Highlight suppression method and system suitable for three-dimensional measurement of dynamic morphology of motor gear rotating shaft

Abstract

The invention belongs to the technical field of three-dimensional measurement, and provides a highlight suppression method and system suitable for three-dimensional measurement of dynamic morphology of a motor gear rotating shaft. The method is realized through the following steps: firstly, deeply analyzing a Fourier transform spectrum of a saturated stripe pattern on the highlight surface of the motor gear rotating shaft; secondly, a Butterworth low-pass filter (BLPF) is provided to filter out higher harmonic components introduced by stripe intensity saturation, so that the intensity saturation problem is suppressed; and finally, because the BLPF also causes the non-sinusoidal fringe pattern, establishing a non-sinusoidal phase error model of the fringe pattern, and proposing to use Hilbert transform (HT) to correct the phase error.

Description

Technical Field

[0001] The present application belongs to the field of three-dimensional measurement technology and provides a highlight suppression method suitable for three-dimensional measurement of the dynamic morphology of a motor gear shaft. Background Art

[0002] Accurate 3D measurement is crucial for the manufacturing, quality inspection, and operational monitoring of motor gear shafts. Due to the limited dynamic range of industrial cameras used in structured light 3D measurement systems, the specular surface of motor gear shafts with non-Lambertian reflectance can saturate and distort the captured image, leading to 3D measurement errors. A technical challenge in achieving 3D measurement of dynamic gear shafts lies in the time-varying and random nature of the saturation characteristics of the captured image, which varies with the shaft's shape.

[0003] To address this issue, researchers have proposed a variety of high dynamic range (HDR) measurement methods, but these methods all have limitations. Existing multi-exposure methods, forward and reverse fringe projection algorithms, adaptive fringe projection algorithms, and forward and reverse adaptive fringe projection methods require additional image support. Polarization filtering methods require additional hardware adjustments and are unsuitable for structured light 3D measurement of sheet metal components in dynamic scenes. To address this, a new high dynamic range 3D measurement technique based on a Butterworth low-pass filter (BLPF) and Hilbert transform (HT) was designed, referred to as BLPFHT.

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

[0005] To overcome the shortcomings of the prior art, the present invention provides a method for suppressing highlight during dynamic 3D topography measurement of motor gear shafts. This method is used for high-precision dynamic 3D measurement of rotating shafts. This method efficiently and accurately reconstructs the 3D shape of non-Lambertian reflective surfaces without the need for additional imaging or hardware assistance, making it suitable for suppressing highlight during dynamic 3D measurement of gear shafts.

[0006] To achieve the above-mentioned object, the technical solution adopted by the present invention is: a highlight suppression method suitable for 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 saturated fringe pattern of the motor gear shaft with local high light reflection;

[0008] S2. Filter the saturated fringe pattern using a Butterworth low-pass filter to remove high-order harmonic components, thereby suppressing local high-light reflections on the motor gear shaft;

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

[0010] S4, using Hilbert transform to correct the phase error;

[0011] S5. Perform three-dimensional reconstruction using the phase information corrected by Hilbert transform.

[0012] Furthermore, the Fourier transform spectrum of the saturated fringe pattern of the motor gear shaft with local high light reflection is analyzed in S1 using the following method:

[0013] S11, project three-step phase-shifted stripes. The height and width of the stripe pattern are H and W respectively. Its intensity can be expressed as 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] Where 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, δ n is the phase shift, φ represents the phase information modulated by the object depth;

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

[0018]

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

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

[0021] Furthermore, in S2, a Butterworth low-pass filter is used to filter the saturated fringe pattern to remove high-order harmonic components, thereby suppressing the local high light reflection of the motor gear shaft. The following method is used:

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

[0023]

[0024] Where 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. Apply the Butterworth low-pass filter to the Fourier transform result of the saturated fringe pattern. The FT of the saturated fringe pattern can be expressed as formula (5):

[0027]

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

[0029]

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

[0031] Furthermore, the Butterworth low-pass filtering in S3 leads to the non-sinusoidal nature of the fringes, and a phase error model is further established using the following method:

[0032] S31, captured distortion fringe intensity It can be expressed as formula (7):

[0033]

[0034] Where α is the surface reflectivity of the object, r is the gamma factor, B0 and B k are the amplitudes of the DC component and the K-order harmonic component, φ n represents the modulation phase coupled with the phase shift, φ n =φ+δn;

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

[0036]

[0037]

[0038] The extracted phase error model is:

[0039]

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

[0041] Furthermore, the Hilbert transform is used in S4 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] Where Η[·] represents the HT operator;

[0044] Perform HT transformation on formula (8), and the HT domain phase φ based on LSA is H It can be expressed 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:

[0049]

[0050] S42, due to Δφ and Δφ H The amplitudes are equal and the directions are opposite. 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 using the following method:

[0053] The three-frequency layered time domain phase unwrapping is used to unwrap the phase and reconstruct the object under test, Φ H , Φ M , Φ L The unwrapped phase corresponding to the frequency is shown in formula (16):

[0054]

[0055] Where, φ H 、φ M 、φ L are the unfolded phases of high, medium and low frequencies, respectively, f HIndicates high frequency, f M Indicates the intermediate frequency, f L Indicates low frequency, and round is the rounding function.

[0056] Compared with the prior art, this application has the following beneficial effects:

[0057] This method uses a Butterworth low-pass filter (BLPF) to effectively suppress grating intensity saturation without additional auxiliary images or hardware adjustments. Combined with HT to correct phase errors, it accurately measures the 3D shape of non-Lambertian reflective surfaces, resolving the inapplicability of traditional methods in dynamic 3D topography measurement scenarios. The proposed method, which requires no additional images or hardware, is suitable for suppressing highlights in dynamic 3D measurement of gear shafts. BRIEF DESCRIPTION OF THE DRAWINGS

[0058] Figure 1 The flowchart of the implementation of the proposed method is shown in Figure 2.

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

[0060] Figure 3 Identification of saturated regions.

[0061] Figure 4 There are three stripe patterns with BLPF.

[0062] Figure 5 For phase comparison.

[0063] Figure 6 For fusion stripe pattern.

[0064] Figure 7 Comparison of the accuracy of 3D geometric reconstruction using the proposed method. DETAILED DESCRIPTION

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

[0066] The present invention provides a high-light suppression method suitable for three-dimensional measurement of the dynamic morphology of a motor gear shaft, thereby realizing three-dimensional measurement of the dynamic gear shaft. 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 comprises the following steps:

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

[0069] First, a measurement system consisting of a camera, a projector, and a computer was established. The number of projected fringe periods based on the triple-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 by the projector onto the surface of the motor gear shaft 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] Where 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, the non-Lambertian reflection on the motor gear shaft surface causes local intensity saturation in the captured fringe pattern. The saturated fringe pattern simulated by a computer can be expressed as:

[0072]

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

[0074] Formula (3) is used to perform Fourier transform (FT) on the collected saturated grating image to analyze its spectrum characteristics (such as Figure 2 shown):

[0075]

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

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

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

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

[0080] The cutoff frequency is optimized by an iterative method. By projecting an image with a grayscale value of 255, pixels with grayscale values ​​greater than 254 are identified as saturated pixels, such as Figure 3 As shown in the figure, the cutoff frequency of the BLPF is gradually increased to perform low-pass filtering on the locally saturated grating image. When the intensity of the filtered fringe image is lower than the saturation threshold (such as 254), the current cutoff frequency is used as the final cutoff frequency D0.

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

[0082]

[0083] Where 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] A Butterworth low-pass filter is applied to the Fourier transform result of the saturated fringe pattern to suppress the high-frequency components. The FT of the saturated fringe pattern can be expressed as formula (6):

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

[0087] The filtered fringe pattern is inversely Fourier transformed to obtain the low-pass filtering result in the spatial domain, as shown in formula (7):

[0088]

[0089] Wherein, M=1280, L=1024.

[0090] The filtered grating image will remove high-order harmonic components until the pixel intensities of all three fringe patterns are not saturated, ensuring the accuracy of the wrapped phase extraction based on the three-step phase shift algorithm. This will reduce the phase error caused by saturation, such as Figure 4 shown.

[0091] 3. Phase correction based on HT:

[0092] from Figure 4As can be seen in Figure 2, after BLPF processing, the intensity of saturated pixels decreases due to the gamma effect of the projector and the quantization error of the camera. Through experiments, we also found that the phase extracted from the fringe pattern processed by BLPF has periodic phase errors.

[0093] The captured distortion fringe intensity can be expressed as formula (8):

[0094]

[0095] Where α is the surface reflectivity of the object, r is the gamma factor, B0 and B k are the amplitudes of the DC component and the K-order harmonic component, φ n represents the modulation phase coupled with the phase shift, φ 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:

[0100]

[0101] Where 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 expressed as:

[0103]

[0104] Where Η[·] represents the HT operator;

[0105] In order to be equal to φ, we perform HT transformation on formula (8), and 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:

[0110]

[0111] Since Δφ and Δφ H The amplitudes are equal and the directions are opposite. The error can be significantly suppressed by averaging the phases of the two domains using formula (15):

[0112]

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

[0114] The three-frequency layered time domain phase unwrapping (TPU) is used to unwrap the phase and reconstruct the object under test. H , Φ M , Φ L The unwrapped phase corresponding to the frequency is shown in formula (17):

[0115]

[0116] Where, φ H 、φ M 、φ L are the unfolded phases of high, medium and low frequencies, respectively, f H Indicates high frequency, f M Indicates the intermediate frequency, f L Indicates low frequency, and round is the rounding function.

[0117] 5. Algorithm:

[0118] The implementation steps of the proposed method are explained by conducting experiments on the motor gear shaft. Figure 5 As shown in S1, the Fourier transform spectrum of the saturated fringe pattern of the local high reflective motor gear shaft is analyzed. The captured fringe pattern is Fourier transformed by a computer and the spectrum data is analyzed. These high-frequency components increase with the increase of the saturation coefficient. Figure 2 (e) and Figure 2 (g) shown.

[0119] S2, using a Butterworth low-pass filter to filter the saturated fringe pattern, filtering out the high-order harmonic components. By projecting an image with a grayscale value of 255, pixels with a grayscale value greater than 254 are identified as saturated pixels (such as Figure 3 The cutoff frequency D0 is determined by iterative estimation. We use a 6th-order BLPF and perform inverse Fourier transform on the fringe pattern according to formula (6) to obtain formula (7) to obtain the low-pass filtering result. Figure 4 Three fringe patterns with BLPF are shown, and the pixel intensities in all three fringe patterns are desaturated.

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

[0121] The absolute phases extracted from the original fringe pattern and the final fused fringe pattern are as follows: Figure 5 (a) and Figure 5 As shown in (b), extract Figure 5 (a) and Figure 5 (b) After a row of cross sections, we get Figure 5 (c) By Figure 5 (c) It can be seen that the error in the highlight area of ​​the motor shaft is compensated.

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

[0123] Since the calculated phase after Butterworth low-pass filtering has periodic phase errors, such as Figure 5 As shown in (d), Hilbert transform is used to compensate for phase error. The compensated result is as follows: Figure 5 As shown in (e), compared Figure 5 (a) and Figure 5 (e) It can be seen that the proposed method suppresses the measurement error caused by the highlight of the motor shaft. Figure 5 (b) and Figure 5 (e) It can be seen that the proposed method suppresses the periodic error caused by the Butterworth low-pass filter.

[0124] S5, using the corrected phase information and combined with the measurement system calibration parameters to perform 3D reconstruction:

[0125] The corrected phase information is used in combination with the calibration parameters of the measurement system to obtain Figure 7 The 3D geometric reconstruction results are shown in Figure 2. Figure 7 Comparison shows that the 3D reconstruction accuracy achieved by the proposed method is significantly higher than that achieved by conventional methods. To achieve a quantitative comparison, we calculated the root mean square error (RMSE) of the conventional and proposed methods. The proposed method achieves an RMSE 85.1% lower than the conventional method. This experiment demonstrates that the proposed method not only effectively suppresses errors in motor shafts with local highlights, but also does so without the need for additional imaging or hardware assistance, making it suitable for highlight suppression in dynamic 3D measurement of gear shafts.

[0126] A high light suppression system suitable for three-dimensional measurement of dynamic morphology of motor gear shaft, comprising a data acquisition unit, a data processing unit and an output unit;

[0127] The data acquisition unit is used to obtain analysis data;

[0128] Data processing unit: Analyze the Fourier transform spectrum of the saturated fringe pattern of the motor gear shaft with local high light reflection; Use Butterworth low-pass filter to filter the saturated fringe pattern to remove high-order harmonic components; Butterworth low-pass filtering causes the non-sinusoidal nature of the fringe, and further establish a phase error model; Use Hilbert transform to correct the phase error; Use the phase information corrected by Hilbert transform to perform three-dimensional reconstruction; Output unit: Visualize the processing results.

Claims

1. A method for suppressing highlights in three-dimensional measurement of dynamic topography of motor gear shafts, characterized in that: The following steps are involved: S1. Analyze the Fourier transform spectrum of the saturated fringe pattern of the motor gear shaft with local high light reflection; S2. Filter the saturated fringe pattern using a Butterworth low-pass filter to remove high-order harmonic components, thereby suppressing local high-light reflections on the motor gear shaft; S3, Butterworth low-pass filtering leads to the non-sinusoidal nature of the fringes, which further establishes the phase error model; S4, using Hilbert transform to correct the phase error; S5. Perform three-dimensional reconstruction using the phase information corrected by Hilbert transform.

2. The method for suppressing highlights in three-dimensional measurement of dynamic topography of a motor gear shaft according to claim 1, characterized in that: The specific steps of S1 are as follows: S11, project three-step phase-shifted stripes. The height and width of the stripe pattern are H and W respectively. Its intensity can be expressed as formula (1): Yo n (x,y)=A(x,y)+B(x,y)cos[φ(x,y)+δ n ],n=1,2...N (1); d n =2π(n-1) / N; Where 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, δ n is the phase shift, φ represents the phase information modulated by the object depth; S12. Perform Fourier transform on the captured fringe pattern to obtain spectrum data, as shown in formula (2): Where, I n (x,y) is the intensity value of the pixel coordinate (x,y) in the image captured by the camera, and (u,v) represents the coordinates in the frequency domain, corresponding to the spatial frequency components of the fringe pattern; S13. Analyze the spectrum data; the high-frequency component introduced by the fringe intensity saturation increases with the increase of the saturation coefficient.

3. The method for suppressing highlights in three-dimensional measurement of dynamic topography of a motor gear shaft according to claim 1, characterized in that: The specific steps of S2 are as follows: S21. Based on the spectrum analysis results, the design parameters of the Butterworth low-pass filter are determined. The Butterworth low-pass filter can be expressed as formula (3): Where 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): S22. Apply the Butterworth low-pass filter to the Fourier transform result of the saturated fringe pattern. The FT of the saturated fringe pattern can be expressed as formula (5): Perform inverse Fourier transform (IFT) on formula (5) to obtain the low-pass filtering result in the spatial domain, as shown in formula (6): Where M and L represent the height and width of the frequency domain image, respectively.

4. The method for suppressing highlights in three-dimensional dynamic topography measurement of a motor gear shaft according to claim 2 is characterized in that step S3 is specifically as follows: S31, captured distortion fringe intensity It can be expressed as formula (7): Where α is the surface reflectivity of the object, r is the gamma factor, B0 and B k are the amplitudes of the DC component and the k-order harmonic component, φ n represents the modulation phase coupled with the phase shift, φ n =φ+δ n ; S32. Calculate the modulation phase using formula (8), and calculate the gamma distortion phase based on LSA using formula (9): The extracted phase error model is: Where G N-1 =B N-1 / B1 is the normalized harmonic amplitude ratio, φ C is the actual phase, and φ is the ideal phase.

5. The method for suppressing highlights in three-dimensional measurement of dynamic topography of a motor gear shaft according to claim 4, characterized in that: Step S4 is specifically as follows: S41. The HT of the nth captured phase-shift image can be expressed as: Where Η[·] represents the HT operator; Perform HT transformation on formula (8), and the HT domain phase φ based on LSA is H It can be expressed as: The gamma distortion phase φ in the HT domain is calculated using formula (13): HC : The phase error model after HT transformation is: S42, due to Δφ and Δφ H The amplitudes are equal and the directions are opposite. The error can be significantly suppressed by averaging the phases of the two domains, as shown in formula (15):

6. The method for suppressing highlights in three-dimensional measurement of dynamic topography of a motor gear shaft according to claim 1, characterized in that: S5 uses the corrected phase information to perform 3D reconstruction, specifically including: The three-frequency layered time domain phase unwrapping is used to unwrap the phase and reconstruct the object under test, Φ H , Φ M , Φ L The unwrapped phase corresponding to the frequency is shown in formula (16): Where, φ H 、φ M 、φ L are the unfolded phases of high, medium and low frequencies, respectively, f H Indicates high frequency, f M Indicates the intermediate frequency, f L Indicates low frequency, and round is the rounding function.

7. A high-light suppression system suitable for three-dimensional measurement of dynamic topography of a motor gear shaft, using the method according to any one of claims 1 to 6, characterized in that: It includes a data acquisition unit, a data processing unit and an output unit; the data acquisition unit is used to obtain analysis data; Data processing unit: Analyze the Fourier transform spectrum of the saturated fringe pattern of the motor gear shaft with local high light reflection; A Butterworth low-pass filter is used to filter the saturated fringe pattern and remove the high-order harmonic components. The Butterworth low-pass filter causes the non-sinusoidality of the fringe, and a phase error model is further established. The Hilbert transform is used to correct the phase error. The phase information corrected by the Hilbert transform is used for three-dimensional reconstruction. The output unit: visualizes the processing results.

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