CN107977939B - Reliability-based weighted least square phase unwrapping calculation method - Google Patents
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Abstract
The invention discloses a reliability-based weighted least square phase unwrapping calculation method. Shooting and collecting a speckle interference pattern of an object to be detected through industrial camera equipment, and obtaining a two-dimensional phase wrapping pattern containing three-dimensional information of the object to be detected through image processing; obtaining the reliability of each point in the phase wrapping graph by utilizing the second-order difference calculation of the wrapping phase value; and calculating to determine a reliability threshold, calculating to obtain a binarization mask factor as a weighted least square phase expansion weight, and performing iterative calculation to obtain a final true phase. The method has the advantages of providing a smooth solution by the weighted least square calculation method, along with high calculation speed, high precision, effective noise propagation inhibition, smooth effect elimination and the like.
Description
Technical Field
The invention relates to the technical field of digital speckle interference, in particular to a weighted least square phase unwrapping calculation method based on reliability.
Background
The Digital Speckle interference technique (DSPI) is an optical interference measurement technique combining laser technology and Digital image processing, and compared with the traditional measurement technique, the Digital Speckle interference technique has the advantages of high precision, non-contact and no damage, high sensitivity, full-field measurement and the like, and is widely applied to the fields of aerospace, biomedicine, ship manufacturing and the like. Phase unwrapping is the most critical step in the application of the DSPI technique, directly affecting the measurement accuracy. In recent years, a plurality of phase unwrapping calculation methods have been proposed by scholars at home and abroad. The least square phase unwrapping calculation method can eliminate the wire pulling phenomenon by unwrapping by using the criterion that the difference between the discrete partial differential of the wrapped phase and the discrete partial differential of the real phase is minimum, and a smooth solution is obtained, so that the least square phase unwrapping calculation method is the most common calculation method which is simple and stable, has high calculation speed and has low memory requirement. However, when there are noise points, zero amplitude points, and low modulation points in the wrapped phase, the least square phase unwrapping calculation method cannot obtain a correct solution. The weighted least square phase unwrapping calculation method overcomes the influence caused by noise and the like through weight, but the correctness of unwrapping is also influenced by the introduced weight, the calculation speed is reduced, and the propagation of noise cannot be inhibited and the error caused by the smoothing effect cannot be eliminated.
Disclosure of Invention
In order to solve the technical problems, the invention provides a weighted least square phase unwrapping calculation method based on reliability, which is high in calculation speed, can effectively inhibit noise propagation and eliminate a smoothing effect.
The invention is realized by the following technical scheme:
the method comprises the following steps: shooting and collecting a speckle interference pattern of an object to be detected by industrial camera equipment, and obtaining a two-dimensional phase wrapping pattern with the size of M multiplied by N and containing three-dimensional information of the object to be detected through image processing;
step two: obtaining the reliability of each point in the phase wrapping graph by utilizing the second-order difference calculation of the wrapping phase value;
step three: determining a reliability threshold value, calculating to obtain a binarization mask factor, and using the binarization mask factor as a weighted least square phase expansion weight;
step four: and performing iterative computation according to the weighted least square phase unwrapping weight to obtain a final true phase.
The fourth step comprises the following steps: number of initialization iterations k and absolute phase phi0Calculating wrapped phase of each point
Weighted discrete partial differential of (a); according to an iterative formula, performing the k-th least square phase expansion to obtain phik+1(ii) a Judgment of phik+1If the convergence condition is satisfied, the true phase phi is obtainedk+1(ii) a If not, the iteration number k is k +1, and the process returns to continue the iteration.
The invention aims at a plate type object to be measured and collects a speckle interference pattern of the surface deformation of the plate type object to be measured.
The plate type object to be detected is a plate made of aluminum, composite materials and the like, the surface of the plate type object to be detected is deformed in an inward concave or outward convex mode through external force stress, and then the method is adopted for detection.
The first step specifically comprises the following steps: the speckle interference patterns before and after deformation of the object to be detected are shot and collected through industrial camera equipment, and then a two-dimensional phase wrapping image which contains three-dimensional deformation information of the object to be detected and has the size of M multiplied by N is obtained through image processing.
The first step is to obtain a wrapped phase diagram by processing with a spatial carrier method: shooting two speckle interference images with carrier wave quantity before and after the surface of an object to be measured deforms by using industrial camera equipment, respectively carrying out Fourier transform on the two speckle interference images to obtain two frequency spectrograms, respectively selecting a primary frequency spectrum in the two frequency spectrograms to obtain two primary frequency spectrograms, then carrying out inverse Fourier transform on the two primary frequency spectrograms and taking an inverse tangent to obtain two phase spectrograms, finally subtracting the two phase spectrograms to obtain a phase wrapping image with the surface deformation information of the object to be measured, and filtering and denoising the phase wrapping image to obtain a two-dimensional phase wrapping image with the size of M multiplied by N
The second step is specifically as follows:
firstly, calculating the second-order difference of the wrapped phase value of each point in the two-dimensional phase wrapping map by adopting the following formula:
where V (i, j) is the second order difference in the horizontal direction, H (i, j) is the second order difference in the vertical direction, D1(i, j) and D2(i, j) is a second order difference in two diagonal directions, the two diagonal directions are two directions which are respectively positioned at two sides at an angle of 45 degrees with the horizontal direction of the image, wrap operation is performed on wrap-around, and the operation result is limited to (-pi, pi)]Within the range; DIF2(i, j) represents the second order difference of the coordinate location point (i, j) in the two-dimensional phase-wrapped map,
representing the wrapping phase value of a point (i, j) in the two-dimensional phase wrapping graph, wherein the point (i, j) represents the ith point of the abscissa and the jth point of the ordinate, i is more than or equal to 0 and less than or equal to M-1, and j is more than or equal to 0 and less than or equal to N-1;
then, the reliability R (i, j) of the wrapped phase value for each point is calculated using the following formula:
where R (i, j) represents the reliability of the wrapped phase value for point (i, j) in the two-dimensional phase wrapping map.
The third step is specifically as follows:
the reliability of all points in the two-dimensional wrapped phase diagram is sequenced from small to large to obtain a one-dimensional sequence q, the reliability value of MxNx 5% of points in the sequence q is taken as a reliability threshold theta, if MxNx 5% is not an integer, rounding is performed downwards, and the binarization mask factor W (i, j) of each point is obtained through calculation according to the following formula:
wherein, W (i, j) represents the binary mask factor of the point (i, j) in the two-dimensional phase wrapping map.
The fourth step is specifically as follows:
4.1) initialization sets the number of iterations k and the absolute phase phi0Firstly, the following formula is adopted to calculate the wrapped phase value of each point
Corresponding weighted discrete partial derivatives c (i, j):
wherein the content of the first and second substances,
representing the first order difference after wrap operation in the wrap phase vertical direction,
representing a first-order difference after wrapping operation in the horizontal direction of a wrapping phase; two first order differences
And
respectively calculated as:
4.2) performing least square phase expansion by adopting the following method to obtain the true phase calculated in each iteration:
calculating the true phase phi of the k-th iterationkSubstituting the equation to obtain the second-order partial derivative rho of the true phase of the (k + 1) th iterative computationk+1：
ρk+1＝c-F(φk)
Wherein, F (phi)k) Representing the true phase phikC represents a vector of weighted discrete partial derivatives c (i, j) of all points in the two-dimensional phase-wrapped plot;
true phase phikWeighted discrete partial differential function F (phi)k) Such as the following equation:
wherein the content of the first and second substances,
representing the first order difference in the vertical direction of the true phase,
representing the first order difference, two first order differences, of the true phase horizontal direction
And
respectively calculated as:
in the initial calculation, the iteration number k is set to be 0 and the real phase phi is set in the specific implementation0Is the absolute phase r, phi0＝r。
4.3) second-order partial derivatives rho of the true phase calculated by the (k + 1) th iterationk+1As input to the poisson equation expressed by the following formula, the poisson equation expressed by the following formula is solved by Discrete Cosine Transform (DCT) to obtain the true phase phi of the (k + 1) th iteration calculationk+1：
4.4) determining the true phase phi of the (k + 1) th iteration calculationk+1Whether the convergence condition is satisfied:
if so, the true phase phi is usedk+1As the final true phase;
if not, repeating the steps 4.2) to 4.3) to obtain the true phase calculated in the next iteration, wherein the iteration number k is k + 1. And then, carrying out iterative processing through the steps until whether the real phase meets the convergence condition or not.
The convergence condition is expressed by the following formula, and the convergence condition is satisfied when the following formula is satisfied:
wherein ε represents the convergence threshold, ε is 10-2；φk+1Represents the true phase, phi, of the (k + 1) th iterationkRepresenting the true phase calculated for the k-th iteration.
Compared with the prior art, the invention has the beneficial effects that:
the invention obtains the binary mask as the weight of the weighted least square method by utilizing the reliability index, only carries out the calculation of the weight once (namely, the weights in all iterative calculation processes are kept consistent), does not relate to the recalculation of the weight in the subsequent iteration, and solves the real phase through iteration, thereby effectively inhibiting the propagation of noise and eliminating the smoothing effect and improving the calculation speed.
The method has the advantages of providing a smooth solution by the weighted least square calculation method, having high calculation speed, effectively inhibiting noise propagation, eliminating the smoothing effect and the like.
Drawings
FIG. 1 is a flow chart of a phase unwrapping calculation method in accordance with the present invention;
FIG. 2 is a two-dimensional phase wrapped graph after filtering according to an embodiment;
FIG. 3 is a composition diagram of weighting factors obtained based on reliability according to an embodiment;
FIG. 4 is a graph of unwrapped phase results for one embodiment;
FIG. 5 is a rewinding diagram of the unwinding phase of the embodiment.
Detailed Description
The invention is further illustrated by the following figures and examples.
The embodiment of the invention is shown in a flow chart of fig. 1, and comprises the following specific steps:
the method comprises the following steps: shooting speckle interference patterns before and after deformation through industrial camera equipment and obtaining a two-dimensional phase wrapping pattern with the size of M multiplied by N and containing three-dimensional deformation information of an object to be measured through corresponding image processing
The embodiment specifically adopts a spatial carrier method, and the specific process is as follows: shooting two speckle interference images with carrier wave quantity before and after deformation by using industrial camera equipment, respectively carrying out Fourier transform on the two speckle interference images to obtain two frequency spectrums, respectively selecting a positive first-level frequency spectrum from the two frequency spectrums to obtain two positive first-level frequency spectrums, then carrying out inverse Fourier transform on the two positive first-level frequency spectrums and taking inverse tangent to obtain two phase maps, finally subtracting the two phase maps to obtain a phase wrapping image with deformation information, filtering and denoising the phase wrapping image to obtain a two-dimensional phase wrapping image to be unwrapped as shown in figure 2, and obtaining a wrapping phase value of each point
Wherein i is more than or equal to 0 and less than or equal to M-1, and j is more than or equal to 0 and less than or equal to N-1.
Step two: the second order difference of the phase values is used to calculate the reliability R (i, j) of each point of the phase wrapping map.
The second order difference of the phase value of each point in the phase diagram is calculated by equation (1):
will be provided with
Substituting the two-order difference into the formula (1) to obtain the second-order difference of each phase value, and calculating the reliability R (i, j) of each phase value by the formula (2):
step three: and determining a reliability threshold value, and obtaining a binary mask factor as the weight of the weighted least square phase expansion calculation method.
The reliability of each point of the two-dimensional wrapped phase diagram is sequenced from small to large to obtain a one-dimensional sequence q, the reliability value of MxNx 5% of points in the sequence q is taken as a reliability threshold theta, if MxNx 5% is not an integer, the reliability value is rounded downwards, and a binarization mask factor W (i, j) is obtained through calculation according to a formula (3), as shown in FIG. 3.
Step four: calculating wrapped phase
Weighted discrete partial differential of (a).
Will be provided with
Substituting equation (4) to calculate the weighted discrete partial derivative c (i, j) for each wrapped phase:
step five: number of initialization iterations k and absolute phase phi0Let the number of iterations k equal to 0 and the absolute phase phi0R, performing k-th least square phase expansion according to an iterative formula to obtain phik+1。
Will phikSubstitution into the iterative formula rhok+1＝c-F(φk) To obtain rhok+1Where F is the operation as shown in equation (5):
then will rhok+1As input to the poisson equation shown in equation (6), the equation is then solved using Discrete Cosine Transform (DCT) to obtain the true phase phik+1。
Step six: judging a convergence condition, if the convergence condition is met, solving a real phase phik+1(ii) a If not, the iteration number k is k +1, and the step five is returned to continue the iteration.
The convergence condition is expressed by equation (7), and the convergence threshold epsilon is 10-2. If the convergence condition is satisfied, the final true phase is phik+1(ii) a If the convergence condition is not met, the iteration number k is k +1, and the step five is returned to continue the iteration.
The phase unwrapping result of the embodiment is shown in fig. 4, which shows that the unwrapping phase of the present invention is smooth, and as shown in fig. 5, which is an unwrapped phase rewinding diagram thereof, which shows that the rewinding fringe diagram of the unwrapping phase is consistent with the fringes of the original wrapped phase diagram, thereby ensuring the effectiveness of the present invention.
Aiming at the problem that the weight is difficult to determine in the weighted least square solution wrapping calculation method, the invention determines the binary mask as the weight by using the reliability, obtains the real phase through iteration and improves the reliability of weighting. The invention has the advantages that the least square calculation method provides smooth solution, eliminates the wire pulling phenomenon, determines the weight by using the reliability index, solves the error caused by the smoothness, improves the precision and inhibits the propagation of noise.
Claims (2)
1. A weighted least square phase unwrapping calculation method based on reliability is characterized by comprising the following steps:
the method comprises the following steps: shooting and collecting a speckle interference pattern of an object to be detected by industrial camera equipment, and obtaining a two-dimensional phase wrapping pattern with the size of M multiplied by N and containing three-dimensional information of the object to be detected through image processing;
step two: obtaining the reliability of each point in the phase wrapping graph by utilizing the second-order difference calculation of the wrapping phase value;
the second step is specifically as follows:
firstly, calculating the second-order difference of the wrapped phase value of each point in the two-dimensional phase wrapping map by adopting the following formula:
where V (i, j) is the second order difference in the horizontal direction, H (i, j) is the second order difference in the vertical direction, D1(i, j) and D2(i, j) is the second order difference in the two diagonal directions, wrap {. is the wrap operation, DIF2(i, j) represents the second order difference of the coordinate location point (i, j) in the two-dimensional phase-wrapped map,
representing the wrapping phase value of a point (i, j) in the two-dimensional phase wrapping graph, wherein i is more than or equal to 0 and less than or equal to M-1, and j is more than or equal to 0 and less than or equal to N-1;
then, the reliability R (i, j) of the wrapped phase value for each point is calculated using the following formula:
wherein, R (i, j) represents the reliability of the wrapping phase value of the point (i, j) in the two-dimensional phase wrapping map;
step three: determining a reliability threshold value, calculating to obtain a binarization mask factor, and using the binarization mask factor as a weighted least square phase expansion weight;
the third step is specifically as follows:
the reliability of all points in the two-dimensional wrapped phase diagram is sequenced from small to large to obtain a one-dimensional sequence q, the reliability value of MxNx 5% of points in the sequence q is taken as a reliability threshold theta, if MxNx 5% is not an integer, rounding is performed downwards, and the binarization mask factor W (i, j) of each point is obtained through calculation according to the following formula:
wherein W (i, j) represents a binarization mask factor of a point (i, j) in the two-dimensional phase wrapping graph;
step four: performing iterative computation according to the weighted least square phase unwrapping weight to obtain a final true phase;
the fourth step is specifically as follows:
4.1) calculating the wrapped phase value of each point by adopting the following formula
Corresponding weighted discrete partial derivatives c (i, j):
wherein the content of the first and second substances,
representing the first order difference after wrap operation in the wrap phase vertical direction,
representing a first-order difference after wrapping operation in the horizontal direction of a wrapping phase; two first order differences
And
respectively calculated as:
4.2) performing least square phase expansion by adopting the following method to obtain the true phase calculated in each iteration:
calculating the true phase phi of the k-th iterationkSubstituting the equation to obtain the second-order partial derivative rho of the true phase of the (k + 1) th iterative computationk+1：
ρk+1＝c-F(φk)
Wherein, F (phi)k) Representing the true phase phikC represents a vector of weighted discrete partial derivatives c (i, j) of all points in the two-dimensional phase-wrapped plot;
true phase phikWeighted discrete partial differential function F (phi)k) Such as the following equation:
wherein the content of the first and second substances,
representing the first order difference in the vertical direction of the true phase,
representing the first order difference, two first order differences, of the true phase horizontal direction
And
respectively calculated as:
4.3) second-order partial derivatives rho of the true phase calculated by the (k + 1) th iterationk+1As input to the poisson equation expressed by the following formula, the poisson equation expressed by the following formula is solved by Discrete Cosine Transform (DCT) to obtain the true phase phi of the (k + 1) th iteration calculationk+1：
4.4) determining the true phase phi of the (k + 1) th iteration calculationk+1Whether the convergence condition is satisfied:
if so, the true phase phi is usedk+1As the final true phase;
if not, repeating the steps 4.2) to 4.3) to obtain the true phase of the next iteration calculation.
2. The reliability-based weighted least squares phase unwrapping method of claim 1, wherein:
the first step is to obtain a wrapped phase diagram by processing with a spatial carrier method:
shooting two speckle interference images with carrier wave quantity before and after the surface of an object to be measured deforms by using industrial camera equipment, respectively carrying out Fourier transform on the two speckle interference images to obtain two frequency spectrograms, respectively selecting a primary frequency spectrum in the two frequency spectrograms to obtain two primary frequency spectrograms, then carrying out inverse Fourier transform on the two primary frequency spectrograms and taking an inverse tangent to obtain two phase spectrograms, finally subtracting the two phase spectrograms to obtain a phase wrapping image with the surface deformation information of the object to be measured, and filtering and denoising the phase wrapping image to obtain a two-dimensional phase wrapping image with the size of M multiplied by N
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