Fringe projection high reflective surface phase unwrapping method based on frequency reuse

Abstract

The invention relates to a fringe projection high-reflection surface phase unwrapping method based on frequency reuse. The fringe projection high-reflection surface phase unwrapping method comprises the steps of collecting a multi-frequency fringe image and dividing the multi-frequency fringe image into an overexposure area and a non-overexposure area, solving a wrapped phase in the non-overexposure area by adopting a generalized phase shift method, obtaining an initial unwrapping phase based on a multi-frequency heterodyne algorithm, and performing block filtering and interpolation processing to obtain a fringe projection high-reflection surface phase unwrapping phase. A continuous unwrapped phase containing a high-reflection area is obtained, a complementary Gray code consistent with a wrapped phase period is constructed in combination with a multi-threshold constraint and is used for correcting the stripe level of an overexposure area, brightness attenuation design is further carried out on low and medium frequency stripes, frequency reuse is achieved, and the high-reflection area is obtained. Obtaining an unwrapped phase of an overexposure point in a non-high-frequency stripe and mapping the unwrapped phase to a high frequency; the method comprises the following steps of: extracting and fusing a wrapped phase by adopting one-dimensional Fourier and Hilbert transform for areas with overexposure of each frequency, and selecting and inhibiting spectrum leakage through a complete period, so that effective correction of the wrapped phase and stripe level of an overexposure point is realized, and a reliable unwrapped phase is obtained.

Description

Technical Field

[0001] This invention relates to the field of optical three-dimensional measurement technology, and in particular to a method for phase unfolding of highly reflective surfaces based on frequency reuse fringe projection. Background Technology

[0002] Fringe projection profilometry (FPP) is widely used in industrial inspection and quality control, reverse engineering, biomedical engineering, and cultural heritage preservation and digitization due to its advantages such as high precision, high efficiency, and non-contact operation. Mainstream FPP technologies can generally be divided into two types: Fourier transform profilometry (FTP) and phase shift profilometry (PSP). PSP technology has greater robustness to phase noise caused by ambient lighting and surface reflectivity, and can achieve pixel-by-pixel phase measurement results with higher resolution and accuracy, thus gaining widespread application in practice.

[0003] However, when the surface of the object being measured has high reflectivity areas or the lighting conditions in the measurement environment are complex, the limited dynamic range of the camera can easily lead to light intensity saturation in the striped images acquired by the camera. In saturated regions, the grayscale values ​​of the image exceed the camera's quantization range, resulting in the loss of some information. The phase values ​​calculated based on conventional phase-shifting algorithms will produce serious errors, thus affecting the accuracy and completeness of the 3D reconstruction.

[0004] To address the aforementioned issues, existing solutions mainly fall into two categories: hardware-based adjustment methods and algorithm-based techniques. The former primarily includes multiple exposure techniques and adaptive projection methods. These methods are essentially inverse multiple exposure techniques, requiring the pre-projection of specific patterns to perceive the reflective properties of the object's surface. However, the required number of projection patterns is typically large, leading to reduced measurement efficiency. The latter focuses on directly calculating the object's phase using saturation fringes and correcting errors introduced by fringe saturation. Increasing the phase shift step or using inverse fringes can extend the system's dynamic range to some extent. However, too few fringes limit the improvement in dynamic range, while too many fringes increase data processing time.

[0005] Therefore, there is an urgent need for a phase unfolding method that can utilize the principle of frequency reuse to complement multi-frequency information in a single set of exposure data, and eliminate overexposure interference through stripe order correction and wrapping phase correction at overexposure points, so as to improve the measurement accuracy and robustness of highly reflective objects. Summary of the Invention

[0006] To address the problems of numerous projection patterns, cumbersome operation, and poor robustness in existing technologies for phase unwrapping of highly reflective objects, this invention provides a method for phase unwrapping highly reflective surfaces based on frequency reuse fringe projection. By fusing multi-frequency fringe information, the fringe order and encapsulation phase of overexposed points are corrected, achieving accurate phase recovery of highly reflective areas. This method requires no additional hardware support and is compatible with existing fringe projection systems. To achieve the above objectives, this invention provides the following solution: A method for phase unfolding of highly reflective surfaces based on frequency reuse fringe projection includes: Multi-frequency phase-shift fringe images of the object under test are acquired. Pixel-level intensity analysis is performed on the highest frequency fringe image in the multi-frequency phase-shift fringe images. Overexposed areas where intensity saturation occurs are detected and marked. The image is divided into overexposed areas and unexposed areas. For unexposed areas, the generalized phase-shift method is used to solve its wrapping phase, which is used to obtain the wrapping phase of the mid-frequency and low-frequency areas and the overexposed area mask. Based on the principle of multi-frequency heterodyne, the initial unfolded phase of each frequency is obtained, and reliable unfolded phase points are obtained through modulation mask filtering, planar block filtering, and median filtering. Then, through data interpolation algorithm, continuous unfolded phases containing highly reflective regions are obtained at each frequency. For each frequency, a multi-threshold constraint is applied to the complete continuous unfolded phase to construct a complementary Gray code consistent with the wrapping phase period, thereby correcting the fringe order of the unfolded phase at each frequency. When designing projection patterns, both mid-frequency and low-frequency projection stripe patterns are multiplied by a preset coefficient less than 1. That is, under the same conditions, the non-high-frequency pattern is set with a target darkness so that the overexposed points at high frequencies will no longer be overexposed at low frequencies. Then, the unfolded phase of the point is obtained at low frequencies, and then converted to the high-frequency unfolded phase according to the frequency relationship to achieve frequency reuse. For points that are overexposed at all frequencies, a one-dimensional Fourier transform is used to extract the fundamental frequency within a certain area of ​​the row containing that point. Then, an inverse Fourier transform is used to obtain a new unexposed fringe pattern, and a wrap phase calculation is performed. The obtained one-dimensional fringe pattern is then subjected to a Hilbert transform, and another wrap phase calculation is performed. The two wrap phase calculations are fused together to perform high-precision correction of the wrap phase of overexposed points.

[0007] Optionally, obtaining the overexposed area mask includes: The multi-frequency phase-shifted stripe image is analyzed pixel by pixel. For a certain frequency stripe pattern, the gray value of each pixel in each frame is compared with the overexposure threshold. If the gray value exceeds the threshold, the pixel is defined as overexposed in that frame. If the number of non-overexposed frames for the pixel is less than 3, the pixel is marked as an overexposed point at that frequency. Other pixels are processed in the same way. Then, overexposure masks and non-overexposure masks are established for each frequency.

[0008] Optionally, after obtaining the continuously unfolded phase, the process includes: Unreliable fringe order points are removed by planar block phase filtering: Based on the ramp characteristics of the unfolded phase, the entire initial unfolded phase region is divided into four regions, and planar filtering is performed based on random consistency. The in-plane point threshold is set to 5, which is less than 2π of a fringe order phase range, in order to remove fringe order error points. This is used to obtain accurate phase fringe order when constructing complementary Gray codes.

[0009] Optionally, constructing the complementary Gray code includes: Based on the expanded phase range of the projected pattern, the expanded phase obtained by the above interpolation is normalized to the interval [-π, π]. Then, the initial expanded phase of each frequency is subject to the following multi-threshold constraints to construct complementary Gray codes: ; ; in, For Gray code diagram order, To normalize the expanded phase to the interval [-π, π], For index number, The m-th frame is the Gray code pattern.

[0010] Optionally, correcting the fringe order of the phase expansion at each frequency includes: Correcting the stripe order of overexposed points in the overexposed region: Based on the constructed Gray code pattern, the correct stripe order is obtained using a complementary Gray code decoding algorithm, which is then used to correct the stripe order of overexposed points in the overexposed region.

[0011] Optionally, implementing the frequency reuse includes: For pixels that are overexposed at high frequencies but not at mid- or low frequencies, frequency reuse is achieved by utilizing the proportional relationship between frequencies and recovering the unfolded phase at high frequencies based on the unfolded phase of that pixel at mid- or low frequencies. For pixels that are overexposed at high frequencies but not at medium frequencies, the high-frequency phase correction is as follows: ; in, This is the intermediate frequency. For high frequency, This represents the expanded phase of that point after high-frequency correction. The mid-frequency expansion phase at this point; For pixels that are overexposed at high and mid frequencies but not at low frequencies, the high-frequency phase correction is as follows: ; in, Low frequency This represents the expanded phase of that point after high-frequency correction. The low-frequency phase at this point is the phase expansion.

[0012] Optionally, calculating the package phase includes: For pixels that are overexposed at all frequencies, a new stripe pattern is constructed based on one-dimensional Fourier transform and one-dimensional Hilbert transform, and the wrapping phase obtained from the two methods is fused to achieve wrapping phase correction for this type of overexposed pixel: The fringe projection is a vertical fringe projection. For pixels (x0, y0) that are overexposed at all frequencies, a local one-dimensional signal is extracted along their row: ; in, L is the one-dimensional fringe signal corresponding to the nth phase shift extracted in the neighborhood of the saturated pixel. L is the half-window length of the local one-dimensional fringe signal, used to limit the range of one-dimensional fringe extraction. The characteristic of the value of L is that the period size is obtained in the non-overexposed area. L is an integer multiple of the period size to prevent spectral leakage during one-dimensional Fourier transform.

[0013] Optionally, extracting the fundamental frequency includes: By performing a Fourier transform on the local one-dimensional fringe signal, a windowed filter is constructed based on fundamental frequency localization to suppress DC components and higher harmonics, and then the fundamental frequency component in the signal is extracted. ; ; in: ; In the formula, This refers to the one-dimensional fringe signal corresponding to the nth phase shift extracted within the neighborhood of the saturated pixel. One-dimensional fringe signal The spectrum representation, This is the spectrum after windowing filtering. This is a frequency domain window function used to suppress DC components and higher harmonic components. For the frequency variable in a one-dimensional Fourier transform, This represents the fundamental frequency position corresponding to the one-dimensional fringe signal. This is the half-bandwidth parameter of the frequency domain window function; The inverse transform yields the filter fringes, from which the Fourier filter phase is calculated. ; ; in, The wrapped phase is calculated based on the one-dimensional Fourier filter fringe pattern. This is the spectrum after windowing filtering. For a one-dimensional inverse Fourier transform operator, N This represents the number of phase shift steps.

[0014] Optionally, the one-dimensional Hilbert transform is used to construct an analytic signal orthogonal to the filtered one-dimensional fringe signal to obtain a wrap-around phase complementary to the Fourier filter phase error, including: ; ; in, The wrapped phase is calculated based on the one-dimensional Hilbert transform fringes. Let N be a one-dimensional Hilbert transform operator, where N is the number of phase shift steps.

[0015] Optionally, high-precision correction of the overexposed point's surrounding phase includes: Local phase fusion is achieved by averaging the two sets of wrapper phases: ; in, This is the corrected wrapper phase obtained through local phase fusion. The wrapped phase is calculated based on one-dimensional Fourier filter fringes. The wrapped phase is calculated based on one-dimensional Hilbert transform fringes; The wrap-around phase of the overexposed point can be extracted from the fused phase. By combining the overexposed point fringe order correction, the unfolded phase correction of the overexposed point can be achieved.

[0016] The beneficial effects of this invention are as follows: This invention improves the accuracy of the unfolded phase by eliminating the influence of overexposed frames on the wrapping phase calculation and stripe order unfolding through effective frame discrimination. Simultaneously, in the pattern design, the mid-frequency and low-frequency patterns are slightly darker so that points that are overexposed at high frequencies are not overexposed at mid-frequency or low-frequency frequencies. Based on the proportional relationship between frequencies, the unfolded phase at high frequencies is corrected, achieving frequency reuse.

[0017] This invention uses non-high-frequency image data to calculate phase, avoiding information loss caused by directly discarding overexposed points in traditional methods. The data utilization rate is improved by more than 30%, and the root mean square error of phase measurement in overexposed areas is <0.1 rad.

[0018] This invention utilizes filtering, interpolation, and other operations to obtain a complete coarse unfolded phase in the overexposed region. By using multiple threshold constraints, a complementary Gray code with the same period size is constructed to achieve stripe order correction at the overexposed point, ensuring that phase unfolding can be achieved at each frequency and providing a reliable stripe order for high-frequency phase correction in frequency reuse.

[0019] This invention utilizes the fusion of wrapping phases obtained from one-dimensional Fourier transform and Hilbert transform to correct the wrapping phase of pixels with overexposed frequencies, significantly improving the accuracy of wrapping phase calculation for such overexposed points. Furthermore, combined with the aforementioned fringe order correction, it achieves expanded phase correction for overexposed points. Specifically, when extracting data for one-dimensional Fourier transform, the fringe period is first obtained through non-overexposed regions, and then integer period data points are extracted from both sides of the row containing the overexposed point. This ensures the periodic integrity of the entire one-dimensional Fourier transform and Hilbert transform, effectively avoiding spectral leakage during the transformation process.

[0020] This invention has strong compatibility, requires no additional hardware or special projection pattern processing, and achieves high reflectivity repair only through algorithm optimization. It is compatible with existing stripe projection systems, reducing the equipment upgrade cost for industrial inspection. Attached Figure Description

[0021] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0022] Figure 1 This is a schematic flowchart of a method for phase unwrapping a highly reflective surface based on frequency reuse fringe projection according to an embodiment of the present invention. Figure 2 This is a comparison image of a certain row of stripes containing an overexposed area before and after correction according to an embodiment of the present invention; (a) is the stripe level before correction; (b) is the stripe level after correction; Figure 3 The diagram shows a comparison of the effects of frequency reuse before and after in an embodiment of the present invention; (a) is the phase before frequency reuse; (b) is the phase after frequency reuse. Figure 4 This is a schematic diagram illustrating the processing of pixels that are overexposed at all frequencies according to an embodiment of the present invention; Figure 5 This is a phase correction effect for pixels that are overexposed at all frequencies in this embodiment of the invention; Figure 6 The following is a schematic diagram of the final unfolded phase in an embodiment of the present invention: (a) is a row of the original image; (b) is a comparison of the unfolded phase before and after correction for that row; (c) is the unfolded phase before correction; (d) is the unfolded phase after correction; (e) is a magnified view of the overexposed area of ​​the unfolded phase before correction; (f) is a magnified view of the overexposed area of ​​the unfolded phase after correction. Detailed Implementation

[0023] 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.

[0024] To make the above-mentioned objects, features and advantages of the present invention more apparent and understandable, the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments.

[0025] like Figure 1 As shown, this embodiment discloses a method for phase unwrapping of highly reflective surfaces based on frequency reuse fringe projection. The method includes: acquiring multi-frequency fringe images of the object under test; preprocessing the multi-frequency fringe images to generate masks for overexposed and non-overexposed areas, and calculating the corresponding wrapping phase; performing three-frequency heterodyne processing on the wrapping phases of different frequencies to obtain the initial unwrapped phase, and performing filtering and plane fitting interpolation. In the plane filtering, the entire initial unwrapped phase image is divided into four regions, and a consensus algorithm is randomly applied, setting the threshold of in-plane points to 5 to prevent errors in fringe order. The unwrapped phase of the plane is restored using multi-threshold binarization to obtain a complementary Gray code pattern, which is used to correct the fringe order of overexposed points in the overexposed region; for high-frequency overexposed points that are not overexposed at mid-frequency or low-frequency, the high-frequency unwrapped phase is corrected based on the frequency ratio relationship to achieve frequency reuse; for pixels that are overexposed at all frequencies, a fused phase is obtained based on one-dimensional Fourier transform and Hilbert transform operations, and then the wrapping phase of that point is corrected. Combined with the fringe order correction result, the unwrapped phase correction for this type of overexposed point is achieved.

[0026] Specifically, this embodiment discloses a method for phase unfolding of highly reflective surfaces based on frequency reuse fringe projection, including: Multi-frequency phase-shifted fringe images of the object under test are acquired. Pixel-level intensity analysis is performed on the highest frequency fringe images to detect and mark overexposed areas where intensity saturation occurs. The image is then divided into overexposed and unexposed areas. For unexposed areas, the generalized phase-shifting method is used to solve for their wrapping phase. Similarly, the wrapping phases and overexposed area masks for mid-frequency and low-frequency areas can be obtained. Based on the multi-frequency heterodyne principle, the wrapping phases of different frequencies are combined to obtain the initial unfolded phase for each frequency. Reliable unfolded phase points are obtained through modulation mask filtering, planar block filtering, median filtering, and other operations. Then, through data interpolation algorithms and interpolation processing, continuous unfolded phases covering the entire highly reflective surface area are obtained at each frequency. Multi-threshold constraints are applied to the complete unfolded phase at each frequency to construct a complementary Gray code with the same period as the wrapping phase, thereby correcting the fringe order of the unfolded phase at each frequency. When designing projection patterns, both mid-frequency and low-frequency projection stripe patterns are multiplied by a coefficient less than 1. That is, under the same conditions, the non-high-frequency pattern design is darker, so that the overexposed points at high frequencies will no longer be overexposed at low frequencies. Then, the unfolded phase of the point is obtained at low frequencies, and then converted to the high-frequency unfolded phase according to the frequency relationship to achieve frequency reuse. For points that are overexposed at all frequencies, a one-dimensional Fourier transform is used within a certain region of the row containing that point to extract the fundamental frequency. Then, an inverse Fourier transform is used to obtain a new unexposed fringe pattern, and a wrap-around phase calculation is performed. The obtained one-dimensional fringe pattern is then subjected to a Hilbert transform, and another wrap-around phase calculation is performed. The two wrap-around phase calculations are then fused to achieve high-precision correction of the wrap-around phase of overexposed points.

[0027] First, a monocular structured light 3D reconstruction experimental platform was built. An industrial camera and projector worked together to acquire multi-frequency fringe images of the surface of the object under test. Three sinusoidal fringe patterns of different frequencies were projected onto the surface of the object. The three sets of frequencies are high frequency... , intermediate frequency low frequency ( > > Each pattern set contains N phase shifts (N≥4), with a phase shift step size of 2π / N. An intensity threshold (determined based on the camera's dynamic range, e.g., threshold=250 in an 8-bit grayscale image) is set, and pixel-by-pixel analysis is performed on the acquired image sequence. For any pixel, if its grayscale value exceeds the threshold in at least one frame of the N-step phase-shifted image at a certain frequency, then the pixel is marked as an overexposed point at that frequency. Masks for overexposed and unexposed regions are generated, and for the unexposed regions, the generalized phase shift method is used to solve for its wrapping phase.

[0028] Based on high-frequency, mid-frequency, and low-frequency wrap-around phase , , The multi-frequency unwrapped phase is obtained by combining the wrapped phases of different frequencies using the multi-frequency heterodyne principle. Block-based planar filtering is then applied to the initial unwrapped phase to remove noise interference and preserve the spatial continuity of the phase field. Planar interpolation is then performed to fill in the entire phase field, resulting in a continuous unwrapped phase covering the entire highly reflective surface. Based on the initial unwrapped phase after block filtering and interpolation, multi-threshold binarization is performed to generate n complementary Gray code patterns (n ​​is determined by the frequency used, e.g., ...). =64, n=6), and the correct fringe orders k1 and k2 are obtained through Gray code decoding. After obtaining the corrected fringe orders, based on frequency reuse, the globally reliable phase is used to the maximum extent to improve data utilization. The traditional practice of discarding other frequency data is abandoned. The corresponding high-frequency fringe phase is replaced and restored using the phase information of the intermediate frequency or low frequency that has not been saturated. If only the intermediate frequency is not overexposed, the high-frequency phase is calculated as: high-frequency phase = intermediate frequency corrected phase × ( / ) to perform the conversion; if only the low frequencies are not overexposed, use the formula: high frequency phase = low frequency corrected phase × ( / Convert the values.

[0029] For pixels that still have saturation errors after frequency reuse, local one-dimensional stripe signals (projected vertical stripes) are extracted from their row. Complementary wrapping phases are constructed using one-dimensional Fourier transform and one-dimensional Hilbert transform, and wrapping phase correction for such overexposed points is achieved based on local phase fusion.

[0030] This method includes the following five steps: Step 1: Fringe Projection and Acquisition. A monocular structured light 3D reconstruction experimental platform was built, and deformed fringe images were acquired using the phase-shifting method. Details are as follows: Step 1: Project sinusoidal fringe patterns of different frequencies sequentially onto the highly reflective object being measured. Based on the optimal frequency selection principle, design three frequency combinations that satisfy the three-frequency heterodyne for each frequency. The frequencies are: high frequency... , intermediate frequency low frequency satisfy( The three frequency combinations used in this experiment are (64, 57, 51). In the pattern intensity design, the mid-frequency stripe pattern is multiplied by a coefficient of 0.8 based on the original intensity, and the low-frequency stripe pattern is multiplied by a coefficient of 0.6 based on the original intensity, in order to ensure that overexposure occurs at high-frequency points but not at mid-frequency or low-frequency points. Then, the proportional relationship between frequencies is used to correct the phase expansion of such points at high frequencies.

[0031] Step 2: Phase Shift Settings: Each frequency band of fringes is phase shifted in N=4 steps (phase shift step size is...). The phase shift sequences are respectively The grayscale values ​​of the projected stripe image can be represented as: (1); in, Background light intensity, For the amplitude of the stripe modulation, These are pixel coordinates. W is the image width. Adjusting the density of the stripes to control the frequency. The values ​​represent the horizontal pixel coordinates. A four-step phase-shifted fringe image sequence (high-frequency, mid-frequency, and low-frequency) was simultaneously acquired using an industrial camera after the object's surface was deformed by reflection.

[0032] Step 2: Overexposure detection and selective phase calculation using the generalized phase shift method. Based on the camera's dynamic range (in this embodiment, the camera is an 8-bit grayscale camera with a grayscale range of 0~255), and considering sensor noise, an overexposure threshold of 250 is defined. For a given frequency, the nth frame phase-shifted image is... ,like: (2); Then that pixel is determined to be overexposed in that frame. If the number of non-overexposed frames in all frames at a certain frequency is less than 3: (3); If S is the set of non-overexposed frames, then the pixel is determined to be an unreliable point (overexposed point) at that frequency.

[0033] The wrap phase can be calculated independently over at least three phase shift intensities; that is, a pixel is considered reliable if the number of unexposed frames is greater than or equal to three. The corresponding wrap phase can be obtained from Equations 4 and 5: (4); (5); Wherein, the coefficients in the formula The linear combination coefficients in the phase shift calculation can be obtained using Equation 6: (6); Here, equations (4)-(6) only apply to pixels with 3 unexposed frames. For pixels without any overexposed frames, their wrapping phase can be simplified to the standard phase shift method, as shown in equation 7: (7); Step 3: Obtain the initial unfolded phase based on the three-frequency heterodyne method. The three-frequency heterodyne method is a time-based phase unfolding method where each pixel's calculation is independent. If overexposure occurs at a certain frequency, it will cause error propagation in the final unfolded phase obtained by the three-frequency heterodyne method. Based on the three wrapper phases calculated in the previous step... Gain the unfolded phase: (8); In the formula, int(·) is the rounding operation, and R is a constant determined by the frequency. The specific calculation is as follows: (9); Where Φ123(x,y) is the composite phase, calculated according to the following formula: (10); Based on the three-frequency heterodyne method, the initial expanded phases at three frequencies can be obtained, denoted as follows: .

[0034] Step 4: Construct Gray code and fringe order correction. After obtaining the initial expanded phase through three-frequency heterodyne, the high-frequency phase of the reliable region is then corrected. Block-based phase filtering and interpolation are performed. The initial unfolded phase map is divided into multiple spatial sub-regions. Within each sub-region, planar filtering and median filtering are applied to the unfolded phase, and parameter estimation is performed using only reliable phase points within that sub-region. After block filtering, missing phase points within each sub-region are interpolated to complete the image, resulting in an unfolded phase map with higher spatial consistency. Block filtering is a structural processing strategy introduced to address the failure of fringe order correction.

[0035] Gray code uniquely determines the fringe order based on the interval in which the phase lies, ensuring the correct unfolding of the wrapped phase. This method constructs a set of multi-threshold binarized patterns based on the positions of continuous wrapped phases in the interval [-π, π]. These patterns are equivalent to standard Gray code but are derived directly from the phase itself, thus being more stable. Binarization of a single-cycle wrapped phase based on different thresholds can be represented as follows: (11); (12); In the formula: m is the Gray code diagram order, To normalize the expanded phase to the interval [-π, π], For index number, The m-th frame is the Gray code pattern.

[0036] The phase of the Gray code is constructed based on the expanded phase obtained by planar interpolation. Although this phase deviates from the real phase to some extent, the correct stripe order can be obtained by constructing the Gray code through the multi-threshold binarization method, thereby realizing the correction of the stripe order in the overexposed area. Figure 2 (a) in the diagram is a schematic diagram of the stripe order distribution before correction; Figure 2 (b) in the figure shows a schematic diagram of the corrected fringe order distribution. This method directly constructs Gray codes based on phase, without the need for additional projection of binary patterns, and has the following advantages: fringe order recovery is completely phase-driven and is not affected by pattern projection noise; the threshold strictly matches the phase space, improving the stability of order decoding; it can be used for reliable compensation of overexposed areas in highly reflective objects or multi-frequency fringes.

[0037] By dividing the continuous unfolded phase of the entire highly reflective surface using different set thresholds, and obtaining the Gray code pattern, the fringe orders k1 and k2 of the phase can be obtained based on the complementary Gray code decoding method. The corresponding unfolded phase can be obtained using Equation 13 for assisted unfolding: (13); Step 5: Phase replacement of overexposed points based on frequency reuse. The phase information of unsaturated mid-frequency or low-frequency fringes is used to replace and restore the corresponding high-frequency fringes, achieving complementary acquisition of phase information in highly reflective areas. This maximizes the utilization of globally reliable phase, breaking through the traditional approach of discarding other frequency data and improving data utilization. This invention performs multi-level phase replacement and restoration on overexposed pixels in high-frequency, mid-frequency, or low-frequency fringes. The core idea is that the unfolded phase of different frequencies has a linearly scalable relationship; therefore, the phase of "other frequencies that are not overexposed" can be used to compensate for the phase of overexposed frequencies.

[0038] Since phase and frequency are linearly proportional, for high-frequency overexposed pixels, if the mid-frequency pixels are not overexposed: (14); If the mid-frequency frequencies are overexposed but the low-frequency frequencies are not: (15); Figure 3 (a) in the diagram is a schematic diagram of the phase distribution before frequency reuse processing; Figure 3 (b) in the diagram shows the phase distribution after frequency reuse processing. This only applies to pixels where at least one frequency is not overexposed; that is, if a pixel has at least one frequency that is not overexposed, the frequency reuse strategy is used to expand its phase and repair the phase of other frequencies. Pixels where all three frequencies are overexposed are processed separately.

[0039] Through the above frequency reuse processing, the phase information loss problem caused by overexposure of high-frequency stripes in highly reflective areas can be effectively compensated without increasing the number of projected stripes, providing a reliable initial phase basis for subsequent fine local phase correction.

[0040] Step Six: Correction of saturation phase error through local phase fusion. Based on this, for pixels that may still have saturation errors, this invention further performs local fine-tuning correction on overexposed pixels. For example... Figure 4 The diagram illustrates the process of one-dimensional stripe extraction, filtering, and phase calculation for the neighborhood of overexposed pixels: Centered on the overexposed pixel, extract the local one-dimensional stripe signal in its neighborhood along the stripe modulation direction: (16); In the formula, Let L be the one-dimensional fringe signal corresponding to the nth phase shift extracted within the neighborhood of the saturated pixel. L is the half-window length of the local one-dimensional fringe signal, used to limit the one-dimensional fringe extraction range. L is an integer multiple of the fringe period to effectively avoid spectral leakage during Fourier transform and Hilbert transform.

[0041] The one-dimensional signal is then subjected to a Fourier transform, and high-order harmonic components introduced by saturation are suppressed by frequency domain windowing filtering. (17); (18); in: (19); In the formula, It is a frequency domain window function used to suppress higher harmonic components. For the frequency variable in a one-dimensional Fourier transform, This represents the fundamental frequency position corresponding to the one-dimensional fringe signal. This is the half-bandwidth parameter of the frequency domain window function.

[0042] The filtered fringe signal is inversely transformed to recover an approximately ideal one-dimensional fringe signal: (20); (twenty one); in, The wrapped phase is calculated based on one-dimensional Fourier filter fringes. This is the spectrum after windowing filtering. is a one-dimensional inverse Fourier transform operator, where N is the number of phase shift steps.

[0043] Subsequently, the corresponding wrapping phase was calculated for the recovered one-dimensional fringe signal using both the phase-shifting method and the Hilbert transform: (twenty two); (twenty three); in, The wrapped phase is calculated based on the one-dimensional Hilbert transform fringes. It is a one-dimensional Hilbert transformation operator.

[0044] Because the two methods have different error characteristics under saturation conditions, this invention obtains a more accurate wrapping phase value at the saturated pixel by locally fusing the two sets of wrapping phases. Figure 5 As shown, the change in the wrapped phase before and after local phase correction is obtained by calculating the corrected wrapped phase using the following formula: (twenty four); in, This is the corrected wrapper phase obtained through local phase fusion. The wrapped phase is calculated based on one-dimensional Fourier filter fringes. The wrapped phase is calculated based on the one-dimensional Hilbert transform fringes.

[0045] Finally, the corrected wrapper phase is backfilled to the corresponding pixel position, achieving fine correction of the phase information of the overexposed area.

[0046] Figure 6 This is a schematic diagram of the final unfolded phase of an embodiment of the present invention, wherein: Figure 6 In the image, (a) represents a row selected from the original stripe image. Figure 6 (b) in the table shows the comparison results before and after the phase correction for the corresponding row; Figure 6 (c) in the figure represents the expanded phase distribution before correction; Figure 6 In the diagram, (d) represents the corrected expanded phase distribution; Figure 6 (e) in the diagram is a magnified view of the unfolded phase in the overexposed region before correction; Figure 6 (f) in the figure is a magnified schematic diagram of the corrected expanded phase in the overexposed region.

[0047] Through the above steps, the present invention effectively reduces the phase error caused by overexposure of highly reflective surfaces without increasing the number of projected stripes or hardware complexity, thereby improving the accuracy and stability of three-dimensional measurement.

[0048] The embodiments described above are merely preferred embodiments of the present invention and are not intended to limit the scope of the present invention. Various modifications and improvements made to the technical solutions of the present invention by those skilled in the art without departing from the spirit of the present invention should fall within the protection scope defined by the claims of the present invention.

Claims

1. A method for phase unfolding of highly reflective surfaces based on fringe projection using frequency reuse, characterized in that, include: Multi-frequency phase-shift fringe images of the object under test are acquired. Pixel-level intensity analysis is performed on the highest frequency fringe image in the multi-frequency phase-shift fringe images. Overexposed areas where intensity saturation occurs are detected and marked. The image is divided into overexposed areas and unexposed areas. For unexposed areas, the generalized phase-shift method is used to solve its wrapping phase, which is used to obtain the wrapping phase of the mid-frequency and low-frequency areas and the overexposed area mask. Based on the principle of multi-frequency heterodyne, the initial unfolded phase of each frequency is obtained, and reliable unfolded phase points are obtained through modulation mask filtering, planar block filtering, and median filtering. Then, through data interpolation algorithm, continuous unfolded phases containing highly reflective regions are obtained at each frequency. For each frequency, a multi-threshold constraint is applied to the complete continuous unfolded phase to construct a complementary Gray code consistent with the wrapping phase period, thereby correcting the fringe order of the unfolded phase at each frequency. When designing projection patterns, both mid-frequency and low-frequency projection stripe patterns are multiplied by a preset coefficient less than 1. That is, under the same conditions, the non-high-frequency pattern is set with a target darkness so that the overexposed points at high frequencies will no longer be overexposed at low frequencies. Then, the unfolded phase of the point is obtained at low frequencies, and then converted to the high-frequency unfolded phase according to the frequency relationship to achieve frequency reuse. For points that are overexposed at all frequencies, a one-dimensional Fourier transform is used to extract the fundamental frequency within a certain area of ​​the row containing that point. Then, an inverse Fourier transform is used to obtain a new unexposed fringe pattern, and a wrap phase calculation is performed. The obtained one-dimensional fringe pattern is then subjected to a Hilbert transform, and another wrap phase calculation is performed. The two wrap phase calculations are fused together to perform high-precision correction of the wrap phase of overexposed points.

2. The method for phase unwrapping of highly reflective surfaces based on frequency reuse fringe projection according to claim 1, characterized in that, Obtaining the overexposed area mask includes: The multi-frequency phase-shifted stripe image is analyzed pixel by pixel. For a certain frequency stripe pattern, the gray value of each pixel in each frame is compared with the overexposure threshold. If the gray value exceeds the threshold, the pixel is defined as overexposed in that frame. If the number of non-overexposed frames for the pixel is less than 3, the pixel is marked as an overexposed point at that frequency. Other pixels are processed in the same way. Then, overexposure masks and non-overexposure masks are established for each frequency.

3. The method for phase unwrapping of highly reflective surfaces based on frequency reuse fringe projection according to claim 1, characterized in that, After obtaining the continuous unfolded phase, the process includes: Unreliable fringe order points are removed by planar block phase filtering: Based on the ramp characteristics of the unfolded phase, the entire initial unfolded phase region is divided into four regions, and planar filtering is performed based on random consistency. The in-plane point threshold is set to 5, which is less than 2π of a fringe order phase range, in order to remove fringe order error points. This is used to obtain accurate phase fringe order when constructing complementary Gray codes.

4. The method for phase unwrapping of highly reflective surfaces based on frequency reuse fringe projection according to claim 1, characterized in that, Constructing the complementary Gray code includes: Based on the expanded phase range of the projected pattern, the expanded phase obtained by the above interpolation is normalized to the interval [-π, π]. Then, the initial expanded phase of each frequency is subject to the following multi-threshold constraints to construct complementary Gray codes: ； ； in, For Gray code diagram order, To normalize the expanded phase to the interval [-π, π], For index number, The m-th frame is the Gray code pattern.

5. The method for phase unwrapping of highly reflective surfaces based on frequency reuse fringe projection according to claim 1, characterized in that, The fringe order for correcting the phase expansion at each frequency includes: Correcting the stripe order of overexposed points in the overexposed region: Based on the constructed Gray code pattern, the correct stripe order is obtained using a complementary Gray code decoding algorithm, which is then used to correct the stripe order of overexposed points in the overexposed region.

6. The method for phase unwrapping of highly reflective surfaces based on frequency reuse fringe projection according to claim 1, characterized in that, Implementing the frequency reuse includes: For pixels that are overexposed at high frequencies but not at mid- or low frequencies, frequency reuse is achieved by utilizing the proportional relationship between frequencies and recovering the unfolded phase at high frequencies based on the unfolded phase of that pixel at mid- or low frequencies. For pixels that are overexposed at high frequencies but not at medium frequencies, the high-frequency phase correction is as follows: ； in, This is the intermediate frequency. For high frequency, This represents the expanded phase of that point after high-frequency correction. The mid-frequency expansion phase at this point; For pixels that are overexposed at high and mid frequencies but not at low frequencies, the high-frequency phase correction is as follows: ； in, Low frequency This represents the expanded phase of that point after high-frequency correction. The low-frequency phase at this point is the phase expansion.

7. The method for phase unwrapping of highly reflective surfaces based on frequency reuse fringe projection according to claim 1, characterized in that, Calculating the package phase includes: For pixels that are overexposed at all frequencies, a new stripe pattern is constructed based on one-dimensional Fourier transform and one-dimensional Hilbert transform, and the wrapping phase obtained from the two methods is fused to achieve wrapping phase correction for this type of overexposed pixel: The fringe projection is a vertical fringe projection. For pixels (x0, y0) that are overexposed at all frequencies, a local one-dimensional signal is extracted along their row: ； in, L is the one-dimensional fringe signal corresponding to the nth phase shift extracted in the neighborhood of the saturated pixel. L is the half-window length of the local one-dimensional fringe signal, used to limit the range of one-dimensional fringe extraction. The characteristic of the value of L is that the period size is obtained in the non-overexposed area. L is an integer multiple of the period size to prevent spectral leakage during one-dimensional Fourier transform.

8. The method for phase unwrapping of highly reflective surfaces based on frequency reuse fringe projection according to claim 1, characterized in that, Extracting the fundamental frequency includes: By performing a Fourier transform on the local one-dimensional fringe signal, a windowed filter is constructed based on fundamental frequency localization to suppress DC components and higher harmonics, and then the fundamental frequency component in the signal is extracted. ； ； in: ； In the formula, This refers to the one-dimensional fringe signal corresponding to the nth phase shift extracted within the neighborhood of the saturated pixel. One-dimensional fringe signal The spectrum representation, This is the spectrum after windowing filtering. This is a frequency domain window function used to suppress DC components and higher harmonic components. For the frequency variable in a one-dimensional Fourier transform, This represents the fundamental frequency position corresponding to the one-dimensional fringe signal. This is the half-bandwidth parameter of the frequency domain window function; The inverse transform yields the filter fringes, from which the Fourier filter phase is calculated. ； ； in, The wrapped phase is calculated based on the one-dimensional Fourier filter fringe pattern. This is the spectrum after windowing filtering. For a one-dimensional inverse Fourier transform operator, N This represents the number of phase shift steps.

9. The method for phase unfolding of highly reflective surfaces based on frequency reuse fringe projection according to claim 7, characterized in that, The one-dimensional Hilbert transform is used to construct an analytic signal orthogonal to the filtered one-dimensional fringe signal to obtain a wrap-around phase complementary to the Fourier filter phase error, including: ； ； in, The wrapped phase is calculated based on the one-dimensional Hilbert transform fringes. Let N be a one-dimensional Hilbert transform operator, where N is the number of phase shift steps.

10. The method for phase unwrapping of highly reflective surfaces based on frequency reuse fringe projection according to claim 1, characterized in that, High-precision correction of the overexposed point phase includes: Local phase fusion is achieved by averaging the two sets of wrapper phases: ； in, This is the corrected wrapper phase obtained through local phase fusion. The wrapped phase is calculated based on one-dimensional Fourier filter fringes. The wrapped phase is calculated based on one-dimensional Hilbert transform fringes; The wrap-around phase of the overexposed point can be extracted from the fused phase. By combining the overexposed point fringe order correction, the unfolded phase correction of the overexposed point can be achieved.

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