A stereoscopic phase unwrapping method based on nonlinear phase encoding

Abstract

The application discloses a kind of stereoscopic phase unwrapping methods based on nonlinear phase coding, comprising the following steps: step one: wavelength-De Bruijn element mapping table is constructed, and non-equivalent period phase shift fringe group is generated;Step two: frame by frame projection phase shift fringe to measured object, obtains modulation pattern and decodes, obtains nonlinear wrapped phase;Step three: construct approximate phase, and do local phase unwrapping to nonlinear wrapped phase, obtain nonlinear local phase;Step four: using stereoscopic phase matching method filters out the phase candidate point and candidate phase order of nonlinear local phase.Step five: using phase candidate point guides nonlinear local phase to carry out phase correlation matching, to filter out unique phase order, to realize phase unwrapping.The method introduced a novel phase distortion feature, using multiple different wavelengths of sinusoidal fringe is connected in series according to DB sequence coding.In decoding stage, by minimizing the local phase difference in left and right views, robust phase disambiguation is realized.Only using 3 projection patterns can realize high-precision measurement, greatly improve the efficiency of three-dimensional measurement.

Description

Technical Field

[0001] The present invention relates to the technical field of three-dimensional shape measurement, and in particular to a three-dimensional phase unwrapping method based on nonlinear phase encoding. Background Art

[0002] With advances in image processing, optics, and computer technology, optical image processing technology, based on optoelectronic imaging theory, has developed rapidly. This technology has undergone extensive research and application over the past few decades, driving significant breakthroughs in computer vision technology. Optical image processing technology, with its advantages in information processing and visual perception, has led to the continuous evolution of computer vision. As demand for information richness and diversity continues to increase, the evolution of computer vision technology has gradually expanded from traditional two-dimensional images to more complex three-dimensional spaces. This shift requires not only more intelligent and efficient technology, but also the ability to efficiently acquire high-quality spatial stereoscopic visual perception information, which has become a current research focus in the field of computer vision.

[0003] Optical 3D measurement technology, as a low-cost, high-precision, and efficient non-contact measurement method, has been widely used in the industrial field. Robot navigation, industrial modeling, microscopic measurement and other fields all rely on the accuracy and reliability of optical 3D measurement technology. Mainstream structured light measurement methods include fringe projection profilometry, which uses a projector to project a grating pattern carrying phase information, and then uses a camera to synchronously capture and phase decode to obtain surface shape information of the object being measured. However, due to the special nature of phase information, that is, the phase circulates in the range of (-π, π], it leads to phase ambiguity. To eliminate this ambiguity, phase unwrapping technology is needed to restore the continuous absolute phase.

[0004] After decades of development, researchers have proposed many effective phase unwrapping methods, including spatial phase unwrapping and temporal phase unwrapping. Spatial phase unwrapping methods usually use the phase relationship between pixels to achieve phase unwrapping. However, when there are depth mutations or isolated objects in the scene, phase unwrapping errors often occur. In contrast, the temporal phase unwrapping method uniquely identifies each phase order of the wrapped phase through additional multi-frame data acquisition, thereby solving the limitations of the spatial phase unwrapping method. However, the temporal phase unwrapping method also has some problems, such as limited measurement speed and accumulation of time domain errors. Therefore, one of the current research focuses is to develop a reliable phase unwrapping method that does not require additional modes to meet the requirements of accuracy and efficiency in practical applications. Summary of the Invention

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

[0006] The technical solutions of the invention are as follows:

[0007] A three-dimensional phase unwrapping method based on nonlinear phase encoding comprises the following steps:

[0008] Step 1: Construct a wavelength-De Bruijn element mapping table to generate a non-uniform periodic phase-shifted fringe group;

[0009] Step 2: Project the fringe images in the phase-shifted fringe group onto the object under test frame by frame, obtain the modulation pattern and decode it to obtain the nonlinear wrapped phase;

[0010] Step 3: Construct an approximate phase and perform local phase unwrapping on the nonlinear wrapped phase to obtain the nonlinear local phase;

[0011] Step 4: Use the stereo phase matching method to screen out the candidate phase points and candidate phase orders of the nonlinear local phase;

[0012] Step 5: Use the phase candidate points to guide the nonlinear local phase to perform phase correlation matching to screen out the unique phase order, thereby achieving phase unwrapping.

[0013] Furthermore, the non-uniform period phase-shifted fringe group in step 1 is obtained by the following steps:

[0014] Step 1.1, select m wavelengths and De Bruijn elements, and construct a wavelength-De Bruijn element mapping table;

[0015] Step 1.2, generate an m-element n-order De Bruijn wavelength sequence and generate non-uniform periodic phase shift coding; m∈Ν + , n∈Ν + , N + represents the set of positive integers;

[0016] The wavelength-De Bruijn element mapping table in step 1.1 is:

[0017] De Bruijn Elements <![CDATA[v0]]> <![CDATA[v1]]> ... <![CDATA[v m-1 ]]> wavelength <![CDATA[f0]]> <![CDATA[f1]]> ... <![CDATA[f m-1 ]]>

[0018] The De Bruijn wavelength sequence in step 1.2 is:

[0019]

[0020] Where m∈Ν + , n∈Ν + , N + Represents the set of positive integers.

[0021] The non-uniform period phase shift encoding formula in step 1.2 is:

[0022]

[0023] in

[0024]

[0025] u and v represent the horizontal and vertical coordinates of the projector pixel plane, respectively, 1≤u≤U, 1≤v≤V; U and V represent the horizontal and vertical pixel resolutions of the projector DMD surface, respectively. is a non-uniform periodic phase shift pattern, N represents the number of phase shift patterns, N≥3, i∈{1,2,...,N}. It can be seen as a function of the pixel coordinate v, that is, the first row of pixels in the coding pattern. Formula There is no u on the right side, which means that the pixel distribution of each row from u=1 to u=U is the same (1≤u≤U). Represents an image with U rows and V columns.

[0026] In step 1.2 Elements in . is not represented individually; it is Sum operation Elements in F DB .

[0027] The nonlinear wrapping phase in step 2 is obtained as follows:

[0028] A projector projects a non-uniform periodic phase-shifted fringe pattern onto the scene to be measured, and an industrial camera synchronously captures the deformed fringe pattern, which is then used to calculate the nonlinear wrapping phase.

[0029] The deformed fringe pattern in step 2 is represented as:

[0030]

[0031] Where x and y represent the horizontal and vertical coordinates of the camera pixel plane, respectively, with 1≤x≤W and 1≤y≤H. W and H represent the horizontal and vertical pixel resolutions of the camera's CCD surface, respectively. α(x,y) represents the object's reflectivity; β1(x,y) represents the intensity of ambient light on the object's surface; and β2(x,y) represents the intensity of ambient light directly entering the camera from the surrounding environment. Indicates the distorted fringe pattern captured by the camera. DB (x,y) is the average pixel intensity of the entire pattern set, B DB (x,y) represents the intensity modulation of a given pixel; φ DB (x,y) represents the nonlinear wrapping phase; i = 1,...,N;

[0032] The nonlinear wrapping phase calculation formula in step 2 is:

[0033]

[0034] The nonlinear local phase in step 3 is obtained as follows:

[0035] Step 3.1, calculate the nonlinear wrapping phase gradient and the nonlinear absolute phase gradient along the x-increasing direction of the nonlinear wrapping phase;

[0036] Step 3.2, construct an approximate phase using the nonlinear phase gradient, and use the approximate phase to unwrap the nonlinear local wrapped phase to obtain the nonlinear local phase;

[0037] The nonlinear wrapping phase gradient calculation formula in step 3.1 is:

[0038]

[0039] Among them, ▽ represents the gradient operator, represents the nonlinear wrapped phase gradient along the increasing x direction, and o represents the pixel product operator.

[0040] The nonlinear absolute phase gradient calculation formula in step 3.1 is:

[0041]

[0042] in, represents the nonlinear absolute phase gradient along the increasing direction of x;

[0043] The approximate phase calculation formula in step 3.2 is:

[0044]

[0045] Indicates approximate phase;

[0046] The nonlinear local phase calculation formula in step 3.2 is:

[0047]

[0048] in

[0049]

[0050] M>(n-1)×max{f0,f1,...f m-1}, round{.} represents the rounding operator, mod[.] represents the remainder operator, represents the nonlinear local phase, 0≤τ≤M-1,τ∈Ν + .

[0051] The phase candidate points in step 4 are obtained as follows:

[0052] Step 4.1: After the industrial cameras on both sides of the projector acquire images, execute step 2 respectively to obtain the wrapping phase in the left and right image planes;

[0053] Step 4.2, estimate the potential absolute phase of the left image plane wrapped phase and calculate the encoded horizontal coordinate of the potential absolute phase;

[0054] Step 4.3: Construct the three-view mapping equation, calculate the wrapped phase candidate points of the right image plane, and perform left and right phase consistency detection to screen out the phase candidate point set and candidate phase order set;

[0055] The wrapping phases in the left and right image planes calculated in step 4.1 are expressed as and Where (x L ,y L ) and (x R ,y R ) represent the horizontal and vertical coordinates of the left and right image planes respectively;

[0056] The formula for calculating the potential absolute phase of the left image plane wrapped phase in step 4.2 is:

[0057]

[0058] Among them, k(x L ,y L ) represents the phase order of the left view, k∈{0,1,...,m n -1}, Indicates that (x L ,y L ) coordinate position potential k-th absolute phase value. Then, calculate The potential encoding abscissa in the corresponding projector view is calculated as:

[0059]

[0060] in

[0061]

[0062] floor(.) is the floor operator, mod(.) is the remainder operator, u k It represents the potential horizontal coordinate of the pixel point in the left image plane mapped to the corresponding point under the projector image plane, and H[.] is the piecewise distortion correction operator;

[0063] The three-view mapping equation in step 4.3 is:

[0064]

[0065] Among them, the t operator represents the transposition calculation of the matrix, s L 、s R and s P represents the scaling factors of the left and right cameras and projector, (u k ,v k ) represents the phase point in the left image plane The potential horizontal and vertical coordinates of the corresponding points mapped to the projector image plane. L 、P R and P P Represent the projection matrices of the left and right cameras and the projector respectively, which are obtained using camera calibration technology (see reference: Zhang ZA Flexible New Technique for Camera Calibration[J].IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22(11):1330-1334.DOI:10.1109 / 34.888718.). express The corresponding wrapped phase candidate points of the right image plane. Therefore, the three-view mapping equation is further simplified to

[0066]

[0067] Among them, the function f lr The function of [.] is to map the absolute phase in the left view to the coordinates in the right view. After combining all the equations in steps 4.2-4.3, we can achieve arrive Calculation of f lr [.] represents the abbreviated joint process;

[0068] The calculation formulas for the wrapped phase candidate point set and candidate phase order set of the right image plane in step 4.3 are:

[0069]

[0070] in

[0071]

[0072] Ω p represents the set of selected phase candidate points, Ω k represents the set of candidate phase orders that have been screened out, Represents the set Ω pThe candidate points in , Δδ is the noise tolerance threshold, Indicates phase deviation.

[0073] The absolute phase in step 5 is obtained as follows:

[0074] Step 5.1: The nonlinear local phase of the left view is combined with different candidate phase orders and mapped to the right view to obtain the candidate local phase of the right view. The unique phase order is selected by minimizing the left and right local phase residuals.

[0075] Step 5.2: Combine the phase order with the nonlinear wrapped phase to perform phase unwrapping to obtain the nonlinear absolute phase, and then calculate the linear absolute phase through piecewise distortion correction;

[0076] The candidate local phase calculation formula in step 5.1 is:

[0077]

[0078] in, Represents each candidate point p in the right view k ∈Ω p The corresponding local phase, Represents the nonlinear local phase of the left view; then, combined with and The unique phase order is selected by minimizing the left and right local phase residuals

[0079]

[0080] in

[0081]

[0082] J sum represents the local phase residual, and |.| represents the absolute value calculation;

[0083] The nonlinear absolute phase calculation formula in step 5.2 is:

[0084]

[0085] in, Represents the nonlinear absolute phase of the left view.

[0086] The linear absolute phase calculation formula in step 5.2 is:

[0087] Right Wrap Phase Only used for auxiliary left wrap phase Phase unwrapping is performed, so there is no need to calculate the absolute phase of the right view. 3D imaging only requires a single absolute phase Φ L (x L,y L ) can be used.

[0088] Among them, Φ L (x L ,y L ) represents the linear absolute phase of the left view with constant gradient, f p Indicates the wavelength of the sinusoidal fringes used during the projector calibration phase.

[0089] Beneficial effects:

[0090] The beneficial effects of the present invention are:

[0091] 1. This invention proposes a three-dimensional phase unwrapping method based on nonlinear phase encoding, using a combination of multiple single-frequency fringes of different frequencies encoded according to the De Bruijn order. This encoding, consisting of pure sinusoidal fringes, is robust to complex object structures and varying reflective regions. Because the amplitude and intensity distribution of the sinusoidal fringes are not modified, high measurement accuracy is guaranteed.

[0092] 2. This invention utilizes the uniqueness of phase distortion through stereo matching of local phases and minimizing matching errors, achieving rapid phase unwrapping without the need for additional patterns or equipment. Compared to image feature matching, local phase matching is more robust and unaffected by image deformation caused by different viewing angles.

[0093] 3. The present invention achieves measurement accuracy similar to that of the advanced multi-frequency heterodyne method using only 1 / 3 of the number of projections, greatly improving coding efficiency;

[0094] 4. The present invention does not require the introduction of additional equipment and does not require the projection of additional stripes, thereby ensuring low cost and high measurement efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0095] Figure 1 Schematic diagram of the phase unwrapping process of the three-dimensional phase unwrapping method based on nonlinear phase encoding in Example 1 of the present invention;

[0096] Figure 2 This is the three-step non-equal period phase shift diagram in Example 1 of the present invention;

[0097] Figure 3 These are three deformed fringe images obtained in Example 1 of the present invention;

[0098] Figure 4 is the nonlinear wrapped phase diagram in Example 1 of the present invention;

[0099] Figure 5 is the nonlinear wrapped phase gradient image in Example 1 of the present invention;

[0100] Figure 6is the nonlinear absolute phase gradient image in Example 1 of the present invention;

[0101] Figure 7 This is the approximate phase diagram in Example 1 of the present invention.

[0102] Figure 8 This is the phase order diagram in Example 1 of the present invention.

[0103] Figure 9 This is the linear absolute phase diagram in Example 1 of the present invention.

[0104] Figure 10 This is the object model in Example 1 of the present invention. DETAILED DESCRIPTION

[0105] The present invention will be further described below with reference to the accompanying drawings and embodiments. However, this should not be construed as limiting the scope of the present invention to the following embodiments, as all technologies implemented based on the present invention fall within the scope of the present invention.

[0106] To better illustrate the method of the present invention, this embodiment takes a 5-element 3rd-order De Bruijn sequence as an example, combined with a three-step phase shift as an encoding scheme, and illustrates the measurement of a complex plaster figure and a calibration plate.

[0107] like Figure 1 FIG. 1 is a flow chart of the present invention, which shows a three-dimensional phase unwrapping method based on nonlinear phase encoding, comprising the following steps:

[0108] Step 1: Construct a wavelength De Bruijn element mapping table to generate a non-uniform periodic phase-shifted fringe group.

[0109] To ensure the uniformity of the calculated phase, five approximate wavelengths are selected for sinusoidal encoding: 16, 18, 20, 22, and 24. The wavelengths are then assigned to five De Bruijn elements to construct a wavelength-De Bruijn element mapping table.

[0110] De Bruijn element-wavelength mapping table

[0111] De Bruijn Elements 1 2 3 4 5 wavelength 16 18 20 22 24

[0112] Then, a set of 5-element 3rd-order De Bruijn wavelength sequences is constructed, as shown in formula (1);

[0113]

[0114] Among them, F DB represents a 5-ary 3rd order De Bruijn sequence. Next, use F DBThe wavelength in generates a three-step De Bruijn phase shift fringe pattern, and the calculation formula is:

[0115]

[0116] in

[0117]

[0118] (u,v) represents the horizontal and vertical coordinates of the projector plane, i∈{1,2,3}. is a non-uniform periodic phase shift pattern, such as Figure 2 shown.

[0119] Step 2: Project the phase-shifted fringes frame by frame, obtain the modulation pattern and decode it to get the nonlinear wrapped phase.

[0120] The projector projects a three-step De Bruijn phase-shifted fringe pattern onto the scene to be tested, and the industrial camera simultaneously captures the deformed fringe pattern. like Figure 3 As shown. The nonlinear wrapping phase is further calculated using formula (4), as Figure 4 As shown;

[0121]

[0122] Step 3: Construct an approximate phase and perform local expansion on the nonlinear wrapped phase to obtain the nonlinear local phase.

[0123] First, the nonlinear wrapping phase φ is calculated using formula (5) DB (x,y) Gradient along the increasing x direction.

[0124]

[0125] Among them, ▽ represents the gradient operator, represents the nonlinear wrapping phase gradient along the increasing y direction, such as Figure 5 As shown. Due to the 2π amplitude phase truncation of the nonlinear wrapping phase, the phase gradient has periodic jumps. Therefore, use formula (6) to Do gradient correction

[0126]

[0127] in, represents the nonlinear absolute phase gradient along the increasing direction of x, such as Figure 6 Then, use formula (7) to calculate the approximate absolute phase

[0128]

[0129] Represents the approximate phase, such as Figure 7 Next, use To assist φ DB (x,y) to perform local phase unwrapping and use formula (8) to calculate φ DB Perform local phase unwrapping on a pixel region of size 1×M in (x,y).

[0130]

[0131] in

[0132]

[0133] M>(n-1)×max{f0,f1,...f m-1}, round{.} represents the rounding operator, mod[.] represents the remainder operator, represents the nonlinear local phase.

[0134] Step 4: Use the stereo phase matching method to screen out phase candidate points.

[0135] After the industrial cameras on both sides of the projector acquire the image, step 2 is performed respectively. The calculated wrapping phases in the left and right image planes are expressed as and Where (x L ,y L ) and (x R ,y R ) represent the horizontal and vertical coordinates of the left and right image planes respectively. L ,y L )middle, With 5 3 = 125 possible phase orders, the corresponding potential absolute phases are calculated using formula (11).

[0136]

[0137] Among them, k(x L ,y L ) represents the phase order of the left view, k∈{0,1,...,124}, Indicates that (x L ,y L ) coordinate position potential k-th absolute phase value. Then, calculate The corresponding potential encoding abscissa is calculated as:

[0138]

[0139] in

[0140]

[0141] floor(.) is the floor operator, u k It represents the potential horizontal coordinate of the pixel point in the left image plane mapped to the corresponding point under the projector image plane. Then, take out the pre-calibrated parameter P L 、P R and P P , construct the three-view mapping equation of the system:

[0142]

[0143] Among them, the t operator represents the transposition calculation of the matrix, s L 、s R and s P represents the scaling factors of the left and right cameras and projector, (u k ,v k ) represents the phase point in the left image plane The potential horizontal and vertical coordinates of the corresponding points mapped to the projector image plane. L 、P R and P P Represent the projection matrices of the left and right cameras and the projector respectively, which are obtained using camera calibration technology (see reference: Zhang Z. A Flexible New Technique for Camera Calibration [J]. IEEE Transactions on Pattern Analysis and Machine Intelligence, 2000, 22 (11): 1330-1334. DOI: 10.1109 / 34.888718.). express The corresponding wrapped phase candidate point of the right image plane. Therefore, the simultaneous formulas (12-16) can construct the following mapping

[0144]

[0145] Among them, the function f lr The function of [.] is to map the absolute phase in the left view to the coordinates in the right view. Next, the left and right phase consistency detection is performed to screen out a small number of phase candidate points. The calculation formula is:

[0146]

[0147] in

[0148]

[0149] Ω prepresents the set of selected phase candidate points, Ω k represents the set of candidate phase orders that have been screened out, Represents the set Ω p The candidate points in , Δδ is the noise tolerance threshold, Indicates phase deviation.

[0150] Step 5: Local phase correlation matching is used to select the unique phase order and achieve phase unwrapping.

[0151] Since the encoding in this patent has nonlinear characteristics, each candidate point p in the right view k ∈Ω p The local phase surface of the left view has different nonlinear distortions. Therefore, only the correct phase order can make the local phase of the left view and right view local wrapping phase The matching consistency is satisfied. The calculation formula is

[0152]

[0153] in represents the nonlinear local phase of the left view. Then, combined with and A unique phase order is obtained by minimizing the matching error between the local phases of the left and right views.

[0154]

[0155] in

[0156]

[0157] k(x L ,y L )like Figure 8 Next, the nonlinear wrapping phase φ DB (x L ,y L ) combined with k(x L ,y L )Use formula (23) for phase unwrapping.

[0158] Φ DB (x L ,y L )=φ DB (x L ,y L )+2π×k(x L ,y L ) (twenty three)

[0159] Among them, Φ DB (xL ,y L ) represents the nonlinear absolute phase of the left view. Next, the nonlinear absolute phase is mapped into a linear absolute phase.

[0160]

[0161] Among them, Φ L (x L ,y L ) represents the linear absolute phase of the left view with a constant gradient, such as Figure 9 As shown. p represents the wavelength of the sinusoidal stripes used in the projector calibration phase. Finally, the linear absolute phase is combined with the structured light system parameters to reconstruct the object model (see the literature: 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.), as shown in Figure 10 shown.

Claims

1. A three-dimensional phase unwrapping method based on nonlinear phase encoding, characterized in that: The following steps are involved: Step 1: Construct a wavelength-De Bruijn element mapping table to generate a non-uniform periodic phase-shifted fringe group; Step 2: Project the fringe images in the phase-shifted fringe group onto the object under test frame by frame, obtain the modulation pattern and decode it to obtain the nonlinear wrapped phase; Step 3: Construct an approximate phase and perform local phase unwrapping on the nonlinear wrapped phase to obtain the nonlinear local phase; The nonlinear local phase in step 3 is obtained as follows: Step 3.1, calculate the nonlinear wrapping phase along Nonlinear wrapping phase gradient and nonlinear absolute phase gradient in increasing direction; Step 3.2, construct an approximate phase using the nonlinear phase gradient, and use the approximate phase to unwrap the nonlinear local wrapped phase to obtain the nonlinear local phase; Step 4: Use the stereo phase matching method to screen out the candidate phase points and candidate phase orders of the nonlinear local phase; Step 5: Use the phase candidate points to guide the nonlinear local phase to perform phase correlation matching to screen out the unique phase order, thereby achieving phase unwrapping; The absolute phase in step 5 is obtained as follows: Step 5.1: The nonlinear local phase of the left view is combined with different candidate phase orders and mapped to the right view to obtain the candidate local phase of the right view. The unique phase order is selected by minimizing the left and right local phase residuals. In step 5.2, the phase order is combined with the nonlinear wrapped phase to perform phase unwrapping to obtain the nonlinear absolute phase, and then the linear absolute phase is calculated through piecewise distortion correction.

2. The three-dimensional phase unwrapping method based on nonlinear phase encoding according to claim 1, characterized in that: The non-uniform period phase-shifted fringe group in step 1 is obtained as follows: Step 1.1, select wavelengths and De Bruijn elements, and construct a wavelength-De Bruijn element mapping; Step 1.2, generate Yuan De Bruijn wavelength sequence of order and generate non-equal period phase shift code; , , represents the set of positive integers; The wavelength-De Bruijn element mapping in step 1.1 is: De Bruijn elements: , ,..., ; wavelength: , ,..., ; The De Bruijn wavelength sequence in step 1.2 is: in, , , represents the set of positive integers; The non-uniform period phase shift encoding formula in step 1.2 is: in and Respectively represent the horizontal and vertical coordinates of the projector pixel plane, , ; and Respectively represent the horizontal and vertical pixel resolutions of the projector DMD surface; is a non-uniform periodic phase shift pattern, represents the number of phase shift patterns, , .

3. The three-dimensional phase unwrapping method based on nonlinear phase encoding according to claim 1, characterized in that: The nonlinear wrapping phase in step 2 is obtained as follows: A projector projects a non-uniform periodic phase-shifted fringe pattern onto the scene to be measured, and an industrial camera synchronously captures the deformed fringe pattern, which is then used to calculate the nonlinear wrapping phase. The deformed fringe pattern in step 2 is represented as: ， in, and Represent the horizontal and vertical coordinates of the camera pixel plane, , ; and Respectively represent the horizontal and vertical pixel resolution of the camera CCD surface; Indicates the reflectivity of an object; Indicates the intensity of ambient light on the surface of an object. Indicates the intensity of ambient light directly entering the camera from the environment; represents the deformed fringe pattern captured by the camera; is the average pixel intensity of the entire pattern set, represents the intensity modulation of a given pixel; represents the nonlinear wrapping phase; ; The nonlinear wrapping phase calculation formula in step 2 is: 。 4. The three-dimensional phase unwrapping method based on nonlinear phase encoding according to claim 1, characterized in that: The nonlinear wrapping phase gradient calculation formula in step 3.1 is: in, represents the gradient operator, Indicates along Nonlinear wrapped phase gradient in increasing direction, represents the pixel product operator; The nonlinear absolute phase gradient calculation formula in step 3.1 is: in, Indicates along Nonlinear absolute phase gradient in increasing direction; The approximate phase calculation formula in step 3.2 is: Indicates approximate phase; The nonlinear local phase calculation formula in step 3.2 is: in , represents the rounding operator, represents the remainder operator, represents the nonlinear local phase, , .

5. The three-dimensional phase unwrapping method based on nonlinear phase encoding according to claim 1, characterized in that: The phase candidate points in step 4 are obtained as follows: Step 4.1: After the industrial cameras on both sides of the projector acquire images, execute step 2 respectively to obtain the wrapping phase in the left and right image planes; Step 4.2, estimate the potential absolute phase of the left image plane wrapped phase and calculate the encoded horizontal coordinate of the potential absolute phase; Step 4.3: Construct the three-view mapping equation, calculate the wrapped phase candidate points of the right image plane, and perform left and right phase consistency detection to screen out the phase candidate point set and candidate phase order set; The wrapping phases in the left and right image planes calculated in step 4.1 are expressed as and ;in and Represent the horizontal and vertical coordinates of the left and right image planes respectively; The formula for calculating the potential absolute phase of the left image plane wrapped phase in step 4.2 is: in, represents the phase order of the left view, , Indicates Coordinate position potential absolute phase values; then, calculate The potential encoding abscissa in the corresponding projector view is calculated as: in is the floor operator, is the remainder operator, Indicates the potential horizontal coordinate of the pixel point in the left image plane mapped to the corresponding point under the projector image plane, is the piecewise distortion correction operator; The three-view mapping equation in step 4.3 is: in, The operator represents the transposition calculation of the matrix. 、 and represents the scaling factors of the left and right cameras and the projector, represents the phase point in the left image plane The potential horizontal and vertical coordinates of the corresponding points mapped to the projector image plane; 、 and Represent the projection matrices of the left and right cameras and projector respectively, which are obtained using camera calibration technology; express The corresponding wrapped phase candidate points of the right image plane; simplify the three-view mapping equation to Among them, the function The function is to map the absolute phase in the left view to the coordinates in the right view; The calculation formulas for the wrapped phase candidate point set and candidate phase order set of the right image plane in step 4.3 are: in represents the set of filtered phase candidate points, represents the set of candidate phase orders that have been screened out, Representing a collection The candidate points in is the noise tolerance threshold, Indicates phase deviation.

6. The three-dimensional phase unwrapping method based on nonlinear phase encoding according to claim 1, characterized in that: The candidate local phase calculation formula in step 5.1 is: in, Represents each candidate point in the right view The corresponding local phase, Represents the nonlinear local phase of the left view; then, combined with and , by minimizing the left and right local phase residuals to select the unique phase order in represents the local phase residual, Indicates absolute value calculation; The nonlinear absolute phase calculation formula in step 5.2 is: in, Indicates the nonlinear absolute phase of the left view; The linear absolute phase calculation formula in step 5.2 is: ； in, represents the linear absolute phase of the left view with a constant gradient, Indicates the wavelength of the sinusoidal fringes used during the projector calibration phase.

Images