CN110095066B - Spectral confocal signal peak wavelength rapid high-precision extraction method based on Mean-shift - Google Patents
Spectral confocal signal peak wavelength rapid high-precision extraction method based on Mean-shift Download PDFInfo
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Abstract
The invention provides a fast high-precision peak wavelength extraction method based on Mean-Shift algorithm, which comprises the following steps: collecting a spectrum confocal signal of a spectrum confocal displacement sensor, executing normalization processing, and intercepting the signal after the normalization processing according to a set light intensity threshold value to obtain a point wavelength sequence corresponding to a light intensity sequence; setting iteration initial wavelength as a Mean-Shift vector corresponding to the current peak value of the point wavelength sequence obtained by calculation, and moving the current point wavelength sequence along the obtained Mean-Shift vector to obtain a new peak wavelength and a new point wavelength sequence; calculating a 2 norm of the obtained Mean-Shift vector; and judging whether the 2 norm of the obtained Mean-Shift vector is smaller than a given allowable error. The extraction method of the peak wavelength can obviously improve the extraction speed and the extraction precision of the peak wavelength.
Description
Technical Field
The invention belongs to the field of rapid high-precision spectral confocal signal peak extraction, and particularly relates to a rapid high-precision peak wavelength extraction method based on a Mean-Shift theory.
Background
The spectrum confocal displacement sensor is a displacement sensor based on wavelength displacement modulation, has the measuring precision reaching submicron and the working frequency reaching thousands of hertz, and is widely applied to medical treatment, optical detection and displacement measurement. The light beams of the polychromatic light in the sensor system are focused at different positions of the optical axis due to the dispersion effect, the light beams focused on the measured surface meet the confocal condition, the light beam flux of the light beam passing through the confocal aperture is large, and the light beam fluxes of the light beams with the other wavelengths are small, so that the spectral confocal signal approximate to a Gaussian curve is obtained. After the mapping relation between the signal peak wavelength and the displacement is established, the displacement of the measured object can be inverted according to the signal peak wavelength during measurement. Therefore, a rapid and high-precision peak wavelength extraction algorithm is a precondition for realizing real-time and accurate measurement of the spectral confocal sensor.
In the prior art, a common peak wavelength extraction algorithm comprises a maximum value method, a centroid method, a fitting method and the like, wherein the maximum value method directly selects a wavelength value with the maximum light intensity as a peak wavelength, so that the operation is simple, the algorithm is easily influenced by noise, and the precision is low; the centroid method is simple in calculation and high in speed, but the non-uniformity of sampling intervals can cause system errors and is low in precision. A.K. Ruprecht and the like derive a centroid method compensation formula according to an error transfer formula, the method needs to know the full width at half maximum of a signal, more time is needed for calculating the full width at half maximum of a discrete signal in actual measurement, fitting methods such as a parabola fitting method and a Gaussian fitting method are used for fitting the signal into a parabola and Gaussian curve form, and then searching a peak value according to curve characteristics, so that the accuracy is high, but the calculation is complex and the speed is slow. The fitting method proposed by Tanshinan et al has improved accuracy compared with the parabola fitting method and the Gauss fitting method, but the efficiency is not greatly improved.
Disclosure of Invention
Aiming at the defects or the improvement requirements in the prior art, the invention provides a quick high-precision peak wavelength extraction method based on the Mean-Shift theory, which comprises the following steps: the method comprises the steps of firstly obtaining an initial peak wavelength by a centroid method, calculating a Mean-Shift vector corresponding to the peak wavelength, moving the peak wavelength along the Mean-Shift vector to obtain a new peak wavelength, and iterating the Mean-Shift vector calculation and moving process for the new peak wavelength until a finishing condition is met.
In order to achieve the above object, according to the present invention, a method for rapidly and highly accurately extracting a peak wavelength of a spectral confocal signal based on Mean-shift is provided, the method comprising the steps of:
STEP1 collecting spectrum confocal signal of spectrum confocal displacement sensor, performing normalization processing, and truncating the normalized signal according to a set light intensity threshold T to obtain a point wavelength sequence
Corresponding light intensity sequence
STEP2 setting iteration initial wavelength as lambda0；
STEP3 calculationObtaining the point wavelength sequence
A Mean-Shift vector corresponding to the current peak value;
STEP4, moving the current point wavelength sequence along the obtained Mean-Shift vector to obtain a new peak wavelength and a new point wavelength sequence;
STEP5, calculating the 2 norm of the obtained Mean-Shift vector;
STEP6 judges whether the 2 norm of the obtained Mean-Shift vector is less than a given allowable error,
if not, jumping to the STEPs STEP 3-STEP 6;
and if so, the new peak wavelength after the movement is the peak wavelength of the extracted spectral confocal signal, and is used for establishing a mapping relation between the peak wavelength of the signal and the displacement in the signal processing of the spectral confocal displacement sensor so as to obtain the measurement displacement.
Further, the Mean-Shift vector of the point wavelength sequence is obtained as follows;
wherein G is a unit kernel function, w is a weight function, h is a kernel radius, i is a serial number of the point wavelength sequence, and j is a serial number of a Mean-Shift vector corresponding to the point wavelength sequence.
Further, the unit kernel function is preferably a gaussian kernel function:
in the formula, n is the number of the current point wavelength sequence calculated iteratively, and σ is the sample variance of the current point wavelength sequence calculated iteratively.
Further, the method can be used for preparing a novel materialPreferably, the weight function is: w (lambda)j)＝[I(λj)]2，I(λj) Represents the wavelength lambdajThe corresponding light intensity.
Further, the iterative initial wavelength is found by a centroid method.
Generally, compared with the prior art, the above technical solution conceived by the present invention has the following beneficial effects:
a fast high-precision peak wavelength extraction method based on a Mean-Shift algorithm is provided, and the method has good comprehensive performance in the aspects of operation speed and extraction precision.
The experimental result shows that the accuracy is improved by 71.8 percent compared with the centroid method; compared with a parabola fitting method, the improvement is 37.5%. Compared with the centroid method, the precision is improved by 58.1%. Compared with a parabola fitting method, the operation speed is improved by 5 times; compared with a Gaussian method, the method is improved by 73 times, the contradiction between the running speed and the calculation accuracy of the existing peak value extraction algorithm is effectively solved, and the method has a wide practical application prospect.
Drawings
FIG. 1 is a flow chart of the steps of the Mean-Shift algorithm implemented in accordance with the prior art;
FIG. 2 is a schematic diagram of the effect of an iterative flow of the Mean-Shift iterative method implemented according to the present invention;
FIG. 3 is a graph of normalized spectral confocal signals achieved in accordance with the present invention;
FIG. 4 is an experimental schematic diagram of a dispersive confocal displacement measurement system and displacement system implemented in accordance with the present invention;
FIG. 5 is a schematic diagram of an error indicator for an evaluation peak extraction algorithm implemented in accordance with the present invention using displacement bias;
FIG. 6 is a graph of expected experimental results comparing displacement deviations at different sample surface heights for different algorithms;
FIG. 7 is a standard deviation test result comparing displacement deviation at different sample surface heights under different algorithms.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is described in further detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention. In addition, the technical features involved in the embodiments of the present invention described below may be combined with each other as long as they do not conflict with each other.
The Mean-Shift theory is used to find local extrema in the density distribution of a set of data, and the main idea is to find the peak along the ascending direction of the probability density gradient.
Finding the peak value based on Mean-Shift theory implemented according to the invention is an iterative process: calculating a Mean-Shift vector corresponding to the current peak value, moving the peak value along the Mean-Shift vector to obtain a new peak value, and continuing the operation on the new peak value until the 2 norm of the Mean-Shift vector is smaller than a given allowable error epsilon.
Sample points λ for n wavelength sequences of d-dimensional space1,λ2,…,λnPoint λjThe calculation method of formula (1) is obtained by solving the Mean-Shift vector:
wherein G is a unit kernel function, w is a weight function, h is a kernel radius, i is an integer between 1 and n, where i is a serial number of the point wavelength sequence, j is a serial number of a Mean-Shift vector corresponding to the point wavelength sequence, a flow diagram for finding a peak value based on the Mean-Shift theory is shown in fig. 1, where the diagram is merely an illustration, where a variable x is a point λ of the wavelength sequencej。
The spectral confocal signal peak wavelength extraction method based on Mean-Shift mainly comprises the following processing steps: light intensity normalization processing is required to be carried out on the spectrum confocal signal collected from the spectrum confocal displacement sensor before peak value extraction, the normalization processing is a processing method for mapping data to a range of 0-1 in the prior art, and the obtaining process is not repeated again; and give out lightThe intensity threshold T is used to intercept the normalized light intensity signal, as shown in fig. 2, in which the points with light intensity higher than the threshold T are used for the operation of extracting the peak wavelength, and the wavelength sequence of these points is assumed to be
Corresponding to a sequence of light intensities of
The peak value extraction method is implemented according to the flow of figure 1, and the initial peak value wavelength lambda is obtained by using the centroid method0The centroid method is a common solving method in the prior art, and is not described in detail in the application, one embodiment technical solution of the invention is to give an allowable error epsilon, the given allowable error is preferably 10e-6, and is smaller than the given error under the range of the given error, the wavelength displacement change in iterative calculation is very small and can be basically ignored, and another specific embodiment recorded scheme can be set as the maximum iteration number epsilon1。
Calculating a Mean-Shift vector corresponding to the current peak value by using a formula (1), wherein the vector points to the actual peak wavelength, moving the current peak wavelength along the Mean-Shift vector to obtain a new peak wavelength as shown by an arrow in fig. 2, and when the 2 norm of the Mean-Shift vector is greater than a given allowable error epsilon, repeating the operation of calculating the Mean-Shift vector according to the formula (1) and moving the peak wavelength along the Mean-Shift vector until the 2 norm of the Mean-Shift vector is less than the given allowable error epsilon, wherein the final peak wavelength is the obtained peak wavelength.
Further, the unit kernel function G and the kernel radius h in the formula (1) are derived from the kernel density estimation, and the unit kernel function is preferably in a common form in the prior art: a Uniform kernel, a Gaussian kernel, an Epanechnikov kernel, a Triangular kernel, and the like.
Statistical experiments show that different kernel functions have little influence on the density estimation result when the kernel radius h is given, and a common Gaussian kernel function is selected in one of the embodiments according to the present embodiment, as shown in formula (2). The larger the kernel radius h, the smoother the estimated density function, but the larger the deviation; the smaller h, the less the estimated density curve may be. According to the rule of thumb, the size of h is determined by using formula (3).
Wherein n is a wavelength sequence
A number of (a) is
The sample variance of (2).
Further, the weight function w (x) represents the weight of the sample points, here the wavelength sequence
The weight of each wavelength in the peak wavelength extraction process. The greater the wavelength corresponds to light intensity, the greater the weight, given a weight function as shown in equation (4),
w(λj)＝[I(λj)]2formula (4)
I(λj) Represents the wavelength lambdajThe corresponding light intensity.
For a sequence of wavelengths
Corresponding light intensity sequence
The extraction of the peak wavelength is completed by combining the vector calculation steps of equations (1) to (4) and the shift step of fig. 2.
Further, the deviation of the peak wavelength extraction method realized according to the invention is evaluated, and the peak extraction algorithm is evaluated mainly by adopting the evaluation method in a confocal microscope. One point to be emphasized is: the former shows the light intensity corresponding to different scanning heights, and the latter shows the light intensity corresponding to different wavelengths, so that part of terms in the evaluation model need to be transformed. In confocal microscopy, changes in sample height introduce asymmetric axial signal sampling, which in turn leads to large systematic errors in peak extraction. Similarly, in a spectral confocal shift sensor, when the focusing wavelength deviates from the sampling wavelength, it also causes a peak wavelength extraction system error similar to that in a confocal microscope.
Further, the effectiveness of the above algorithm is evaluated as follows: a sampling wavelength value is given as a reference wavelength, the shift of the focusing wavelength relative to the reference wavelength is defined as a wavelength shift Δ λ, as shown in fig. 3, a line corresponding to a symmetric sampling signal in the way is set as the reference wavelength, and if the wavelength shift is 0, a discrete point in the spectral confocal signal is symmetric about an ideal peak value; if the wavelength shift is not 0, as shown by the line corresponding to the asymmetric sampling signal shown in fig. 3, the discrete signal point is not symmetric about the ideal peak, and the transition from symmetric to asymmetric would generate a systematic error in the extraction of the peak wavelength. Such system error variations are periodic and the period is the wavelength sequence sampling interval.
Under this evaluation model, the peak extraction formula is expressed as:
Δ λ represents a wavelength shift, Peak (Δ λ) represents a Peak wavelength extracted at the wavelength shift of Δ λ, a represents a Peak extraction algorithm,
representing the confocal axial intensity response,
representing normally distributed zero mean noise.
In simulation experiment, the sampling interval of the wavelength sequence is set to be L and is set to be between-1/2L and 1/2L]Setting a plurality of wavelength shifts in intervals, and performing 10000 sets of simulation on each wavelength shiftThe peak wavelength is found. For four peak extraction algorithms: the centroid method, the parabola fitting method and the Gaussian fitting method are compared with the Mean-Shift iteration method realized by the invention. The simulation experiment steps are as follows: normalizing the analog spectrum confocal signal, setting a threshold value T to cut off the normalized signal, extracting the peak wavelength, calculating the error between the actual peak wavelength and the calculated peak wavelength, and comparing the quality of the algorithm. In the simulation experiment, the sampling interval of the wavelength sequence is set to be one tenth of the full width at half maximum (FWHM) of a signal, and the cutoff threshold T is set to be 0.35. The accuracy and the efficiency need to be considered simultaneously when the given allowable error epsilon is set, the epsilon is set to be too large, the iteration times of the algorithm are few, the accuracy is low, the epsilon is set to be too small, the iteration times of the algorithm are many, the efficiency is low, and the epsilon is set to be 10 finally-6。
Further, another accuracy of the rms estimation algorithm expected by using the peak wavelength extraction error, and the precision of the rms estimation algorithm using the standard deviation of the peak wavelength extraction error are shown in formulas (6) and (7).
Where E (Δ λ) represents the peak wavelength extraction error, E represents the expectation, SD represents the standard deviation, RMS represents the root mean square, and step represents the wavelength sequence sampling interval. The calculation result shows that the accuracy of the Mean-Shift iteration method is improved by 77.1% compared with the centroid method and is improved by 39.8% compared with the parabola fitting method; the accuracy is improved by 42 percent compared with the centroid method.
In order to evaluate the efficiency of the algorithm, Matlab is used to record the 10000 times of operation of different peak wavelength extraction algorithms on a computer with a processor main frequency of 3.7GHZ, and the single operation time of the centroid method, the Gaussian fitting method, the parabola fitting method and the MS iteration method is respectively 0.0064MS, 6.0817MS, 0.5021MS and 0.0972 MS. The efficiency of the Mean-Shift iteration method is improved by 61 times compared with the Gaussian fitting method and is improved by 4 times compared with the parabolic fitting method. From the view of the calculation complexity, the MS iteration method only needs to iterate for a plurality of times of simple formula calculation, and the fitting method needs to use a least square method which is more time-consuming, so that the efficiency of the Mean-Shift iteration method is greatly improved compared with that of the fitting method.
The experimental verification system mainly comprises a dispersion confocal displacement measurement system and a displacement system, as shown in fig. 4, the dispersion confocal displacement measurement system comprises a spectrometer 5 (Ocean optics Ocean Maya Pro 2000, pixel resolution 0.46nm), an optical fiber coupler 6, a white light source 4(Thorlabs MWWHF2, spectral range 380-780 nm), a confocal probe 1(STILCL20Mg210) and the like, and the displacement system uses a piezoelectric ceramic 3 with high positioning precision and a plane mirror 2(PI P721, axial resolution 10nm) positioned on the piezoelectric ceramic 3.
The experimental procedure was as follows: during the run of the piezoelectric ceramic 3 from 0 to 100 μm, spectral confocal signals were recorded at 1 μm intervals, and 25 frames were acquired for each position, for a total of 101 displacement data and 25 × 101 sets of spectral confocal signal data. The following operations are respectively carried out by different peak value extraction methods: and extracting the peak wavelength of the spectrum confocal signal to obtain 25 multiplied by 101 groups of peak wavelength data, and matching the displacement data with each group of peak wavelength to obtain 25 groups of wavelength-displacement sequences. For each set of wavelength-shift sequences, if the peak wavelength extraction algorithm has no systematic error, the three adjacent points A, B, C are in a straight line, as the shift between two adjacent points varies by only 1 μm, as shown in FIG. 5. A straight line is constructed by using the point A, C, the displacement deviation at the point B is the difference between the displacement value of B and the displacement value corresponding to the wavelength of B on the straight line, and the displacement deviation is used as an index for evaluating the error of the peak value extraction algorithm. Two adjacent odd indexed data points form a straight line, and the even points between the two points are used for extracting the displacement deviation.
The accuracy and precision of the algorithms evaluated according to equations (6) and (7) are shown in fig. 6 and 7 for obtaining the expected and standard deviation at different sample surface heights under different algorithms, respectively. As can be seen from the calculation results: the accuracy of the Mean-Shift iteration method is improved by 71.8% compared with that of a centroid method and is improved by 37.5% compared with that of a parabola fitting method, and the method is similar to a Gaussian fitting method; the precision is improved by 58.1 percent compared with the centroid method, and is similar to the parabola fitting method and the Gaussian fitting method.
The experiment also records the single operation time of different methods, and the centroid method, the parabola fitting method, the Gaussian fitting method and the Mean-Shift iteration method are respectively 0.0064ms, 6.0817ms, 0.5021ms and 0.0972ms, and the efficiency of the Mean-Shift iteration method is calculated to be improved by 73 times compared with the Gaussian fitting method and 5 times compared with the parabola fitting method.
The invention provides a fast high-precision peak wavelength extraction method based on a Mean-Shift algorithm. Simulation results show that the method has good comprehensive performance in the aspects of running speed and extraction precision. The experimental result shows that the method is improved by 71.8% in accuracy compared with the centroid method; compared with a parabola fitting method, the improvement is 37.5%. Compared with the centroid method, the precision is improved by 58.1%. Compared with a parabola fitting method, the operation speed is improved by 5 times; compared with a Gaussian method, the method is improved by 73 times, the contradiction between the running speed and the calculation accuracy of the existing peak value extraction method is effectively solved, and the method has a wide practical application prospect.
It will be understood by those skilled in the art that the foregoing is only a preferred embodiment of the present invention, and is not intended to limit the invention, and that any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. A spectrum confocal signal peak wavelength rapid high-precision extraction method based on Mean-shift comprises the following steps:
STEP1 collecting spectrum confocal signal of spectrum confocal displacement sensor, performing normalization processing, and truncating the normalized signal according to a set light intensity threshold T to obtain a point wavelength sequence
Corresponding light intensity sequence
STEP2 setting iteration initial wavelengthIs λ0；
STEP3 calculating to obtain the point wavelength sequence
A Mean-Shift vector corresponding to the current peak value;
STEP4, moving the current point wavelength sequence along the obtained Mean-Shift vector to obtain a new peak wavelength and a new point wavelength sequence;
STEP5, calculating the 2 norm of the obtained Mean-Shift vector;
STEP6 judges whether the 2 norm of the obtained Mean-Shift vector is less than a given allowable error,
if not, jumping to the STEPs STEP 3-STEP 6;
and if so, the new peak wavelength after the movement is the peak wavelength of the extracted spectral confocal signal, and is used for establishing a mapping relation between the peak wavelength of the signal and the displacement in the signal processing of the spectral confocal displacement sensor so as to obtain the measurement displacement.
2. The Mean-Shift-based spectral confocal signal peak wavelength fast high-precision extraction method according to claim 1, wherein a Mean-Shift vector of the point wavelength sequence is obtained as follows;
wherein G is a unit kernel function, w is a weight function, h is a kernel radius, i is a serial number of the point wavelength sequence, i is an integer between 1 and n, j is a serial number of a Mean-Shift vector corresponding to the point wavelength sequence, and lambda isiAre the wavelength sequence sample points under the corresponding sequence numbers.
3. The Mean-shift-based rapid high-precision extraction method for peak wavelength of spectral confocal signals according to claim 2, wherein the unit kernel function is a gaussian kernel function:
in the formula, n is the number of the current point wavelength sequence calculated iteratively, and σ is the sample variance of the current point wavelength sequence calculated iteratively.
4. The Mean-shift-based rapid high-precision extraction method for peak wavelength of spectral confocal signals according to claim 3, wherein the weight function is as follows: w (lambda)j)＝[I(λj)]2Wherein I (λ)j) Represents the wavelength lambdajThe corresponding light intensity.
5. The Mean-shift-based rapid high-precision extraction method for peak wavelength of spectral confocal signals according to claim 4, wherein the iterative initial wavelength is obtained by a centroid method.
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| CN113074814B (en) * | 2021-03-11 | 2022-03-29 | 华中科技大学 | Method and device for evaluating quality of spectral signal of dispersion confocal sensor |
| CN114370820B (en) * | 2022-03-22 | 2022-07-01 | 武汉精立电子技术有限公司 | Peak extraction method, detection method and system of spectrum confocal displacement sensor |
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