boundary characteristic points of the upper edge of the groove through the obtained workpiece conformal curve and the curve equation of the notch groove, and obtaining the accurate characteristic points of the groove by adopting a centering and averaging mode. The method comprises the following specific steps: first step, signal preprocessing is carried out based on median filtering and wavelet threshold denoising
Because the original two-dimensional data collected by the laser sensor contains noise influence, x represents the abscissa and z represents the ordinate respectively; in order to improve the robustness and stability of subsequent characteristic position identification and extraction, discrete signal preprocessing is firstly carried out, including median filtering and wavelet transformation threshold denoising, so as to obtain a smooth and stable data signal;
1) median filtering
Assuming that an original noisy data signal is x (k), where k is 1, 2.., n, where n is a length of acquired data, and x (k) is a corresponding original data signal value z under the length of k; when the median filtering processing is carried out, firstly, an L long sliding window with the length being an odd number is defined, wherein L is 2N +1, N belongs to Z, Z is an integer, and 2N +1 represents an odd number; thus, if the signal sample value within a certain time window is { x (i-N),.. multidot.x (i),. multidot.x (i + N) }, where x (i) is the center signal sample value within the window; sorting L signal values in the window from small to large, taking the value as a filtering output value to replace x (i) sample values of the original signal, wherein the mathematical expression is as follows:
y(i)=med{x(i-N),...,x(i),...,x(i+N)} (1)
wherein med { } denotes the median in the sequence of data in braces, y (i) denotes the median in the x (i) window;
2) wavelet threshold denoising
The noise in the original data signal is suppressed through median filtering, and spike pulse noise and isolated noise points in the original data are suppressed; in order to obtain a smoother and more stable data curve, a wavelet threshold denoising method is adopted for further denoising and smoothing;
and performing discrete wavelet transform on the low-noise signal y (k), k being 1,2, and n after median filtering to obtain a set of wavelet transform coefficients wy(s, j), j is 1,2, s, s is the number of layers of wavelet decomposition, j is the frequency corresponding to s; then to wy(s, j) performing threshold processing, selecting a proper threshold lambda, suppressing the wavelet coefficients below the threshold, retaining the useful signals above the threshold, and estimating the wavelet coefficients
Figure GDA0002230624450000031
The following were used:
Figure GDA0002230624450000041
wherein λ is a selected threshold value,
Figure GDA0002230624450000042
wavelet coefficients of the data signals subjected to threshold denoising; by using
Figure GDA0002230624450000043
Performing wavelet reconstruction to obtain a denoised signal z (k), wherein k is 1,2, and n, and processing the signal through the above threshold to effectively remove noise and reserve a useful signal to the maximum extent; second step is based on adaptive curve fitting reduction line laserShape of position work
1) Fitting of workpiece surface conformal curve
The actual workpiece surface is typically a small curvature change surface or plane, and therefore the conformal curve fit of the workpiece surface falls into two categories: fitting a straight line and a quadratic curve;
first according to the denoised effective data (x)i,zi) N, where a straight line is fitted, and z (x) is a fitted straight line0+a1x, then fitting the mean square error W (a)0,a1) Comprises the following steps:
Figure GDA0002230624450000044
xiis the ith signal, ziFor the original signal value corresponding to the ith signal, z (x)i) Denotes xiCorresponding denoised signal values; n is the total number of valid data;
taking a minimum value according to the mean square error to perform straight line fitting to obtain:
Figure GDA0002230624450000045
calculating the mean square error of the fitted straight line
Figure GDA0002230624450000051
Wherein d isiThe distance from each point of the measured data to the fitting straight line; setting a certain threshold value R, and if Re is less than or equal to R, determining that the surface of the workpiece is a plane and reasonably fitting a straight line; whereas if Re>R, considering that the straight line fitting is out of tolerance, and fitting the workpiece surface by adopting a quadratic curve, wherein the workpiece surface is a small-curvature curved surface; let the fitted quadratic curve equation be z (x) a0+a1x+a2x2Then the fitted mean square error is:
Figure GDA0002230624450000052
by the extreme principle of a multivariate function, W (a)0,a1,a2) Minimum value of (A) satisfies
Figure GDA0002230624450000053
The equation set for obtaining the quadratic curve fitting is
Figure GDA0002230624450000054
Solving the equation system to obtain a fitted quadratic curve function z (x) with the minimum mean square error;
the self-adaptive workpiece surface conformal curve fitting algorithm from the straight line to the quadratic curve can accurately calculate the surface shape of the workpiece, and the position of a groove processed by laser scribing can be conveniently determined;
2) curve fitting of carved groove
The curve fitted in the second step 1) is taken as an accurate workpiece surface curve, and the measurement data (x) after denoising is utilizedi,zi) N is calculated as the distance d to the curve fitted, i 1,2iThe position x corresponding to the maximum distance is considered0Taking m measurement data points on the left and right of the position of the groove to form groove area data, fitting a groove curve, and selecting a quadratic curve for fitting according to the expression form of the measurement data at the groove; thereby obtaining a curve fitting function at the groove as
z(x)=b0+b1x+b2x2
3) Reticle feature position extraction
Analyzing the obtained groove curve, and extracting the characteristic position of the engraving line;
thirdly, extracting characteristic points of laser engraving lines
The surface curve of the workpiece and the groove curve equation which are respectively fitted by the steps 1) and 2) in the second step are simultaneously solved, and the intersection point of the two curves is as follows
Figure GDA0002230624450000061
If the workpieceThe surface is a plane, the corresponding coefficient a2Automatically is 0; solving the above equation system can obtain the coordinates of two boundary points of the groove as a (x)1,z1),b(x2,z2) (ii) a Therefore, the characteristic point coordinate c (x) of the position of the groovec,zc) Is composed of
Figure GDA0002230624450000062
Therefore, the coordinate values of characteristic points of the laser engraving profile line are accurately extracted, and the laser engraving type machining position is accurately measured.
The method has the advantages that the shape of the engraving groove curve is confirmed and the boundary characteristic is extracted after the original signal acquired by the laser sensor is subjected to denoising pretreatment, so that whether the laser engraving machining position meets the digital-analog requirement or not can be accurately measured in the production process of parts, the purpose of guiding the machining and assembly of the workpiece is realized, the engraving line types can be automatically identified and classified, the conditions of the curve and the straight line are respectively processed, the robustness is high, the position of the characteristic point of the engraving line is extracted to be accurate, the finally fitted engraving line profile curve also meets the requirement of comparing with the digital-analog, and the method has great significance for guiding the machining and assembly of the workpiece.
Drawings
Fig. 1 is a flowchart of a line laser-based laser scribing line feature extraction method.
Fig. 2 shows the raw noisy signal acquired by the laser sensor, with the horizontal axis representing the signal number and the vertical axis representing the signal value.
Fig. 3 shows the results of median filtering and wavelet threshold denoising, where the horizontal axis represents the signal number and the vertical axis represents the signal value.
Fig. 4 shows a pattern characteristic position finally extracted by the present invention, where the horizontal axis represents a signal number and the vertical axis represents a signal value. Points a and b respectively represent coordinate points of the left boundary position point and the right boundary position point of the notch groove, and a protruding part between the two points is the characteristic generated by the notch line.
Detailed Description
The following detailed description of the embodiments of the invention refers to the accompanying drawings and claims.
Example 1, the test object of the invention is a 600 x 800mm aluminum sample with a flatness of 0.01 mm. The laser is projected on the surface of the part by the carved line boundary left after the chemical milling cutting. And acquiring original signal data through a KEYNECCE laser sensor and blue laser thereof, and processing the original signal data as an original noise-containing signal. The raw noisy signal is obtained as shown in figure 2. The following operation is then performed according to the flow chart shown in fig. 1.
The first step is signal preprocessing based on median filtering and wavelet threshold denoising. And carrying out median filtering processing on the original noisy data signal. A long sliding window is first defined. If the signal sample value within a certain time window is { x (i-N),.. times, x (i) }. And (3) sequencing the signal values in the window from small to large, taking the value of the sequence as a filtering output value, and replacing the x (i) sample value of the original signal to obtain the expression of the formula (1).
The data is then further denoised by a small threshold. The noise in the original data signal can be preliminarily suppressed through median filtering, and spike pulse noise and isolated noise points in the original data are mainly suppressed to a greater extent; in order to obtain a smoother and more stable data curve, a wavelet threshold denoising method is adopted for further denoising and smoothing;
performing discrete wavelet transform on the low-noise signal after median filtering to obtain a group of wavelet transform coefficients wy(s, j), j ═ 1, 2.., and s, s is the number of layers in the wavelet decomposition; then to wy(s, j) performing threshold processing, selecting a proper threshold lambda, suppressing the wavelet coefficients lower than the threshold, retaining the useful signals higher than the threshold, and estimating the wavelet coefficients by using a formula (2).
Wavelet reconstruction is carried out by utilizing wavelet coefficients to obtain a denoised signal z (k), wherein k is 1, 2. The results are shown in FIG. 3.
And secondly, fitting the shape of the workpiece at the laser position of the reduction line based on the self-adaptive curve.
Firstly, the surface of the workpiece is subjected to conformal curve fitting, and the actual surface of the workpiece is usually a surface or a plane with small curvature change, so that the conformal curve fitting of the surface of the workpiece is mainly divided into two types: fitting a straight line and a quadratic curve;
first according to the denoised effective data (x)i,zi) N, where a straight line is fitted, and z (x) is a fitted straight line0+a1x, then the mean square error W (a) can be fitted using equation (3)0,a1)。
Taking minimum value to perform straight line fitting by mean square error, namely obtaining a by using formula (4)0And a1
Calculating the mean square error of the fitted straight line
Figure GDA0002230624450000091
Setting a certain threshold value R, and if Re is less than or equal to R, determining that the surface of the workpiece is a plane and reasonably fitting a straight line; whereas if Re>R, considering that the straight line fitting is out of tolerance, and fitting the workpiece surface by adopting a quadratic curve, wherein the workpiece surface is a small-curvature curved surface; let the fitted quadratic curve equation be z (x) a0+a1x+a2x2Then the fitting mean square error is as shown in equation (5).
By the extreme principle of a multivariate function, W (a)0,a1,a2) The minimum value of (2) meets the condition of the formula (6), and an equation set (7) of quadratic curve fitting is obtained through arrangement.
Solving the equation set to obtain a fitted quadratic curve function z (x) with the minimum mean square error; the self-adaptive workpiece surface conformal curve fitting algorithm from the straight line to the quadratic curve can accurately calculate the surface shape of the workpiece, and the position of the groove processed by laser scribing can be conveniently determined.
Then curve fitting of the sculptured grooves is carried out.
The curve fitted in the previous step is an accurate workpiece surface curve, and the de-noised measurement data (x) is utilizedi,zi) N is calculated as the distance d to the curve fitted, i 1,2iThe position x corresponding to the maximum distance is considered0Taking m measurement data points on the left and right of the position of the groove to form groove area data, fitting a groove curve, and selecting a quadratic curve for fitting according to the expression form of the measurement data at the groove; the fitting principle and method are consistent with the curve fitting method of the surface of the workpiece, so that the curve fitting function at the groove is z (x) b0+b1x+b2x2
And finally, analyzing the obtained groove curve and extracting the characteristic position of the carved line.
And thirdly, extracting characteristic points of the laser engraving lines.
And (3) solving the intersection point of the two curves through a formula (8) by respectively fitting the workpiece surface curve and the groove curve equation obtained in the second step.
If the surface of the workpiece is flat, the corresponding coefficient a2Automatically is 0; solving the above equation system can obtain the coordinates of two boundary points of the groove as a (x)1,z1),b(x2,z2) (ii) a Therefore, the coordinate c (x) of the position characteristic point of the groove is solved by using the formula (9)c,zc)。
Fig. 4 shows a last extracted feature position of a notch line, where points a and b respectively represent coordinates of left and right boundary position points of the notch groove. The protrusion between the two points is the feature created by the scribe line.
The extraction method can automatically identify and classify the types of the carved lines, respectively process the conditions of curves and straight lines, has high robustness, and has great significance for guiding the processing and assembly of workpieces, and the positions of the extracted characteristic points are accurate.

Claims (1)

1. A line laser-based laser engraving line feature extraction method is characterized in that the method is used for carrying out data preprocessing on an obtained original signal based on median filtering and wavelet threshold denoising aiming at line laser detection of a laser engraving machining position of a large aviation wallboard part milling area to obtain a smooth and stable signal; fitting the accurate shapes of a reduction line laser position workpiece conformal curve and an engraving groove curve by adopting a self-adaptive curve; determining boundary characteristic points of the upper edge of the groove according to the obtained workpiece conformal curve and an engraving groove curve equation, and obtaining accurate characteristic points of the groove by adopting a centering and averaging mode; the method comprises the following specific steps:
first step, signal preprocessing is carried out based on median filtering and wavelet threshold denoising
Because the original two-dimensional data collected by the laser sensor contains noise influence, x represents the abscissa and z represents the ordinate respectively; in order to improve the robustness and stability of subsequent characteristic position identification and extraction, discrete signal preprocessing is firstly carried out, including median filtering and wavelet transformation threshold denoising, so as to obtain a smooth and stable data signal;
1) median filtering
Setting an original noisy data signal as x (k), wherein k is 1, 2.., and p, wherein p is the length of acquired data, and x (k) is a corresponding original data signal value z under the length of k; when the median filtering processing is carried out, firstly, an L long sliding window with the length being an odd number is defined, wherein L is 2N +1, N belongs to Z, Z is an integer, and 2N +1 represents an odd number; thus, if the signal sample value within a certain time window is { x (i-N),.. multidot.x (i),. multidot.x (i + N) }, where x (i) is the center signal sample value within the window; sorting L signal values in the window from small to large, taking the value as a filtering output value to replace x (i) sample values of the original signal, wherein the mathematical expression is as follows:
y(i)=med{x(i-N),...,x(i),...,x(i+N)} (1)
wherein med { } denotes the median in the sequence of data in braces, y (i) denotes the median in the x (i) window;
2) wavelet threshold denoising
The noise in the original data signal is suppressed through median filtering, and spike pulse noise and isolated noise points in the original data are suppressed; in order to obtain a smoother and more stable data curve, a wavelet threshold denoising method is adopted for further denoising and smoothing;
and performing discrete wavelet transform on the low-noise signal y (k), k being 1,2, and p after median filtering to obtain a set of wavelet transform coefficients w (k)y(s, j), j is 1,2, s, s is the number of layers of wavelet decomposition, j is the frequency corresponding to s; then to wy(s, j) performing threshold processing, selecting a proper threshold lambda, suppressing the wavelet coefficients below the threshold, retaining the useful signals above the threshold, and estimating the wavelet coefficients
Figure FDA0002363828280000021
The following were used:
Figure FDA0002363828280000022
wherein λ is a selected threshold value,
Figure FDA0002363828280000023
wavelet coefficients of the data signals subjected to threshold denoising; by using
Figure FDA0002363828280000024
Performing wavelet reconstruction to obtain a denoised signal z (k), wherein k is 1,2, and p, and processing through the above threshold to remove noise and keep a useful signal;
second step, reducing the shape of the workpiece at the laser position based on adaptive curve fitting
1) Fitting of workpiece surface conformal curve
The actual workpiece surface is typically a small curvature change surface or plane, and therefore the conformal curve fit of the workpiece surface falls into two categories: fitting a straight line and a quadratic curve;
first according to the denoised effective data (x)i,zi) N, where a straight line is fitted, and z (x) is a fitted straight line0+a1x, then fitting the mean square error W (a)0,a1) Comprises the following steps:
Figure FDA0002363828280000031
xiis the ith signal, ziFor the original signal value corresponding to the ith signal, z (x)i) Denotes xiCorresponding denoised signal values; n is the total number of valid data;
taking a minimum value according to the mean square error to perform straight line fitting to obtain:
Figure FDA0002363828280000032
calculating the mean square error of the fitted straight line
Figure FDA0002363828280000033
Wherein d isiThe distance from each point of the measured data to the fitting straight line; setting a certain threshold value R, and if Re is less than or equal to R, determining that the surface of the workpiece is a plane and reasonably fitting a straight line; otherwise, if Re is larger than R, the straight line fitting is out of tolerance, the surface of the workpiece is a small-curvature curved surface, and quadratic curve fitting is adopted; let the fitted quadratic curve equation be z (x) a0+a1x+a2x2Then the fitted mean square error is:
Figure FDA0002363828280000034
by the extreme principle of a multivariate function, W (a)0,a1,a2) Minimum value of (A) satisfies
Figure FDA0002363828280000041
The equation set for obtaining the quadratic curve fitting is
Figure FDA0002363828280000042
Solving the equation system to obtain a fitted quadratic curve function z (x) with the minimum mean square error;
calculating the surface shape of the workpiece by the self-adaptive workpiece surface conformal curve fitting algorithm from the straight line to the quadratic curve, and determining the position of the groove processed by laser scribing;
2) curve fitting of carved groove
The curve fitted in the second step 1) is taken as an accurate workpiece surface curve, and the measurement data (x) after denoising is utilizedi,zi) N is calculated as the distance d to the curve fitted, i 1,2iThe position x corresponding to the maximum distance is considered0Taking m measurement data points on the left and right of the position of the groove to form groove area data, fitting a groove curve, and selecting a quadratic curve for fitting according to the expression form of the measurement data at the groove; thereby obtaining a curve fitting function at the groove as
z(x)=b0+b1x+b2x2
3) Reticle feature position extraction
Analyzing the obtained groove curve, and extracting the characteristic position of the engraving line;
thirdly, extracting characteristic points of laser engraving lines
The surface curve of the workpiece and the groove curve equation which are respectively fitted by the steps 1) and 2) in the second step are simultaneously solved, and the intersection point of the two curves is as follows
Figure FDA0002363828280000051
If the surface of the workpiece is flat, the corresponding coefficient a2Automatically is 0; solving the above equation system can obtain the coordinates of two boundary points of the groove as a (x)1,z1),b(x2,z2) (ii) a Therefore, the characteristic point coordinate c (x) of the position of the groovec,zc) Is composed of
Figure FDA0002363828280000052
Therefore, the coordinate values of characteristic points of the laser engraving profile are extracted, and the laser engraving type processing position is measured.
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