Three-dimensional measurement method based on nonlinear cosine coding

Abstract

The invention discloses a three-dimensional measurement method based on non-linear cosine coding, and the method comprises the steps: 1, generating an N-step phase shift code, constructing a wavelength-De Bruijn element mapping table, and generating a non-linear cosine code and a non-linear cosine component code; 2, projecting the phase shift fringes and the non-linear cosine coding fringes to a measured object frame by frame, obtaining a modulation pattern, and decoding the modulation pattern to obtain a wrapped phase and a non-linear cosine component; 3, constructing an approximate phase to unwrap the wrapped phase to obtain a local continuous phase, and segmenting the local continuous phase into a local phase; 4, a cosine component error of a local phase region is minimized to retrieve a phase order, so that phase unwrapping is realized, and an error absolute phase is obtained; and 5, performing phase repair on the error absolute phase to obtain an errorless absolute phase, and reconstructing a three-dimensional model of the object in combination with the parameters of the structured light system. According to the invention, high-precision phase unwrapping can be realized only by using a single-frame pattern, and the three-dimensional measurement efficiency is greatly improved.

Description

Technical Field

[0001] This invention relates to a three-dimensional measurement method based on nonlinear cosine coding. Background Technology

[0002] With the rapid development of image processing, optics, and computer technology, optical image processing technology based on photoelectric imaging theory has made significant progress. This technology has been widely researched and applied over the past few decades, driving numerous breakthroughs in computer vision technology. Optical image processing, with its unique advantages in information processing and visual perception, has become a crucial support for the continuous evolution of the computer vision field. As people's demands for the richness, detail, and diversity of image information continue to increase, computer vision research has gradually shifted from traditional two-dimensional image processing to the acquisition and analysis of complex three-dimensional spatial data. This transformation not only requires more intelligent and efficient technology but also demands that computer vision be able to process three-dimensional image data accurately and at high speed, providing more comprehensive spatial perception. This has become one of the current research focuses in computer vision and intelligent sensing technologies.

[0003] Optical 3D measurement technology, with its high precision, low cost, and non-contact characteristics, has shown broad application prospects in various fields such as industry, medicine, and engineering. It is particularly prevalent in scenarios such as robot navigation, industrial modeling, and microscopic measurement due to its high precision and stability. Currently, structured light measurement is one of the mainstream methods in optical 3D measurement. This method utilizes a projector to project a grating pattern with phase information, combined with a camera for simultaneous imaging and phase decoding, thereby acquiring the 3D shape information of an object's surface. This technology is highly valued because it can stably acquire depth information under various lighting conditions. However, phase information has periodicity, which... Cyclic phases within a given range can easily lead to phase ambiguity. Therefore, phase unwrapping techniques are needed to obtain continuous absolute phases in order to recover the complete three-dimensional information of an object.

[0004] After years of development, phase unwrapping technology has made significant progress, mainly divided into spatial phase unwrapping and temporal phase unwrapping. Spatial phase unwrapping is usually based on the phase relationship between pixels and is suitable for reconstructing the phase on surfaces with good continuity. However, in scenes with drastic depth changes or the presence of independent objects, spatial phase unwrapping is prone to errors, affecting accuracy. In contrast, temporal phase unwrapping uses multi-frame image acquisition to uniquely identify each phase order, effectively solving the limitations of spatial unwrapping in discontinuous regions, and thus performing better in complex scenes. However, temporal phase unwrapping also faces problems such as slow measurement speed and accumulation of temporal errors, affecting measurement efficiency and accuracy. Although Chinese patent application CN119251276A, a three-dimensional measurement method with non-uniform periodic phase shift, discloses a method of forming a combined code using multiple single-frequency fringes of different frequencies in De Bruijn order, which improves coding efficiency and reduces cost, this scheme uses sinusoidal fringes of different wavelengths to form the combined code, resulting in uneven measurement accuracy, which still affects the final measurement results. Furthermore, this scheme calculates the phase order point-by-point using local phase and employs frequency domain transformation in the calculation. This computational approach is computationally intensive, resulting in low efficiency and making it difficult to meet the demands of rapid measurement. Therefore, developing an efficient and reliable phase unfolding method that does not require additional data patterns to meet the application requirements of higher real-time performance, accuracy, and stability has become an important research direction in the field of optical 3D measurement. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a three-dimensional measurement method based on nonlinear cosine encoding.

[0006] The technical solution of the invention is as follows:

[0007] A three-dimensional measurement method based on nonlinear cosine coding includes the following steps:

[0008] Step 1: Generate N-step phase shift codes, and then construct a wavelength-De Bruijn element mapping table to generate nonlinear cosine codes and nonlinear cosine component codes;

[0009] Nonlinear cosine component coding is generated from nonlinear cosine coding, which is used for subsequent phase expansion steps.

[0010] Step 2: Project the phase-shifted fringes and nonlinear cosine-coded fringes frame by frame onto the object under test, and use the camera to acquire the modulation pattern and decode it to obtain the wrapping phase and nonlinear cosine components;

[0011] Step 3: Construct an approximate phase and perform phase expansion on the wrapped phase to obtain a locally continuous phase, and then divide it into local phases; the local phases are obtained by dividing the locally continuous phases. The locally continuous phases are truncated in the global scope, while the local phases are continuous in the global scope.

[0012] Step 4: Minimize the cosine component error of the local phase region to retrieve the phase order, thereby realizing phase expansion and obtaining the error absolute phase.

[0013] Step 5: Perform phase repair on the error absolute phase to obtain the error-free absolute phase, and reconstruct the three-dimensional model of the object by combining the structured light system parameters.

[0014] The nonlinear cosine encoding in step 1 is obtained as follows:

[0015] Step 1.1: Generate N-step phase shift codes.

[0016] Step 1.2: Select m wavelengths and De Bruijn elements to construct a wavelength-De Bruijn element mapping table.

[0017] Step 1.3 generates an m-ary n-order De Bruijn wavelength sequence and generates nonlinear cosine codes and nonlinear cosine component codes. m is an integer greater than 0.

[0018] The N-step phase shift encoding in step 1.1 is as follows:

[0019] ;

[0020] and Let x and y represent the horizontal and vertical coordinates of the projector plane, respectively. , . and These represent the horizontal and vertical pixel resolutions of the projector plane, respectively. For N-step phase shift coding, It is the wavelength of the sine fringes. Indicates the total number of phase-shifting patterns. ; This represents the intensity of the encoded background; it can be understood as the average gray level of the background. , Indicates the coded modulation strength. ; and The preferred value is 127.5.

[0021] The wavelength-De Bruijn element mapping table in step 1.2 is shown in Table 1 below: Table 1 Wavelength-De Bruijn element mapping table.

[0022] .

[0023] The De Bruijn wavelength sequence in step 1.3 is as follows:

[0024] The De Bruijn sequence is a sequence of m De Bruijn elements with a length of... The pseudo-random sequence, therefore The number of wavelengths in There are [number] unknowns. Since it is pseudo-random, it is represented by an unknown.

[0025] in, The De Bruijn wavelength sequence is used; then, a nonlinear cosine code is generated using the following formula:

[0026] ;

[0027] in:

[0028] ; This formula covers all possible cases, because the index of the pixel coordinate is always a positive number and will not exceed the maximum pixel.

[0029] in, It is a nonlinear cosine coding; then, nonlinear cosine component coding is generated:

[0030] .

[0031] The wrapping phase and nonlinear cosine components in step 2 are obtained as follows:

[0032] Step 2.1: The N-step phase-shift coded pattern is projected onto the scene to be tested by a projector, and the deformed phase-shift fringe pattern is captured simultaneously by an industrial camera. The average fringe intensity, intensity modulation, and wrapping phase are then calculated.

[0033] Step 2.2: The nonlinear fringe pattern is projected onto the scene to be tested by the projector, and the nonlinear cosine deformed fringe pattern is captured by the industrial camera at the same time. The phase cosine component is calculated by combining the average intensity of the fringe and the intensity modulation.

[0034] The deformed phase-shift fringe pattern in step 2.1 is as follows:

[0035] ;

[0036] in, and Representing the x and y coordinates of the camera plane, respectively. , ; and These represent the horizontal and vertical pixel resolutions (i.e., the number of pixels) of the camera plane, respectively. Indicates the average intensity of the stripes. Indicates the intensity modulation of the stripes. Indicates the phase of the package. ;

[0037] The average intensity, intensity modulation, and wrapping phase of the deformed phase-shifted fringes were calculated using the phase-shift method. , and The calculation formula is:

[0038] ; I is the pattern captured by the camera, so parameters A, B, etc. are unknowns. This equation is used to solve for these unknowns.

[0039] in, Indicates the average intensity of the stripes. Indicates intensity modulation. This indicates the wrap-around phase.

[0040] The nonlinear cosine deformation fringe pattern in step 2.2 is as follows:

[0041] ;

[0042] in, This represents a nonlinear cosine deformation fringe pattern. This represents the nonlinear wrapping phase. Next, the nonlinear cosine components are calculated:

[0043] ;

[0044] in, It represents the nonlinear cosine component. It is the nonlinear cosine component of the camera pixel (x,y). It is the nonlinear cosine component of the projector pixel v. They are completely different.

[0045] The local phase in step 3 is obtained as follows:

[0046] Step 3.1, calculate the wrapping phase along each and The directional wrapping phase gradient is corrected to the absolute phase gradient.

[0047] Step 3.2, through and The absolute phase gradient of each direction is used to predict its approximate phase gradient, and the approximate phase is calculated.

[0048] Step 3.3: Use the approximate phase to perform phase expansion on the wrapped phase to obtain the local continuous phase, and then perform phase segmentation on the local continuous phase to obtain the local phase;

[0049] In step 3.1 and The formulas for calculating the phase gradient of the wrapping direction are as follows:

[0050] ;

[0051] ;

[0052] in, and They are and The direction of the wrapping phase gradient, and These are the horizontal and vertical Prewitt kernels, respectively. p and q These represent the x and y coordinates in the computation kernel, respectively. It is the core size. It is the pixel product operator;

[0053] Next, respectively and Corrected to absolute phase gradient, the calculation formulas are as follows:

[0054] ;

[0055] ;

[0056] in, and They are and Absolute phase gradient in direction;

[0057] In step 3.2 and The formulas for calculating the approximate phase gradient in the direction are as follows:

[0058] ;

[0059] ;

[0060] in, , This represents the adaptive binarization operator (see: Huang, Deng-Yuan, and Chia-Hung Wang. "Optimal multi-level thresholding using a two-stage Otsu optimization approach." Pattern Recognition Letters 30.3(2009): 275-284.). Operator This is an indicator function that takes the value 1 if the condition is true, and 0 otherwise. and They are and The approximate phase gradient in the direction; then, the approximate phase is calculated using the formula:

[0061] ;

[0062] in, It is an approximate phase;

[0063] The formula for calculating the local continuous phase in step 3.3 is as follows:

[0064] ;

[0065] in, This represents the rounding operator. This represents a locally continuous phase, which includes multiple locally continuous phases; therefore, it is further defined as follows: The phase is divided into multiple local phases with continuous characteristics, and the calculation formula is as follows:

[0066] ;

[0067] in, Indicates a local phase group. This represents the flood filling segmentation operator. Indicates the obtained first One local phase; This represents the operator for counting the number of pixels. This indicates that the number of retained pixels is greater than Local phase, This indicates the number of local phases obtained.

[0068] The absolute phase error in step 4 is obtained as follows:

[0069] Step 4.1: By constructing the mapping from the local continuous phase to the ordinate of the projector plane, and the mapping from the ordinate of the projector plane to the nonlinear cosine component encoding, the mapping from the local continuous phase to the nonlinear cosine component encoding is realized.

[0070] Step 4.2: Minimize the cosine component error of the local phase region to retrieve the phase order, thereby realizing phase expansion and obtaining the error absolute phase;

[0071] The formula for mapping the ordinate from the image plane to the projector plane in step 4.1 is:

[0072] ;

[0073] in, express The first in the region Each pixel. express Local continuous phase value of the position. express The corresponding ordinate of the projector plane. Next, the mapping from the projector plane's ordinate to the nonlinear cosine component encoding is performed, calculated using the following formula:

[0074] ;

[0075] ;

[0076] in, express The corresponding nonlinear cosine component encoding values. Therefore, step 4.1 established... The mapping relationship realizes the mapping from local phase to nonlinear cosine component encoding.

[0077] The formula for calculating the phase order in step 4.2 is:

[0078] ;

[0079] in, express The nonlinear cosine component value of the pixel coordinate position. For absolute value operators, This represents the local phase order. Then, all the acquired values ​​are fused. The local continuous phase order is obtained by the following formula:

[0080] ;

[0081] in, For union operators, This represents the locally continuous phase order. Next, we will... Combination Phase expansion is achieved using the following formula:

[0082] ;

[0083] in, This indicates the absolute phase of the error.

[0084] Furthermore, in the aforementioned three-dimensional measurement method based on nonlinear cosine coding, the three-dimensional model of the object in step 5 is obtained as follows:

[0085] because It contains noise and a small amount of phase error, therefore... The formula for phase repair is as follows:

[0086] ;

[0087] in This is the median filtering operator. For filtering kernel, This is the accurate absolute phase. Finally, Object models can be reconstructed by combining structured light system parameters (see: Li, Beiwen, et al. "High-accuracy, high-speed 3D structured light imaging techniques and potential applications to intelligent robotics." International journal of intelligentrobotics and applications 1.1 (2017): 86-103.).

[0088] Beneficial effects:

[0089] 1. This invention proposes a three-dimensional measurement method based on nonlinear cosine encoding, which uses multiple sinusoidal fringes of different frequencies to be combined and encoded in De Bruijn order. This encoding, composed of pure sinusoidal fringes, is robust to complex object structures and different reflection regions. Because the amplitude and intensity distribution of the sine wave are not modified, high measurement accuracy is ensured.

[0090] 2. This invention achieves measurement accuracy similar to advanced multi-frequency heterodyne methods using only 1 / 6 of the additional projections, greatly improving coding efficiency;

[0091] 3. This invention does not require the introduction of additional equipment and only projects a single frame of additional stripes, ensuring low measurement cost and high measurement efficiency.

[0092] The method proposed in this invention introduces an additional nonlinear cosine-coded pattern, which uses multiple sinusoidal fringes of different wavelengths cascaded in a DB sequence. During the decoding stage, the phase order is calculated by minimizing the cosine component error in local phase regions, achieving robust phase disambiguation. High-precision phase unfolding can be achieved using only a single frame pattern, significantly improving the efficiency of 3D measurement. Attached Figure Description

[0093] Figure 1 This is a schematic diagram of the measurement process of the three-dimensional measurement method based on nonlinear cosine encoding in Embodiment 1 of the present invention;

[0094] Figure 2 The N-step phase-shift coding diagram and nonlinear cosine coding diagram in Embodiment 1 of the present invention are shown below. Figure 2 (a) Figure 2 (b) and Figure 2 (c) Phase shift coding diagrams for I1, I2, and I3, respectively. Figure 2 (d) is the nonlinear cosine deformation fringe pattern;

[0095] Figure 3 The deformed phase-shift fringe pattern and the nonlinear cosine deformed fringe pattern obtained in Embodiment 1 of the present invention are shown below. Figure 3 (a) Figure 3 (b) and Figure 3 (c) are respectively the corresponding Figure 2 (a) Figure 2 (b) and Figure 2 (c) A photograph of the deformed phase-shifted fringe pattern. Figure 3 (d) is a photograph of a nonlinear cosine deformation fringe pattern;

[0096] Figure 4 The average intensity map, intensity modulation map, wrapping phase map, and nonlinear cosine component map in Embodiment 1 of the present invention are shown below. Figure 4 (a) is the average intensity map. Figure 4 (b) is the intensity modulation diagram. Figure 4 (c) is the wrapping phase map. Figure 4 (d) is the nonlinear cosine component diagram;

[0097] Figure 5 As in Embodiment 1 of the present invention and Directional wrapping phase gradient map, and and Directional absolute phase gradient map, where Figure 5 (a) is Directional wrapping phase gradient map, Figure 5 (b) is Directional wrapping phase gradient map, Figure 5 (c) is Directional absolute phase gradient map Figure 5 (d) is Directional absolute phase gradient map;

[0098] Figure 6 The approximate phase map, local continuous phase, and local phase map in Embodiment 1 of the present invention are shown below. Figure 6 (a) is an approximate phase diagram. Figure 6 (b) is a locally continuous phase map. Figure 6 (c) and Figure 6 (d) are respectively and Local phase map;

[0099] Figure 7 This is the phase order diagram in Embodiment 1 of the present invention;

[0100] Figure 8 This is the absolute phase diagram in Embodiment 1 of the present invention.

[0101] Figure 9 This is the object model in Embodiment 1 of the present invention. Detailed Implementation

[0102] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. However, this should not be construed as limiting the scope of the above-described subject matter of the present invention to the following embodiments; all technologies implemented based on the content of the present invention fall within the scope of the present invention.

[0103] To better illustrate the method of this invention, this embodiment uses a quaternary 3rd order De Bruijn sequence as an example, combined with... The three-step phase-shift coding scheme is used to illustrate the three-dimensional measurement of a plaster figure.

[0104] like Figure 1 The diagram shows a flowchart of the present invention, a three-dimensional measurement method based on nonlinear cosine coding, comprising the following steps:

[0105] Step 1: Generate N-step phase shift codes, and then construct a wavelength-De Bruijn element mapping table to generate nonlinear cosine codes and nonlinear cosine component codes.

[0106] To ensure measurement accuracy, use The three-step phase-shift method is used for sinusoidal encoding, and the encoding formula is as follows:

[0107] (1);

[0108] in, and These represent the horizontal and vertical coordinates of the projector plane, respectively. The three-step phase shift coding is as follows: Figure 2 (a)- Figure 2 As shown in (c) Next, a wavelength De Bruijn element mapping table is constructed to generate nonlinear cosine codes.

[0109] To ensure the uniformity of the calculated phase, four approximate wavelengths were selected for sinusoidal encoding: 26, 29, 32, and 35. These wavelengths were then assigned to four De Bruijn elements, constructing the wavelength-De Bruijn element mapping table shown in Table 2 below.

[0110] Table 2 De Bruijn element-wavelength mapping table.

[0111] .

[0112] Next, a set of 4-element, 3rd-order De Bruijn wavelength sequences was constructed, as shown in formula (2): (2);

[0113] in, This represents a 4-element, 3rd-order De Bruijn wavelength sequence. Next, using... The wavelength in the formula is used to generate a nonlinear cosine fringe pattern, and the calculation formula is as follows:

[0114] (3);

[0115] in

[0116] (4);

[0117] Represents the horizontal and vertical coordinates of the projector plane. For nonlinear cosine coding patterns, such as Figure 2 As shown in (d). Based on the properties of De Bruijn pseudorandom sequences, In The nonlinear distribution among adjacent wavelengths is unique within the global coding range.

[0118] Step 2: Project the phase-shifted fringes and nonlinear cosine-coded fringes frame by frame onto the object under test. The camera acquires the modulation pattern and decodes it to obtain the wrapped phase and nonlinear cosine components.

[0119] Phase-shifted fringes and nonlinear cosine-coded patterns are projected onto the scene under test by a projector, and deformed fringe patterns are simultaneously captured by an industrial camera. Their resolution is 1920×1440 pixels, as shown below. Figure 3 (a)- Figure 3 As shown in (d). Further calculations using formula (5) yielded the fringe average intensity, intensity modulation, and wrapping phase, as shown in [the diagram]. Figure 4 (a)- Figure 4 As shown in (c);

[0120] (5);

[0121] in, Indicates the average intensity of the stripes. Indicates intensity modulation. This represents the wrapping phase. Next, the nonlinear cosine components are calculated using formula (6):

[0122] (6);

[0123] in, Representing nonlinear cosine components, such as Figure 4 As shown in (d).

[0124] Step 3: Construct an approximate phase and perform phase expansion on the wrapped phase to obtain a local continuous phase, and then divide it into local phases.

[0125] First, calculate using formulas (7)-(8). exist and The phase gradient of the direction:

[0126] (7);

[0127] (8);

[0128] in, and They are and The phase gradient of the direction is as follows: Figure 5 (a)- Figure 5 As shown in (b). and These are the horizontal and vertical Prewitt processing kernels, each 3x3 pixels in size. p and q These represent the x and y coordinates in the computation kernel, respectively. This is the pixel product operator. However, the edge-truncation property of the wrapped phase causes periodic jumps in the phase gradient. Therefore, equations (9)-(10) are used to further transform the wrapped phase gradient into a continuous absolute phase gradient:

[0129] (9);

[0130] (10);

[0131] in, and They are and The absolute phase gradient in the direction, respectively, are as follows: Figure 5 (c)- Figure 5 As shown in (d). Next, the approximate phase gradient of the scene under test is estimated using formulas (11)-(12):

[0132] (11);

[0133] (12);

[0134] in, , This represents the adaptive binarization operator (see: Huang, Deng-Yuan, and Chia-Hung Wang. "Optimal multi-level thresholding using a two-stage Otsu optimization approach." Pattern Recognition Letters 30.3(2009): 275-284.). Operator This is an indicator function that takes the value 1 if the condition is true, and 0 otherwise. and They are and The approximate phase gradient in the direction. Next, the approximate phase is calculated using formula (13):

[0135] (13);

[0136] in, For approximate phase, such as Figure 6 As shown in (a). Due to Phase with package Having similar phase gradients, therefore, using formula (14) for Perform preliminary phase expansion:

[0137] (14);

[0138] in, This represents the rounding operator. Representing a locally continuous phase, such as Figure 6As shown in (b), it contains multiple local phases with continuous characteristics. Since the truncation edges of the local continuous phases provide good segmentation conditions, formula (15) is further used to further divide... Divide into multiple local phases with continuous characteristics:

[0139] (15);

[0140] in, Indicates a local phase group. This represents the flood filling segmentation operator. Indicates the obtained first A local phase, such as Figure 6 (c)- Figure 6 As shown in (d). This represents the operator for counting the number of pixels. This indicates that the local phase with more than 10 pixels is retained.

[0141] Step 4: Minimize the cosine component error of the local phase region to retrieve the phase order, thereby realizing phase expansion and obtaining the error absolute phase;

[0142] First, the ordinate mapping from the local continuous phase to the projector plane is constructed using formula (16):

[0143] (16);

[0144] in, express The first in the region Each pixel. express Local continuous phase value of the position. express The corresponding ordinate of the projector plane. Next, using formulas (17)-(18), the mapping from the ordinate of the projector plane to the nonlinear cosine component encoding is constructed:

[0145] (17);

[0146] (18);

[0147] in, express The corresponding nonlinear cosine component encoding value. Therefore, formulas (16)-(18) establish... The mapping relationship realizes the mapping from local phase to nonlinear cosine component encoding. Then, using formula (19), the phase order is retrieved by minimizing the cosine component error in the local phase region:

[0148] (19);

[0149] in, express The nonlinear cosine component value of the pixel coordinate position. For absolute value operators, This represents the local phase order. Then, all the obtained phases are fused using formula (20). The local continuous phase order is obtained:

[0150] (20);

[0151] in, For union operators, For locally continuous phase orders, such as Figure 7 As shown. Next, use formula (21) to... Combination Achieve phase expansion:

[0152] (twenty one);

[0153] in, This represents the absolute phase of the error, which includes noise and a small amount of error phase.

[0154] Step 5: Perform phase repair on the error absolute phase to obtain the error-free absolute phase, and reconstruct the three-dimensional model of the object by combining the structured light system parameters;

[0155] In order to eliminate The error in the formula (22) is used to calculate the error. Perform phase repair:

[0156] (twenty two);

[0157] in This is the median filtering operator. For filtering kernel, For an accurate absolute phase, such as Figure 8 As shown. Finally, Object models can be reconstructed using structured light system parameters (see: Li, Beiwen, et al. "High-accuracy, high-speed 3D structured light imaging techniques and potential applications to intelligent robotics." International journal of intelligent robotics and applications 1.1 (2017): 86-103.). Figure 9 As shown.

[0158] It should be emphasized that the examples described in this invention are illustrative rather than limiting. Therefore, this invention is not limited to the examples described in the specific embodiments. Any other embodiments derived by those skilled in the art based on the technical solutions of this invention, without departing from the spirit and scope of this invention, whether modifications or substitutions, are also within the protection scope of this invention.

Claims

1. A three-dimensional measurement method based on nonlinear cosine coding, characterized in that, Includes the following steps: Step 1: Generate N-step phase shift codes, and then construct a wavelength-De Bruijn element mapping table to generate nonlinear cosine codes and nonlinear cosine component codes; Step 2: Project the phase-shifted fringes and nonlinear cosine-coded fringes frame by frame onto the object under test, and use the camera to acquire the modulation pattern and decode it to obtain the wrapping phase and nonlinear cosine components; Step 3: Construct an approximate phase, perform phase unrolling on the wrapped phase to obtain a local continuous phase, and then segment it into local phases; Step 4: Minimize the cosine component error of the local phase region to retrieve the phase order, thereby realizing phase expansion and obtaining the error absolute phase; Step 5: Perform phase repair on the error absolute phase to obtain the error-free absolute phase, and reconstruct the three-dimensional model of the object by combining the structured light system parameters.

2. The three-dimensional measurement method based on nonlinear cosine encoding according to claim 1, characterized in that, The nonlinear cosine encoding in step 1 is obtained as follows: Step 1.1: Generate N-step phase shift codes; Step 1.2: Select m wavelengths and De Bruijn elements to construct a wavelength-De Bruijn element mapping table; Step 1.3: Generate an m-ary n-order De Bruijn wavelength sequence, and generate nonlinear cosine coding and nonlinear cosine component coding.

3. The three-dimensional measurement method based on nonlinear cosine encoding according to claim 2, characterized in that, The N-step phase shift encoding in step 1.1 is as follows: ； and These represent the horizontal and vertical coordinates of the projector plane, respectively. , ; and These represent the horizontal and vertical pixel resolutions of the projector plane, respectively. For N-step phase shift coding, It is the wavelength of the sine fringes. Indicates the total number of phase-shifting patterns. ; Indicates the intensity of the encoded background. , Indicates the coded modulation strength. ; The wavelength-De Bruijn element mapping table in step 1.2 is used to map m wavelengths f0-f m-1 , with m De Bruijn elements μ0-μ m-1 Each number corresponds to the other in a one-to-one mapping. The De Bruijn wavelength sequence in step 1.3 is as follows: ； in, The De Bruijn wavelength sequence is used; then, a nonlinear cosine code is generated using the following formula: ； in: ； in, It is a nonlinear cosine coding; then, nonlinear cosine component coding is generated: 。 4. The three-dimensional measurement method based on nonlinear cosine encoding according to claim 3, characterized in that, The wrapping phase and nonlinear cosine components in step 2 are obtained as follows: Step 2.1: The N-step phase-shift coded pattern is projected onto the scene to be tested by a projector, and the deformed phase-shift fringe pattern is captured simultaneously by an industrial camera. The average fringe intensity, intensity modulation, and wrapping phase are then calculated. Step 2.2: The nonlinear fringe pattern is projected onto the scene to be tested by the projector, and the nonlinear cosine deformed fringe pattern is captured by the industrial camera at the same time. The phase cosine component is calculated by combining the average intensity of the fringe and the intensity modulation. The deformed phase-shift fringe pattern in step 2.1 is as follows: ； in, and Representing the x and y coordinates of the camera plane, respectively. , ; and These represent the horizontal and vertical pixel resolutions of the camera plane, respectively. Indicates the average intensity of the stripes. Indicates the intensity modulation of the stripes. Indicates the phase of the package. ; The average intensity, intensity modulation, and wrapping phase of the deformed phase-shifted fringes were calculated using the phase-shift method. , and The calculation formula is: ； in, Indicates the average intensity of the stripes. Indicates intensity modulation. Indicates the package phase; The nonlinear cosine deformation fringe pattern in step 2.2 is as follows: ； in, This represents a nonlinear cosine deformation fringe pattern. The nonlinear wrapping phase is represented; then, the nonlinear cosine components are calculated: ； in, It represents the nonlinear cosine component.

5. The three-dimensional measurement method based on nonlinear cosine coding according to claim 4, characterized in that, The local phase in step 3 is obtained as follows: Step 3.1, calculate the wrapping phase along each and The directional wrapping phase gradient is corrected to an absolute phase gradient; Step 3.2, through and The absolute phase gradient of each direction is used to predict its approximate phase gradient, and the approximate phase is calculated. Step 3.3: Use the approximate phase to perform phase expansion on the wrapped phase to obtain a local continuous phase, and then perform phase segmentation on the local continuous phase to obtain a local phase; In step 3.1 and The formulas for calculating the phase gradient of the wrapping direction are as follows: ； ； in, and They are and The direction of the wrapping phase gradient, and These are the horizontal and vertical Prewitt kernels, respectively. p and q These represent the x and y coordinates in the computation kernel, respectively. It's the core size. It is the pixel product operator; Next, respectively and Corrected to absolute phase gradient, the calculation formulas are as follows: ； ； in, and They are and Absolute phase gradient in direction; In step 3.2 and The formulas for calculating the approximate phase gradient in the direction are as follows: ； ； in, , Represents the adaptive binarization operator; operator This is an indicator function; if the condition is true, it takes the value 1, otherwise it takes the value 0. and They are and The approximate phase gradient in the direction; then, the approximate phase is calculated using the formula: ； in, It is an approximate phase; The formula for calculating the local continuous phase in step 3.3 is as follows: ； in, This represents the rounding operator. This represents a locally continuous phase, which includes multiple locally continuous phases; therefore, it is further defined as follows: The phase is divided into multiple local phases with continuous characteristics, and the calculation formula is as follows: ； in, Indicates a local phase group. This represents the flood filling segmentation operator. Indicates the obtained first One local phase; This represents the operator for counting the number of pixels. This indicates that the number of pixels to be retained is greater than Local phase, This indicates the number of local phases obtained.

6. The three-dimensional measurement method based on nonlinear cosine coding according to claim 5, characterized in that, The absolute phase error in step 4 is obtained as follows: Step 4.1: By constructing the mapping from the local continuous phase to the projector plane's ordinate and the mapping from the projector plane's ordinate to the nonlinear cosine component encoding, the mapping from the local continuous phase to the nonlinear cosine component encoding is realized. Step 4.2: Minimize the cosine component error of the local phase region to retrieve the phase order, thereby realizing phase expansion and obtaining the error absolute phase; The formula for mapping the ordinate from the image plane to the projector plane in step 4.1 is: ； in, express The first in the region 1 pixel; express Local continuous phase value of the position, express The corresponding vertical coordinate of the projector plane; next, the mapping from the vertical coordinate of the projector plane to the nonlinear cosine component encoding is performed, and the calculation formula is: ； ； in, express The corresponding nonlinear cosine component encoding values; step 4.1 established The mapping relationship realizes the mapping from local phase to nonlinear cosine component encoding; The formula for calculating the phase order in step 4.2 is: ； in, express The nonlinear cosine component value of the pixel coordinate position; For absolute value operators, Indicate the local phase order; then, fuse all the obtained... The local continuous phase order is obtained by the following formula: ； in, For union operators, For locally continuous phase orders; then, Combination Phase expansion is achieved using the following formula: ； in, This indicates the absolute phase of the error.

7. The three-dimensional measurement method based on nonlinear cosine encoding according to claim 6, characterized in that, The absolute phase error in step 5 is obtained as follows: because It contains noise and a small amount of phase error, therefore... The formula for phase repair is as follows: ； in This is the median filtering operator. For filtering kernel, This is the final absolute phase obtained.

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