A three-dimensional dynamic measurement method using time-domain least squares fitting for multi-frequency structured light

Abstract

This invention belongs to the field of three-dimensional dynamic topography measurement, specifically a multi-frequency structured light time-domain least squares fitting three-dimensional dynamic measurement method. It includes multi-frequency structured light projection, capturing images of stripes at different frequencies and performing Fourier analysis to extract the Fourier phase corresponding to each stripe image; obtaining the corresponding difference phase sequence centered on each frame of the multi-frequency stripe sequence; performing time-domain least squares fitting analysis on the extracted difference phase sequence to solve the wrapping phase of each frame of sampled stripes; and expanding the wrapping phase using the multi-frequency information in the sampling sequence to obtain the three-dimensional topography corresponding to each frame of sampled stripes. This invention integrates information from multiple frames of stripes at different frequencies to perform time-domain least squares fitting to solve the wrapping phase of each frame of stripes in the sampling sequence. Compared with the traditional single-frame Fourier transform method, the solution information is richer, which helps to improve measurement accuracy.

Description

Technical Field

[0001] This invention belongs to the field of three-dimensional dynamic measurement, specifically involving a three-dimensional dynamic measurement method using multi-frequency structured light time-domain least squares fitting. Background Technology

[0002] The rapid advancements in electronic devices and computer technology have spurred continuous breakthroughs in 3D measurement, leading to its commercialization. Currently, 3D measurement has relatively mature applications in various fields such as industrial reverse engineering, medical aesthetics, and cultural relic preservation, but these are mostly limited to static measurement scenarios. As research deepens, real-time measurement and analysis of the 3D morphological characteristics of objects in motion is gradually becoming a new hot topic. This includes studying the excited deformation and vibration characteristics of materials, as well as the motion process of objects, to deeply analyze the physical parameters, dynamic characteristics, and motion parameters of materials and objects. Traditional 3D measurement methods struggle to simultaneously meet the accuracy and efficiency requirements of dynamic measurement; therefore, researching new 3D dynamic measurement methods is of great significance.

[0003] Structured light projection measurement technology is widely used in the field of 3D measurement due to its advantages of being non-contact, high-precision, and efficient. Structured light projection profilometry is mainly divided into two categories: traditional phase-shifting methods and single-frame image transformation methods. Traditional phase-shifting methods require at least three frames of phase-shifted image sequences for phase resolution. Because it integrates information from multiple frames and resolves each pixel independently, this method boasts high precision and robustness. However, in dynamic scenes, object motion can cause phase shift errors between different image frames, thus traditional phase-shifting methods are only suitable for static measurement scenarios. In contrast, single-frame image transformation methods only require single-frame sampling for phase resolution, making them an efficient dynamic measurement method, with the Fourier transform method being the most representative. However, the Fourier transform method has an inherent defect of spectral leakage, which can easily lead to measurement distortion in complex surface feature areas, thus making it difficult to meet the high-precision measurement requirements in dynamic scenes.

[0004] Therefore, traditional structured light phase-shifting methods and single-frame Fourier transform methods face the challenge of balancing measurement efficiency and accuracy in new dynamic measurement scenarios. To meet the demands of efficient and high-precision dynamic measurements, a balance between accuracy and efficiency needs to be struck between these two methods. Summary of the Invention

[0005] The purpose of this invention is to provide a three-dimensional dynamic measurement method for multi-frequency structured light using time-domain least squares fitting. By performing phase analysis through time-domain multi-frequency image fitting, the measurement error caused by leakage of the Fourier transform spectrum of a single frame image is eliminated, thereby improving the efficiency and accuracy of the three-dimensional dynamic measurement method for structured light.

[0006] The specific solution provided by this invention includes the following steps:

[0007] S1. Multi-frequency structured light temporal projection sampling: A projector continuously and cyclically projects sinusoidal structured light of multiple frequencies (no less than 3 kinds) onto the object under test. Multiple stripe images obtained by the reflection of sinusoidal structured light are acquired by a camera. All stripe images are cyclically projected according to frequency to form a multi-frequency stripe sequence and transmitted to the computer.

[0008] S2. Fourier Transform of Sampled Images: The computer performs Fourier transform and spectral filtering on each stripe image in the multi-frequency stripe sequence to obtain the Fourier phase of each stripe image.

[0009] S3. Fourier phase difference: In the multi-frequency stripe sequence, a center image is made for each stripe image. The difference phase between the center image and its adjacent stripe images is calculated based on the Fourier phase, so as to obtain the difference phase sequence corresponding to each stripe image.

[0010] S4. Least Squares Fitting: Each stripe image is fitted using its corresponding differential phase sequence to obtain the wrapping phase of each stripe image.

[0011] S5. Multi-frequency phase unwrapping: By combining the frequency difference information between consecutive stripe images in the multi-frequency stripe sequence, the phase unwrapping of the wrapped phase corresponding to each stripe image is performed to obtain the three-dimensional morphological features corresponding to each stripe image.

[0012] Furthermore, the expression for the multi-frequency stripe sequence described in step S1 is:

[0013] I n (x,y)=a n (x,y)+b n (x,y)cos[2πf n x+φ n [x,y)],n=1,2,…,N

[0014] Where (x,y) represents the pixel coordinates on the sampled stripe image, I n (x,y) represents the light intensity of the nth stripe image, a n (x,y) represents the background light intensity of the nth striped image, b n (x,y) represents the modulation intensity of the nth stripe image, f n This represents the sinusoidal structured light frequency corresponding to the nth fringe image, with a total frequency count of at least 3, cyclically projected into the fringe sequence, φ n (x,y) represents the phase corresponding to the three-dimensional shape to be measured, and N is the sampling sequence length during dynamic measurement.

[0015] Further, step S2 performs Fourier transform and spectral filtering on each stripe image to obtain the Fourier phase of each stripe image, including:

[0016] S21. Perform a Fourier transform on each stripe image to obtain the corresponding spectrum;

[0017] S22. Extract the positive frequency spectrum of each spectrogram to obtain the corresponding positive frequency signal;

[0018] S23. Perform an inverse Fourier transform on each positive frequency signal to obtain the Fourier phase corresponding to each stripe image.

[0019] Furthermore, three consecutive adjacent stripe images are selected from the multi-frequency stripe sequence, with the second stripe image as the center image. The differential phase sequence calculation in step S3 is expressed as follows:

[0020]

[0021] in, Represents the Fourier phase of the center image. The Fourier phase of the fringe image adjacent to the center image. δ represents the Fourier phase of the fringe image adjacent to the center image. n (x,y) represents the difference phase between the central image and itself, δ n-1 (x,y) represents the differential phase between the central image and its preceding adjacent stripe image, δ n+1 (x,y) represents the differential phase between the central image and its adjacent stripe images.

[0022] Furthermore, the least squares fitting operation in step S4 is expressed as:

[0023]

[0024] in, m = n-1, n, n+1 represents the signal intensity of the actual sampled stripe image sequence, δ m m = n-1, n, n+1 represent the center image. The corresponding differential phase sequence, where 'a' represents the stripe image sequence. The average background intensity of m = n-1, n, n+1, α n and β n The least squares fitting solution term is theoretically represented as follows:

[0025]

[0026] Where b(x,y) represents the stripe image sequence The average modulation index of m = n-1, n, n+1, Φ n (x,y)=2πf n x+φ n Represents the central image The corresponding phase to be solved.

[0027] Furthermore, based on least squares fitting, the wrapping phase corresponding to each fringe is calculated. The calculation of the wrapping phase is expressed as:

[0028]

[0029] Where, Φ′ n (x,y) represents the wrap phase.

[0030] The beneficial effects of this invention are:

[0031] This invention provides a multi-frequency structured light temporal least squares fitting three-dimensional dynamic measurement method. It can acquire a multi-frequency stripe image sequence through temporal sampling, and then calculate the wrapping phase corresponding to each stripe frame by frame using the least squares fitting method. Then, it combines the information of multiple adjacent stripe images of different frequencies to perform phase unwrapping calculation, thereby restoring the three-dimensional shape corresponding to each stripe image. This method can effectively suppress the spectral leakage problem existing in the traditional single-frame Fourier transform method, improve the edge measurement effect, and improve the measurement efficiency, ensuring efficient and high-precision three-dimensional dynamic measurement.

[0032] This invention extracts the minute phase differences between the Fourier phase spectra of multi-frequency fringes and solves for the wrapping phase of each fringe through time-domain least squares fitting analysis. The calculated wrapping phase integrates information from multiple fringe images of different frequencies, providing richer information compared to traditional single-frame Fourier transform methods, thus helping to improve measurement accuracy.

[0033] In this invention, multi-frequency fringes can be used to solve for both wrapped phase and unwrapped phase, ensuring phase solution for each frame of the image. This further improves measurement efficiency while meeting high-precision measurement requirements, achieving an effective balance between measurement accuracy and measurement efficiency. Attached Figure Description

[0034] Figure 1 This is a preferred embodiment of the multi-frequency structured light time-domain least squares fitting three-dimensional dynamic measurement method of the present invention;

[0035] Figure 2 This is a schematic diagram of the measurement device principle of the multi-frequency structured light time-domain least squares fitting three-dimensional dynamic measurement method according to an embodiment of the present invention;

[0036] Figure 3 This is a schematic diagram of Fourier transform analysis in an embodiment of the present invention;

[0037] Figure 4 This is a schematic diagram of multi-frequency fringe Fourier phase difference analysis according to an embodiment of the present invention;

[0038] Figure 5 This is a schematic diagram of least squares fitting analysis in an embodiment of the present invention;

[0039] Figure 6 This is a schematic diagram of multi-frequency fringe joint phase unwrapping in an embodiment of the present invention. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] This embodiment provides a preferred implementation of a multi-frequency structured light time-domain least squares fitting three-dimensional dynamic measurement method, such as... Figure 1 As shown, it includes:

[0042] S1. Multi-frequency structured light temporal projection sampling: A projector continuously and cyclically projects sinusoidal structured light of multiple frequencies (no less than 3 kinds) onto the object under test. The camera captures the stripe image obtained by each sinusoidal structured light reflection. All stripe images are cyclically projected according to frequency to form a multi-frequency stripe sequence and transmitted to the computer.

[0043] S2. Fourier Transform of Sampled Images: The computer performs Fourier transform and spectral filtering on each stripe image in the multi-frequency stripe sequence to obtain the Fourier phase of each stripe image.

[0044] S3. Fourier phase difference: In the multi-frequency stripe sequence, a center image is made for each stripe image. The difference phase between the center image and its adjacent stripe images is calculated based on the Fourier phase, so as to obtain the difference phase sequence corresponding to each stripe image.

[0045] S4. Least Squares Fitting: Each stripe image is fitted using its corresponding differential phase sequence to obtain the wrapping phase of each stripe image.

[0046] S5. Multi-frequency phase unwrapping: By combining the frequency difference information between consecutive stripe images in the multi-frequency stripe sequence, the phase unwrapping of the wrapped phase corresponding to each stripe image is performed to obtain the three-dimensional morphological features corresponding to each stripe image.

[0047] In a preferred embodiment, based on the above embodiments, the present invention provides... Figure 2 The schematic diagram of the measurement principle shows that a projector continuously projects sinusoidal structured light of multiple different frequencies (no less than three) onto the object being measured, and a camera continuously acquires the reflected fringe images. The multi-frequency projection of this invention uses different frequencies in each projection to introduce a small phase difference in different fringe images. During dynamic measurement, multiple frequencies are used cyclically. During projection, a rotary table drives the object to move, thereby achieving dynamic process projection sampling. The computer system is responsible for performing Fourier transform analysis, difference operations, least squares fitting analysis, and phase unwrapping operations on the sampled multi-frequency fringe image sequence, thereby obtaining the three-dimensional morphological features corresponding to each frame of sampled fringe (i.e., each fringe image).

[0048] Specifically, in step S1, the multi-frequency structured light stripe signal is theoretically represented as follows:

[0049] I n (x,y)=a n (x,y)+b n (x,y)cos[2πf n x+φ n [(x,y)],n=1,2,…,N (1)

[0050] Where (x,y) represents the pixel coordinates on the sampled stripe image, I n (x,y) represents the light intensity of the nth stripe image, a n (x,y) represents the background light intensity of the nth striped image, b n (x,y) represents the modulation intensity of the nth stripe image, f n This represents the sinusoidal structured light frequency of the nth fringe. Here, only a one-dimensional distribution is considered for analysis purposes; the two-dimensional distribution is equally applicable. φ n (x, y) represents the phase to be determined, and N is the sampling sequence length during dynamic measurement. The multi-frequency method in this invention uses a 3-frequency approach with cyclic projection.

[0051] Specifically, step S2 performs Fourier transform and spectral filtering on each stripe image to obtain the Fourier phase of each stripe image, such as... Figure 3 As shown, it includes:

[0052] S21. Perform a Fourier transform on each stripe image to obtain the corresponding spectrum;

[0053] S22. Extract the positive frequency spectrum of each spectrogram to obtain the corresponding positive frequency signal;

[0054] S23. Perform an inverse Fourier transform on each positive frequency signal to obtain the corresponding Fourier phase.

[0055] Specifically, the extracted Fourier phase spectrum contains 2π phase ambiguity, the theoretical expression of which is as follows:

[0056] Φ n (x,y)=2πf n x+φ n (x,y),n=1,2,…,N (2)

[0057] Specifically, three consecutive adjacent multi-frequency fringe images are selected, with the second fringe image as the center image. The small Fourier phase difference between the center image and the adjacent frequency fringes is extracted, such as... Figure 4 As shown, the differential phase sequence calculation in step S3 is expressed as follows:

[0058]

[0059] Furthermore, based on the differential phase sequence in formula (3) and combined with the multi-frequency fringe information in formula (1), least-squares fitting operations can be performed on fringes of different frequencies. Figure 5 As shown, in this process, according to formulas (1) and (3), the three selected image signals can be transformed as follows:

[0060]

[0061] in,

[0062]

[0063] In formulas (4) and (5), a and b(x,y) represent the average background signal and average modulation of the three images.

[0064] For any given pixel, its least squares error can be expressed as follows:

[0065]

[0066] In the formula, This represents the actual sampled signal strength. Combining formulas (3) to (6), a least-squares fitting analysis can be performed to obtain the solution.

[0067]

[0068]

[0069] In the formula, Φ′ n (x,y) indicates that the phase being solved contains 2π phase ambiguity, which needs to be expanded through subsequent phase unwrapping. Referring to the above analysis and calculation process, it can also be represented by image I. n-1 (x,y) and I n+1Centered on (x,y), the corresponding wrapping phase Φ′ is obtained by performing least-squares fitting analysis using the Fourier phase difference sequence between the image and its preceding and following adjacent images. n-1 (x,y) and Φ′ n+1 (x,y). Clearly, Φ′ n-1 (x,y), Φ′ n (x,y) and Φ′ n+1 (x,y) combines information from multiple frames of images at different frequencies for joint solution, and its accuracy is better than that of the single-frame image Fourier transform method.

[0070] Specifically, the phase unwrapping of the multi-frequency stripes is performed to obtain the three-dimensional morphological features corresponding to each frame of stripes, as shown below:

[0071] Φ n (x,y)=Φ′ n (x,y)+2πk n (x,y),n=1,2,…,N (9)

[0072] In the formula, Φ n (x,y) represents the unwrapping phase, k n (x, y) represents the phase order. Clearly, solving for the phase order k... n (x,y) is the key to unpacking. In dynamic measurement scenarios, the phases of three adjacent fringes of different frequencies sampled at high speeds satisfy the following approximate relationship:

[0073] T n-1 Φ n-1 =T n Φ n =T n+1 Φ n+1 (10)

[0074] In the formula, T n-1 ,T n ,T n+1 Let represent the fringe periods of fringe images at different frequencies. Based on the above equations, the phase order of high-frequency fringes can be solved using only the unwrapped phase of a low-frequency fringe and its corresponding fringe period, thus achieving phase unwrapping for all frequencies. Here, low-frequency fringes can be equivalently obtained by subtracting adjacent frequency fringes, as shown below:

[0075]

[0076] In the formula, Φ eq (x,y) represents the equivalent low-frequency phase without 2π phase ambiguity, T eq(x,y) represents the equivalent low-frequency fringe period length. This can be achieved by designing a reasonable fringe frequency or by performing a secondary equivalent calculation using formula (11). The phase order of fringes at different frequencies can be solved using formulas (9) to (11):

[0077]

[0078] In the formula, Round[·] represents the floor function. Substituting formula (12) into formula (9), the unwrapped phase Φ corresponding to each frequency fringe can be obtained. n (x,y). Finally, eliminate the phase and frequency f. n By using the relevant tilt datum, three-dimensional topographic information φ at different frequencies can be obtained. n (x,y), such as Figure 6 As shown.

[0079] Through the analysis of the above steps, the three-dimensional dynamic measurement method based on multi-frequency structured light time-domain least squares fitting integrates multi-frame image information to solve the three-dimensional shape of a single-frequency stripe image. This method can effectively avoid the spectral leakage problem in the traditional Fourier transform method, improve the measurement accuracy, and also improve the measurement efficiency of the traditional method, thus achieving fast and high-precision dynamic measurement of the three-dimensional shape of objects.

[0080] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A multi-frequency structured light time-domain least square fitting three-dimensional dynamic measurement method, characterized in that, Includes the following steps: S1. Multi-frequency structured light temporal projection sampling: A projector continuously and cyclically projects sinusoidal structured light of various frequencies onto the object under test. Multiple stripe images obtained by the reflection of the sinusoidal structured light are acquired by a camera. All stripe images are arranged into a multi-frequency stripe sequence according to the cyclic projection order of frequency and transmitted to the computer. S2. Fourier Transform of Sampled Images: The computer performs Fourier transform and spectral filtering on each stripe image in the multi-frequency stripe sequence to obtain the Fourier phase of each stripe image. S3. Fourier phase difference: In the multi-frequency stripe sequence, a center image is made for each stripe image. The difference phase between the center image and its adjacent stripe images is calculated based on the Fourier phase, so as to obtain the difference phase sequence corresponding to each stripe image. S4. Least Squares Fitting: Each stripe image is fitted using its corresponding differential phase sequence to obtain the wrapping phase of each stripe image. S5. Multi-frequency phase unwrapping: By combining the frequency difference information between consecutive stripe images in the multi-frequency stripe sequence, the phase unwrapping of the wrapped phase corresponding to each stripe image is performed to obtain the three-dimensional morphological features corresponding to each stripe image.

2. The method according to claim 1, wherein, The expression for the multi-frequency stripe sequence mentioned in step S1 is: wherein, represents the coordinates of a pixel point on the sampled fringe image, represents the light intensity of the nth fringe image, represents the background light intensity of the nth fringe image, represents the modulation intensity of the nth fringe image, represents the sinusoidal structured light frequency corresponding to the nth fringe image, represents the phase corresponding to the three-dimensional topography to be measured, and N is the length of the sampling sequence in the dynamic measurement process.

3. The method of claim 1, wherein, Step S2 performs Fourier transform and spectral filtering on each stripe image to obtain the Fourier phase of each stripe image, including: S21. Perform a Fourier transform on each stripe image to obtain the corresponding spectrum; S22. Extract the positive frequency spectrum of each spectrogram to obtain the corresponding positive frequency signal; S23. Perform an inverse Fourier transform on each positive frequency signal to obtain the Fourier phase corresponding to each stripe image.

4. The method of claim 1, wherein, In the multi-frequency fringe sequence, three consecutive adjacent fringe images of different frequencies are selected. Taking the second fringe image as the center image, the differential phase sequence calculation in step S3 is expressed as follows: wherein φc represents the Fourier phase of the center image, φc-1 represents the Fourier phase of the preceding fringe image adjacent to the center image, φc+1 represents the Fourier phase of the succeeding fringe image adjacent to the center image, φc-c represents the differential phase of the center image with respect to itself, φc-c-1 represents the differential phase between the center image and the preceding fringe image adjacent thereto, φc-c+1 represents the differential phase between the center image and the succeeding fringe image adjacent thereto.

5. The three-dimensional dynamic measurement method for multi-frequency structured light time-domain least squares fitting according to claim 1, characterized in that, The least squares fitting operation in step S4 is expressed as: in, , This represents the signal strength of the actual sampled stripe image sequence. Represents the central image The corresponding differential phase sequence, Representative stripe image sequence Average background intensity, and The least squares fitting solution term is theoretically represented as follows: in, Representative stripe image sequence average modulation system Represents the central image The corresponding phase to be solved, This represents the sinusoidal structured light frequency of the nth fringe image. This indicates the phase to be determined.

6. The three-dimensional dynamic measurement method for multi-frequency structured light time-domain least squares fitting according to claim 5, characterized in that, Based on least squares fitting, the wrapping phase corresponding to each stripe image is obtained. The calculation of the wrapping phase is expressed as follows: in, This indicates the wrap-around phase.

7. The three-dimensional dynamic measurement method for multi-frequency structured light time-domain least squares fitting according to claim 6, characterized in that, By combining the frequency difference information between consecutive stripe images in the multi-frequency stripe sequence, phase unwrapping is performed on the wrapped phase corresponding to each stripe image to obtain the three-dimensional morphological features corresponding to each stripe image. The solution formula is as follows: in, To unwrap the phase, For phase order, Let n be the fringe period of the nth fringe image. The equivalent low-frequency phase without 2π phase ambiguity. is the equivalent low-frequency fringe period length, and N is the sampling sequence length during dynamic measurement.

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