A method and system for suppressing specular highlights in the three-dimensional measurement of the dynamic morphology of motor gear shafts.

Abstract

The application belongs to the technical field of three-dimensional measurement, and provides a high light suppression method and system suitable for three-dimensional measurement of dynamic topography of motor gear rotating shafts. The method is realized through the following steps: firstly, the Fourier transform spectrum of the saturated stripe pattern of the high light surface of the motor gear rotating shaft is analyzed in depth; then, the Bartlett low-pass filter (BLPF) is used to filter out the high harmonic components introduced by the saturation of the stripe intensity, so as to suppress the intensity saturation problem; finally, because the BLPF also leads to the non-sinusoidal nature of the stripe pattern, a phase error model of the non-sinusoidal nature of the stripe pattern is established, and the Hilbert transform (HT) is used to correct the phase error.

Description

Technical Field

[0001] This application relates to the field of three-dimensional measurement technology, and provides a method for suppressing highlights in three-dimensional measurement of the dynamic shape of motor gear shafts. Background Technology

[0002] Accurate 3D measurement is crucial in the manufacturing, quality inspection, and operational monitoring of motor gear shafts. Due to the limited dynamic range of industrial cameras in structured light 3D measurement systems, the high-gloss surface of motor gear shafts with non-Lambertian reflection characteristics causes saturation distortion in the acquired images, leading to 3D measurement errors. The technical challenge in achieving 3D measurement of dynamic gear shafts lies in the time-varying and random nature of the saturation characteristics of the acquired images, which varies with the shape.

[0003] To address this issue, researchers have proposed various high dynamic range (HDR) measurement methods, but these methods all have certain limitations. Existing methods such as multi-exposure, positive and negative fringe projection algorithms, adaptive fringe projection algorithms, and positive and negative adaptive fringe projection methods all require additional image assistance; polarization filtering methods require additional hardware adjustments and are not suitable for structured light 3D measurement of sheet metal components in dynamic scenes. Therefore, a novel high dynamic range 3D measurement technique based on a Butterworth low-pass filter (BLPF) and Hilbert transform (HT), abbreviated as BLPFHT, was designed.

[0004] In summary, existing measurement methods cannot adequately meet the demands for high-precision, high-efficiency three-dimensional measurement of motor gear shafts and gears. Developing a new measurement method that effectively overcomes the problem of stripe pattern intensity saturation and improves measurement accuracy and efficiency is of significant practical importance for promoting the development of motor-related industries. Summary of the Invention

[0005] To overcome the shortcomings of the prior art, this invention provides a method for suppressing specular highlights in the dynamic three-dimensional measurement of motor gear shafts, used for high-precision dynamic three-dimensional measurement of rotating shafts. This method can efficiently and accurately reconstruct the 3D shape of non-Lambertian reflective surfaces without additional image or hardware assistance, and is suitable for specular highlight suppression in the dynamic three-dimensional measurement of gear shafts.

[0006] To achieve the above objectives, the technical solution adopted by this invention is: a method for suppressing highlights in three-dimensional measurement of the dynamic morphology of a motor gear shaft, comprising the following steps:

[0007] S1. Analyze the Fourier transform spectrum of the saturation fringe pattern on the motor gear shaft with localized specular reflection.

[0008] S2. Use a Butterworth low-pass filter to filter the saturated stripe pattern, filter out high-order harmonic components, and thus suppress local high-gloss reflections on the motor gear shaft.

[0009] S3. The Butterworth low-pass filter leads to the non-sinusoidal nature of the fringes, which further establishes a phase error model;

[0010] S4. Use Hilbert transform to correct phase error;

[0011] S5. Use the phase information corrected by Hilbert transform to perform three-dimensional reconstruction.

[0012] Furthermore, in S1, the Fourier transform spectrum of the saturation fringe pattern of the motor gear shaft with localized specular reflection is analyzed using the following method:

[0013] S11, Projected three-step phase-shifting fringes, the height and width of the fringe pattern are H and W respectively, and its intensity can be expressed by formula (1):

[0014] I n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ], n=1,2...N (1);

[0015] δ n =2π(n-1) / N;

[0016] In the formula, A and B represent the background and modulation intensity, respectively, n is the phase shift exponent, n∈[1,N], N is the total number of phase shift steps, and δ n The phase shift is represented by φ, which indicates the phase information modulated by the object's depth.

[0017] S12. Perform a Fourier transform on the captured stripe pattern to obtain the spectrum data, as shown in formula (2):

[0018]

[0019] In the formula, I n (x,y) is the intensity value of the image captured by the camera at pixel coordinates (x,y), and (u,v) represents the coordinates in the frequency domain, corresponding to the spatial frequency components of the stripe pattern.

[0020] S13. Analyze the spectrum data. The high-frequency component introduced by the stripe intensity saturation increases with the increase of the saturation coefficient.

[0021] Furthermore, in S2, a Butterworth low-pass filter is used to filter the saturation stripe pattern, removing higher harmonic components, thereby suppressing localized high-gloss reflections from the motor gear shaft. The following method is employed:

[0022] S21. Based on the spectrum analysis results, determine the design parameters of the Butterworth low-pass filter. The Butterworth low-pass filter can be expressed as formula (3):

[0023]

[0024] In the formula, H(u,v) is the Butterworth filter, D0 is the cutoff frequency, c represents the order of the BLPF, and D(u,v) can be expressed as formula (4):

[0025]

[0026] S22. Applying the Butterworth low-pass filter to the Fourier transform of the saturated fringe pattern, the Fourier transform of the saturated fringe pattern can be expressed as formula (5):

[0027]

[0028] Perform an inverse Fourier transform (IFT) on equation (5) to obtain the low-pass filtering result in the spatial domain, as shown in equation (6):

[0029]

[0030] In the formula, M and L represent the height and width of the frequency domain image, respectively.

[0031] Furthermore, the Butterworth low-pass filter in S3 causes non-sinusoidal fringes, so a phase error model was established using the following method:

[0032] S31, Intensity of captured distorted fringes This can be expressed as formula (7):

[0033]

[0034] In the formula, α is the surface reflectance of the object, r is the gamma factor, and B0 and B k φ represents the amplitudes of the DC component and the Kth harmonic component, respectively. n φ represents the modulation phase coupled with the phase shift. n =φ+δn;

[0035] S32. The modulation phase is calculated using formula (8), and the gamma distortion phase based on LSA is calculated using formula (9):

[0036]

[0037]

[0038] The extracted phase error model is as follows:

[0039]

[0040] In the formula, G N-1 =B N-1 / B1 is the normalized harmonic amplitude ratio, φ C φ represents the actual phase, φ represents the ideal phase, and N represents the total number of phase shift steps.

[0041] Furthermore, in S4, the Hilbert transform is used to correct the phase error, using the following method: S41, the HT of the nth captured phase-shifted image can be expressed as:

[0042]

[0043] In the formula, Η[·] represents the HT operator;

[0044] Performing an HT transform on equation (8), the HT domain phase φ based on LSA is obtained. H It can be represented as:

[0045]

[0046] The gamma distortion phase φ in the HT domain is calculated using formula (13). HC :

[0047]

[0048] The phase error model after HT transformation is as follows:

[0049]

[0050] S42, due to Δφ and Δφ H With equal amplitudes and opposite directions, the error can be significantly suppressed by averaging the phases of the two domains, as shown in formula (15):

[0051]

[0052] Furthermore, in S5, the phase information corrected by Hilbert transform is used for 3D reconstruction, employing the following method:

[0053] The phase expansion and reconstruction of the measured object are performed using a three-frequency layered time-domain phase expansion method. H Φ M Φ L The unwrapped phase corresponding to the frequency is shown in formula (16):

[0054]

[0055] In the formula, φ H φ M φ L These represent the expanded phases for high, mid, and low frequencies, respectively, f HIndicates high frequency, f M Indicates intermediate frequency, f L This indicates low frequency, and round is the rounding function.

[0056] Compared with the prior art, the beneficial effects of this application are as follows:

[0057] This invention utilizes a Butterworth low-pass filter (BLPF) to effectively suppress grating intensity saturation without the need for additional auxiliary images or hardware adjustments. Combined with High-Temperature (HT) correction for phase errors, it enables accurate measurement of the 3D shape of non-Lambertian reflective surfaces, overcoming the limitations of traditional methods in dynamic 3D topography measurement scenarios. The proposed method requires no additional images or hardware assistance and is suitable for specular suppression in dynamic 3D measurements of gear shafts. Attached Figure Description

[0058] Figure 1 The flowchart shows the implementation process of the proposed method.

[0059] Figure 2 The FT spectra of stripe patterns with different saturation coefficients.

[0060] Figure 3 For the identification of saturated regions.

[0061] Figure 4 Three striped patterns with BLPF.

[0062] Figure 5 For phase comparison.

[0063] Figure 6 To incorporate striped patterns.

[0064] Figure 7 A comparison of the accuracy of the proposed method in 3D geometric reconstruction. Detailed Implementation

[0065] The present invention will now be described in detail with reference to the accompanying drawings and specific embodiments.

[0066] This invention provides a method for suppressing highlights in the three-dimensional measurement of the dynamic shape of motor gear shafts, enabling three-dimensional measurement of dynamic gear shafts. This method can effectively suppress the three-dimensional measurement error caused by grating intensity saturation without adding additional images or hardware assistance.

[0067] The method of the present invention includes the following steps:

[0068] 1. Analyze the Fourier transform spectrum of the saturated fringe pattern:

[0069] First, a measurement system is established, consisting of a camera, a projector, and a computer. The number of projection fringe periods based on a three-frequency (layered) TPU is {180, 15, 1}, and the height and width of the fringe pattern are H and W, respectively. The intensity of the fringe pattern projected onto the surface of the motor gear shaft by the projector is captured, and the intensity of the fringe projection is calculated using formula (1):

[0070] I n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ], n=1,2...N (1)

[0071] In the formula, A and B represent the background and modulation intensity, respectively, n is the phase shift index (n∈[1,N]), N is the total number of phase shift steps, and δ n =2π(n-1) / N is the phase shift, and φ represents the phase information modulated by the object's depth. From the camera's perspective, non-Lambertian reflections on the surface of the motor gear shaft cause local intensity saturation of the captured fringe pattern. The saturated fringe pattern, as simulated by a computer, can be expressed by the formula:

[0072]

[0073] In the formula, F is the saturation coefficient of the computer-simulated stripe pattern. If F > 1, the computer-simulated stripe pattern will introduce intensity saturation.

[0074] The Fourier transform (FT) of the acquired saturated grating image was analyzed using formula (3) to determine its spectral characteristics (e.g., Figure 2 As shown):

[0075]

[0076] Figure 2 (a) shows a computer-simulated object. Figure 2 (b) shows a computer-simulated stripe pattern using k=1.

[0077] Figure 2 (c) shows the computer-simulated fringe pattern using k=2. The cross-section in the figure is shown. We analyzed the fringe patterns with k=1 and k=2 using the Fourier Transform (FT), and the corresponding Fourier Transform spectra are shown below. Figure 2 (e) and Figure 2 As shown in (g), the zero-frequency component (f0) represents the background intensity, and the fundamental frequency component (f1) represents the modulation intensity. If the fringe intensity is saturated, in addition to the fundamental frequency component (f1), frequency components (f2, f3, etc.) are also introduced. The high-frequency components increase with the increase of the saturation coefficient k.

[0078] These higher harmonic components are caused by grating intensity saturation and need to be filtered out in subsequent steps.

[0079] 2. Filter the saturation stripe pattern using a Butterworth low-pass filter:

[0080] The cutoff frequency is optimized through an iterative method. This involves projecting an image with a grayscale value of 255 and identifying pixels with grayscale values ​​greater than 254 as saturated pixels. Figure 3 As shown, the cutoff frequency of the BLPF is gradually increased to perform low-pass filtering on the locally saturated raster image. When the intensity of the filtered fringe image is lower than the saturation threshold (e.g., 254), the current cutoff frequency is taken as the final cutoff frequency D0.

[0081] The Butterworth low-pass filter can be expressed as formula (4):

[0082]

[0083] In the formula, H(u,v) is the Butterworth filter, D0 is the cutoff frequency, c represents the order of the BLPF, and D(u,v) can be expressed as formula (5):

[0084]

[0085] Applying a Butterworth low-pass filter to the Fourier transform of the saturated fringe pattern to suppress high-frequency components, the Fourier transform of the saturated fringe pattern can be expressed as Equation (6):

[0086] L(u,v)=I n FT (u,v)*H(u,v) (6);

[0087] The filtered stripe pattern is subjected to inverse Fourier transform to obtain the low-pass filtering result in the spatial domain, as shown in Equation (7):

[0088]

[0089] In the formula, M = 1280 and L = 1024.

[0090] The filtered raster image will remove high-order harmonic components until the pixel intensity of all three fringe patterns is not saturated, ensuring the accuracy of the wrap-around phase extraction based on the three-step phase shift algorithm. This reduces phase errors caused by saturation, such as... Figure 4 As shown.

[0091] 3. Phase correction based on HT:

[0092] from Figure 4As can be seen, after BLPF processing, the intensity of saturated pixels decreases due to the gamma effect in the projector and quantization errors in the camera. Through experiments, we also found that the phase extracted from the BLPF-processed stripe pattern exhibits periodic phase errors.

[0093] The intensity of the captured distorted fringes can be expressed as formula (8):

[0094]

[0095] In the formula, α is the surface reflectance of the object, r is the gamma factor, and B0 and B k φ represents the amplitudes of the DC component and the Kth harmonic component, respectively. n φ represents the modulation phase coupled with the phase shift. n =φ+δ n .

[0096] Based on the least squares method (LSA), the modulation phase is calculated using formula (9), and the gamma distortion phase based on LSA is calculated using formula (10):

[0097]

[0098]

[0099] The phase error model extracted by the least squares phase shift algorithm (LSA) is as follows:

[0100]

[0101] In the formula, G N-1 =B N-1 / B1 is the normalized harmonic amplitude ratio.

[0102] The HT of the nth captured phase-shifted image can be represented as:

[0103]

[0104] In the formula, Η[·] represents the HT operator;

[0105] To achieve equality with φ, we perform an HT transform on equation (8). The HT-domain phase based on LSA can be expressed as:

[0106]

[0107] The gamma distortion phase in the HT domain is calculated using formula (13):

[0108]

[0109] The phase error model after HT transformation is as follows:

[0110]

[0111] Due to Δφ and Δφ H With equal amplitudes and opposite directions, averaging the phase of the two domains using formula (15) can significantly suppress errors:

[0112]

[0113] 4. Perform 3D reconstruction using the corrected phase information:

[0114] The phase unfolding and reconstruction of the measured object are performed using three-frequency layered time-domain phase unfolding (TPU), Φ H Φ M Φ L The unwrapped phase corresponding to the frequency is shown in formula (17):

[0115]

[0116] In the formula, φ H φ M φ L These represent the expanded phases for high, mid, and low frequencies, respectively, f H Indicates high frequency, f M Indicates intermediate frequency, f L This indicates low frequency, and round is the rounding function.

[0117] 5. Algorithm:

[0118] The implementation steps of the proposed method are illustrated through experiments on the motor gear shaft, such as... Figure 5 As shown in Figure S1, the Fourier transform spectrum of the saturated stripe pattern on the locally highly reflective motor gear shaft is analyzed. A computer is used to perform a Fourier transform on the captured stripe pattern, and the spectral data is analyzed. These high-frequency components increase with the increase of the saturation coefficient. For example... Figure 2 (e) and Figure 2 As shown in (g).

[0119] S2, using a Butterworth low-pass filter to filter the saturation stripe pattern, removing higher harmonic components, and projecting an image with a grayscale value of 255, identifying pixels with grayscale values ​​greater than 254 as saturated pixels (e.g., ...). Figure 3 (As shown). The cutoff frequency D0 is determined by iterative estimation. We use a 6th-order BLPF and perform an inverse Fourier transform on the fringe pattern according to formula (6) to obtain formula (7), thus obtaining the low-pass filtering result. Figure 4 Three stripe patterns with BLPF are shown, and the pixel intensity in all three stripe patterns is unsaturated.

[0120] S3, fringe fusion and absolute phase calculation:

[0121] The absolute phase extracted from the original stripe pattern and the final fused stripe pattern is as follows: Figure 5 (a) and Figure 5 As shown in (b), extract Figure 5 (a) and Figure 5 (b) Obtained after a cross-section Figure 5 (c). By Figure 5 (c) It can be seen that the error in the highlight area of ​​the motor shaft has been compensated.

[0122] S4, Hilbert transform for phase error compensation:

[0123] Because the calculated phase after Butterworth low-pass filtering has a periodic phase error, such as Figure 5 As shown in (d), phase error compensation is performed using Hilbert transform, and the result after compensation is as follows. Figure 5 As shown in (e), in comparison Figure 5 (a) and Figure 5 (e) It can be seen that the proposed method suppresses the measurement error caused by the highlights on the motor shaft. (Comparison) Figure 5 (b) and Figure 5 (e) It can be seen that the proposed method suppresses the periodic error caused by Butterworth low-pass filter.

[0124] S5, using the corrected phase information and combined with the measurement system calibration parameters, performs three-dimensional reconstruction:

[0125] Using the corrected phase information and combined with the calibration parameters of the measurement system, we can obtain, as follows Figure 7 The results of the three-dimensional geometric reconstruction are shown. Figure 7 The comparison shows that the 3D reconstruction accuracy obtained by the proposed method is much higher than that of the traditional method. To achieve quantitative comparison, we calculated the root mean square error (RMSE) of the traditional method and the proposed method respectively. The RMSE of the proposed method is 85.1% lower than that of the traditional method. The experiment shows that the proposed method not only effectively suppresses the error of the motor shaft with local specular highlights, but also does not require additional image and hardware assistance, and is suitable for specular suppression in dynamic 3D measurement of gear shafts.

[0126] A specular suppression system for three-dimensional measurement of the dynamic morphology of motor gear shafts includes a data acquisition unit, a data processing unit, and an output unit.

[0127] The data acquisition unit is used to acquire and analyze data;

[0128] Data Processing Unit: Analyzes the Fourier transform spectrum of the saturated fringe pattern of the motor gear shaft with localized high-light reflection; filters the saturated fringe pattern using a Butterworth low-pass filter to remove higher harmonic components; the Butterworth low-pass filter causes non-sinusoidal fringes, further establishing a phase error model; corrects the phase error using a Hilbert transform; performs 3D reconstruction using the phase information corrected by the Hilbert transform; Output Unit: Visualizes the processing results.

Claims

1. A method for high light suppression for dynamic profile three-dimensional measurement of a motor gear rotating shaft, characterized in that, It comprises the following steps: S1, analyzing the Fourier transform spectrum of the saturated fringe pattern of the motor gear rotating shaft with local highlight reflection; S11. Projecting three-step phase shift fringe, the height and width of the fringe pattern are H and W respectively, and its intensity can be expressed as formula (1): （1）； wherein A and B denote the background and modulation intensity, respectively, n is the phase shift index, ，N is the total number of phase shift steps, is the phase shift amount, denotes the phase information modulated by the object depth; S12. Fourier transform is performed on the captured fringe pattern to obtain frequency spectrum data, as shown in formula (2): ; wherein x,y is an intensity value of the image captured by the camera at pixel coordinates x,y denotes coordinates in the frequency domain, corresponding to spatial frequency components of the fringe pattern;​​ S13. Analyzing the frequency spectrum data, the high-frequency component introduced by the saturation of fringe intensity increases with the increase of saturation coefficient; S2, filtering the saturated fringe pattern with a Butterworth low-pass filter to filter out high harmonic components, thereby suppressing the local highlight reflection of the motor gear rotating shaft; S3, the non-sinusoidal nature of the fringe caused by Butterworth low-pass filtering further establishes a phase error model; S4, correcting the phase error by Hilbert transform; S5, three-dimensional reconstruction is performed using the phase information corrected by Hilbert transform.

2. The method of claim 1, wherein the method is used for dynamic profile 3D measurement of a motor gear rotating shaft with highlight suppression. The specific steps of S2 are as follows: S21, based on the results of spectral analysis, the design parameters of the Butterworth low-pass filter are determined, and the Butterworth low-pass filter can be expressed as formula (3): (3); In the formula, is a Butterworth filter, is a cutoff frequency, c denotes the order of the BLPF, may be expressed as formula (4): (4); S22, applying the Butterworth low-pass filter to the Fourier transform result of the saturated fringe pattern, and the FT of the saturated fringe pattern can be expressed as formula (5): (5); Performing inverse Fourier transform IFT on formula (5) to obtain the low-pass filtering result in the spatial domain, as shown in formula (6): (6); wherein M and L denote the height and width of the frequency domain image, respectively.

3. The highlight suppression method for dynamic topography three-dimensional measurement of motor gear rotating shaft according to claim 1, wherein step S3 is specifically as follows: S31, captured distorted fringe intensity may be expressed as equation (7): (7); wherein is the surface reflectivity of the object, is the gamma factor, B 0 and B k are the direct current and k amplitudes of the mth indicates the modulation phase of the phase-shifted coupling, ; S32, the modulation phase is calculated by formula (8), and the gamma distortion phase based on LSA is calculated by formula (9): (8); (9); The extracted phase error model is: (10); wherein is the normalized harmonic amplitude ratio, is the actual phase, represents the phase information modulated by the depth of the object.

4. The method of claim 3, wherein the method further comprises: Step S4 is specifically as follows: S41, the HT of the nth captured phase shift image is expressed as: （11）； Wherein H[•] represents the HT operator; HT transforming equation (8), the HT domain phase based on LSA is represented as: （12）； The gamma distortion phase of the HT domain is calculated using equation (13) : （13）； The phase error model after HT transformation is: （14）； S42、Since With The error can be significantly suppressed by averaging the phase of the two domains with equal magnitude and opposite direction, as shown in equation (15): （15）。 5. The method of claim 1, wherein the method further comprises: In S5, three-dimensional reconstruction is performed using the corrected phase information, which specifically includes: The three-frequency layered time-domain phase unwrapping is used for phase unwrapping and reconstruction of the measured object, The unwrapped phase of the corresponding frequency is shown as formula (16): （16）； wherein are the unwrapped phases of high, medium and low frequencies, respectively, denotes high frequency, denotes medium frequency, denotes low frequency, and round is a rounding function.

6. A system for high light suppression in dynamic profile three-dimensional measurement of a motor gear rotating shaft, using the method of any one of claims 1-5. It comprises a data acquisition unit, a data processing unit and an output unit; The data acquisition unit is used to acquire analysis data; Data processing unit: analyze the Fourier transform spectrum of the saturated fringe pattern of the motor gear rotating shaft with local highlight reflection; use Butterworth low-pass filter to filter the saturated fringe pattern to filter out high harmonic components; Butterworth low-pass filtering leads to the non-sinusoidal nature of the fringe, further establishing a phase error model; Hilbert transform is used to correct the phase error; three-dimensional reconstruction is performed using the phase information corrected by Hilbert transform; Output unit: visual output of the processing result.

Images