CN111968178A - Sub-pixel positioning method based on particle swarm algorithm - Google Patents
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Abstract
The invention relates to a sub-pixel positioning method based on a particle swarm algorithm, which belongs to the field of computer vision and comprises the following steps: simulating a digital speckle image by using the matlab as an original image, and translating the original image to obtain a target image; selecting a point to be measured in an original image, calculating a correlation coefficient, finding an integer pixel coordinate point in the deformed speckle image by using a particle swarm algorithm, and solving the integer pixel displacement according to the located integer pixel coordinate point; taking an integer pixel coordinate point as a center, interpolating the region by using a bicubic interpolation algorithm, and then finding a point with the maximum relation number in the interpolated region by using a particle swarm algorithm; and calculating the sub-pixel coordinates by using a quadratic polynomial fitting algorithm for the point with the maximum correlation coefficient found in the last step. The invention uses a particle swarm search algorithm, and combines a binary polynomial fitting algorithm and a bicubic interpolation method to achieve the final precision of 0.01-0.02 pixel in order to improve the sub-pixel search precision.
Description
Technical Field
The invention relates to the field of computer vision, in particular to a sub-pixel positioning method based on a particle swarm algorithm.
Background
In recent years, a deformation measurement method based on digital image correlation has become an attractive test method in the field of modern optical measurement mechanics, and the application field of the deformation measurement method is more and more extensive. Since the advent of Digital Image Correlation (DIC), it has been widely used in research in many disciplines, such as materials mechanics, biomechanics, fracture mechanics, microscopic nano strain measurement, macroscopic large-scale deformation measurement, performance testing of various new materials, etc. Compared with the traditional contact type strain measurement technology, the method has the advantages of low speed, limited measuring range and inflexible operation, and the digital image related measurement method has the advantages of non-contact, high precision, full-field measurement and easy automation.
In early studies, point-by-point search methods were mostly used, which took a lot of time. Subsequently, through continuous improvement, a plurality of related searching methods based on the classical mathematical theory are proposed, such as a coarse-fine searching method, a cross searching method, a hill climbing method, a Newton-Raphson iterative algorithm and the like. The rough-fine search method searches the displacement and the displacement derivative at the same time, and the calculated amount is large; the cross search method only carries out displacement search and relevant correction if necessary, and the calculation speed of the cross search method is faster than that of the coarse-fine search method; the Newton-Raphson iterative algorithm is time-saving compared with the coarse-fine search method, but the calculation amount is large when the dimension of the Hessian matrix of the objective function and the inverse matrix thereof is high. These conventional correlation search methods are prone to fall into local optima if the correlation coefficient is distributed with multiple peaks.
Disclosure of Invention
In order to solve the problem that the conventional method is easy to fall into the condition of local optimum during whole pixel search, a sub-pixel positioning method based on a particle swarm algorithm is provided.
The invention adopts the following technical scheme:
a sub-pixel positioning method based on a particle swarm algorithm comprises the following steps:
s1: simulating a digital speckle image by using the matlab as an original image, and translating the original image to obtain a target image;
s2: selecting a point to be measured in an original drawing, recording a coordinate (x, y) of the point to be measured, dividing a rectangular region with the size of 2R as a target region by taking the coordinate (x, y) as a center in the deformed speckle pattern, wherein R is a search radius, and dividing a rectangular region with the size of 2R as a sample subregion for calculating a correlation coefficient by taking the point to be measured as the center in the original drawing, wherein R is the radius of the sample subregion;
s3: in the target area, randomly initializing n points as n randomly initialized particles in a particle swarm algorithm, dividing a 2r x 2r rectangular area as a target sub-area by taking the particles as the center for each particle, finding out an integer pixel coordinate point in the deformed speckle image by using the particle swarm algorithm, and solving out integer pixel displacement according to the located integer pixel coordinate point;
s4: aiming at the whole pixel coordinate point obtained in the step S3, dividing a 10 × 10 rectangular area as an area to be interpolated by taking the point as a center, interpolating the area by using a bicubic interpolation algorithm, and then finding out a point with the maximum relation number in the interpolated area by using a particle swarm algorithm;
s5: and calculating the sub-pixel coordinates by using a quadratic polynomial fitting algorithm for the point with the maximum correlation coefficient found in the last step.
Further, the radius of the sample sub-region selected in the target map in step S2 is 10 pixels.
Further, the particle swarm algorithm in step S3 has an initial population size of 400, the coordinates of the start point of each particle are initialized randomly, the flying speed is initialized randomly, the number of iterations is 150, and the search is stopped after the algorithm converges.
Further, in step S4, the interpolating the region to be interpolated by the bicubic interpolation algorithm includes: and performing cubic interpolation once in the x direction and the y direction of the region respectively to obtain bicubic interpolation, and performing gray level interpolation by adopting a sinc function in the image interpolation process.
Further, in step S4, a bicubic interpolation algorithm is used to select 16 points around the target point as stagnation points, then the interpolation area is enlarged by 20 times, and a particle swarm algorithm is used to find the point with the largest correlation coefficient in the enlarged sub-area.
Further, in step S5, after obtaining the coordinates of the integer pixel in the target graph, 8 points around the point are used to calculate the parameters in the bivariate polynomial fitting, where the coordinates of the 8 points are (x) respectively0,y0)、(x0,y1)、(x0,y2)、(x1,y0)、(x2,y0)、(x1,y1)、(x1,y2)、(x2,y1)、(x2,y2) For the coordinates found after fitting, the calculated displacement is divided by 20 to obtain the final sub-pixel displacement.
Further, the fitting function in the bivariate polynomial is:
f(x,y)＝a00+a10x+a01y+a20x2+a11xy+a02y2
taking a 3 × 3 fitting window, there are:
f(x0,y0)＝a00+a10x0+a01y0+a20x0 2+a11x0y0+a02y0 2
f(x0,y1)＝a00+a10x0+a01y1+a20x0 2+a11x0y1+a02y1 2
f(x0,y2)＝a00+a10x0+a01y2+a20x0 2+a11x0y2+a02y2 2
f(x1,y0)＝a00+a10x1+a01y0+a20x1 2+a11x1y0+a02y0 2
f(x2,y0)＝a00+a10x2+a01y0+a20x2 2+a11x2y0+a02y0 2
f(x1,y1)＝a00+a10x1+a01y1+a20x1 2+a11x1y1+a02y1 2
f(x1,y2)＝a00+a10x1+a01y2+a20x1 2+a11x1y2+a02y2 2
f(x2,y1)＝a00+a10x2+a01y1+a20x2 2+a11x2y1+a02y1 2
f(x2,y2)＝a00+a10x2+a01y2+a20x2 2+a11x2y2+a02y2 2
wherein, a00、a01、a10、a20、a11、a02For the coefficient to be solved, 6 coefficients in the equation set are obtained by using a least square method, and at the extreme point of the fitted surface, the following conditions are satisfied:
solving to obtain sub-pixel coordinates:
the sub-pixel displacement can be obtained from the obtained sub-pixel coordinates.
The invention has the following advantages and beneficial effects: the invention uses a particle swarm search algorithm, and combines a binary polynomial fitting algorithm and a bicubic interpolation method to achieve the final precision of 0.01-0.02 pixel in order to improve the sub-pixel search precision.
Drawings
FIG. 1 is a diagram: a sinc function image.
FIG. 2 is a diagram of: and (c) generating an original image (a) by matlab simulation and a picture after displacement (b).
FIG. 3 is a diagram of: a structure diagram of a particle group algorithm in a digital image correlation sub-pixel positioning algorithm.
FIG. 4 is a diagram of: a flow chart of the whole digital image correlation sub-pixel positioning method.
Detailed Description
Referring to fig. 4, a sub-pixel positioning method based on a particle swarm algorithm includes the following steps:
s1: simulating a digital speckle image by using matlab as an original image, and translating the original image (a small number of units) to obtain a target image (shown in fig. 2);
s2: selecting a point to be measured in an original drawing, recording a coordinate (x, y) of the point to be measured, dividing a rectangular region with the size of 2R as a target region by taking the coordinate (x, y) as a center in the deformed speckle pattern, wherein R is a search radius, and dividing a rectangular region with the size of 2R as a sample subregion for calculating a correlation coefficient by taking the point to be measured as the center in the original drawing, wherein R is the radius of the sample subregion;
s3: in the target area, randomly initializing n points as n randomly initialized particles in a particle swarm algorithm, dividing a 2r x 2r rectangular area as a target sub-area by taking the particles as the center for each particle, finding out an integer pixel coordinate point in the deformed speckle image by using the particle swarm algorithm, and solving out integer pixel displacement according to the located integer pixel coordinate point;
s4: aiming at the whole pixel coordinate point obtained in the step S3, dividing a 10 × 10 rectangular area as an area to be interpolated by taking the point as a center, interpolating the area by using a bicubic interpolation algorithm, and then finding out a point with the maximum relation number in the interpolated area by using a particle swarm algorithm;
s5: and calculating the sub-pixel coordinates by using a quadratic polynomial fitting algorithm for the point with the maximum correlation coefficient found in the last step.
The radius of the sample sub-area selected in the target map in step S2 is 10 pixels.
Referring to fig. 3, in step S3, a Particle Swarm Optimization (PSO) is used to find out an integer pixel having the largest correlation coefficient with a point to be measured in an original image in a target region. The PSO algorithm has no crossing and variation operation of a genetic algorithm and a differential evolution algorithm, and is easy to realize. In order to overcome the defects that the result is easy to be locally optimal and the like based on the traditional DIC method, the PSO algorithm is introduced into the DIC method. The optimal sample subregion size, particle number, maximum speed of particle flight and maximum number of iterations are found through experiments. In this embodiment, the initial population size is 400, the start point coordinates of each particle are initialized randomly, the flight speed is initialized randomly, the number of iterations is 150, and the search is stopped after the algorithm converges.
The principle of the particle swarm algorithm is as follows:
particle Swarm Optimization (PSO) was first proposed by Eberhart and Kennedy in 1995, and its basic concept stems from studies on foraging behavior of bird flocks. Consider a scenario in which: a flock of birds randomly searches for food, with only one piece of food in this area, and all birds do not know where the food is, but they know how far away from the food the current location is. The simplest and most effective strategy? Individuals in the flock closest to the food are sought for searching. The PSO algorithm is elicited from this biological population behavior characteristic and used to solve the optimization problem.
Simulating said bird individuals with a particle, each particle being considered as a search individual in an N-dimensional search space, the current position of the particle being a candidate solution to the corresponding optimization problem, the flight of the particle being the search process of the individual. Speed, which represents how fast the movement is, and position, which represents the direction of the movement. The optimal solution searched by each particle independently is called an individual extremum, and the optimal individual extremum in the particle swarm is used as the current global optimal solution. And continuously iterating, and updating the speed and the position. And finally obtaining the optimal solution meeting the termination condition.
The objective function of the particle swarm optimization is to solve the correlation coefficient function of the two regions, and the correlation coefficient C is:
wherein f and g are the gray values of the pixel points in the regions I and I ', respectively, and f' and g 'are the average values of the gray values of the regions I and I', respectively.
In step S4, after the integer pixel coordinate point is obtained, the region to be interpolated is selected with the integer pixel coordinate as the center, and the region to be interpolated is interpolated by using the bicubic interpolation algorithm. And then finding out the point with the maximum interpolated correlation coefficient by using a particle swarm algorithm. The bicubic interpolation method is similar to the bilinear interpolation method, and bicubic spline interpolation can be obtained by respectively carrying out one-time cubic interpolation on the x direction and the y direction. The bicubic interpolation algorithm interpolates the region to be interpolated, and comprises the following steps: bicubic interpolation is obtained by performing cubic interpolation once respectively in the x direction and the y direction of the region. In the image interpolation process, not only the influence of the direct neighboring point on it but also the influence of the gray levels of 16 neighboring points around the point on it should be considered. The gray interpolation is performed by using the sinc function, and the value of any point between sampling points can be accurately obtained, and the characteristic diagram of the interpolation function s (x) ═ sin (pi x) is shown in fig. 1.
The specific method comprises the following steps:
let f (x, y) be the pixel coordinate of each point of the two-dimensional image after interpolation, and assume that the pixel coordinate after interpolation (x) is required0,y0) Pixel value of a point, i.e. the required value f (x)0,y0). First, s (1+ α), s (1- α), s (2- α), s (1+ β), s (1- β), and s (2- β) are calculated. Where α and β are interpolation steps that can be set to 1, then f (x +1, y), f (x +1, y), f (x +2, y) can be calculated0And y) the specific process is as follows:
f(x0,y)＝s(1+α)f(x-1,y)+s(α)f(x,y)+s(1-α)f(x+1,y)+s(2-α)f(x+2,y)
using the same method, it was calculated: f (x)0,y-1)、f(x0,y+1)、f(x0Y + 2). Then according to f (x)0,y-1)、f(x0,y+1)、f(x0,y+2)、f(x0Y) calculating f (x)0,y0) The calculation method is as follows:
f(x0,y0)＝s(1+β)f(x0-1,y)+s(β)f(x0,y)+s(1-β)f(x0,y+1)+s(2-β)f(x0,y+2)
assuming A, B, C three matrices, the above calculation process can be expressed as:
A＝[s(1+α) s(α) s(1-α) s(2-α)]
C＝[s(1+β) s(β) s(1-β) s(2-β)]T
the pixel of the point to be solved after solving the three matrices can be expressed as:
f(x0,y0)＝ABC
in the above formula, α and β are parameters and can be set to 1.
In step S4, a bicubic interpolation algorithm is used to select 16 points around the target point as stagnation points, the area to be interpolated is enlarged by 20 times, and a particle swarm algorithm is used to find the point with the largest correlation coefficient in the enlarged sub-area.
In step S5, after the coordinates of the integer pixel in the target map are obtained, 8 points around the point are used to calculate the parameters in the bivariate polynomial fitting, where the coordinates of the 8 points are (x) respectively0,y0)、(x0,y1)、(x0,y2)、(x1,y0)、(x2,y0)、(x1,y1)、(x1,y2)、(x2,y1)、(x2,y2) For the coordinates found after fitting, the calculated displacement is divided by 20 to obtain the final sub-pixel displacement. And positioning to the sub-pixel coordinates by using a binary polynomial fitting algorithm according to the point with the maximum correlation coefficient obtained in the step S4, wherein the fitting function in the binary polynomial is as follows:
f(x,y)＝a00+a10x+a01y+a20x2+a11xy+a02y2
taking a 3 × 3 fitting window, there are:
f(x0,y0)＝a00+a10x0+a01y0+a20x0 2+a11x0y0+a02y0 2
f(x0,y1)＝a00+a10x0+a01y1+a20x0 2+a11x0y1+a02y1 2
f(x0,y2)＝a00+a10x0+a01y2+a20x0 2+a11x0y2+a02y2 2
f(x1,y0)＝a00+a10x1+a01y0+a20x1 2+a11x1y0+a02y0 2
f(x2,y0)＝a00+a10x2+a01y0+a20x2 2+a11x2y0+a02y0 2
f(x1,y1)＝a00+a10x1+a01y1+a20x1 2+a11x1y1+a02y1 2
f(x1,y2)＝a00+a10x1+a01y2+a20x1 2+a11x1y2+a02y2 2
f(x2,y1)＝a00+a10x2+a01y1+a20x2 2+a11x2y1+a02y1 2
f(x2,y2)＝a00+a10x2+a01y2+a20x2 2+a11x2y2+a02y2 2
wherein, a00、a01、a10、a20、a11、a02For the coefficient to be solved, 6 coefficients in the equation set are obtained by using a least square method, and at the extreme point of the fitted surface, the following conditions are satisfied:
solving to obtain sub-pixel coordinates:
the sub-pixel displacement can be obtained from the obtained sub-pixel coordinates.
The final calculated sub-pixel displacement data is shown in table 1:
TABLE 1 Final calculated sub-pixel Displacement data
| Magnitude of displacement | Calculated sub-pixel displacement | Error of the measurement |
| 0.1 | 0.0968 | 0.0031 |
| 0.5 | 0.5097 | 0.0097 |
| 0.9 | 1.0067 | 0.0067 |
| 2 | 1.9045 | 0.0055 |
| 6 | 5.9967 | 0.0033 |
| 8 | 7.9938 | 0.0062 |
Although the preferred embodiments of the present invention have been described in detail, the present invention is not limited to the specific embodiments, and modifications and equivalents within the scope of the claims may be made by those skilled in the art and are included in the scope of the present invention.
Claims (7)
1. A sub-pixel positioning method based on a particle swarm algorithm is characterized by comprising the following steps:
s1: simulating a digital speckle image by using the matlab as an original image, and translating the original image to obtain a target image;
s2: selecting a point to be measured in an original drawing, recording a coordinate (x, y) of the point to be measured, dividing a rectangular region with the size of 2R as a target region by taking the coordinate (x, y) as a center in the deformed speckle pattern, wherein R is a search radius, and dividing a rectangular region with the size of 2R as a sample subregion for calculating a correlation coefficient by taking the point to be measured as the center in the original drawing, wherein R is the radius of the sample subregion;
s3: in the target area, randomly initializing n points as n randomly initialized particles in a particle swarm algorithm, dividing a 2r x 2r rectangular area as a target sub-area by taking the particles as the center for each particle, finding out an integer pixel coordinate point in the deformed speckle image by using the particle swarm algorithm, and solving out integer pixel displacement according to the located integer pixel coordinate point;
s4: aiming at the whole pixel coordinate point obtained in the step S3, dividing a 10 × 10 rectangular area as an area to be interpolated by taking the point as a center, interpolating the area by using a bicubic interpolation algorithm, and then finding out a point with the maximum relation number in the interpolated area by using a particle swarm algorithm;
s5: and calculating the sub-pixel coordinates by using a quadratic polynomial fitting algorithm for the point with the maximum correlation coefficient found in the last step.
2. The particle swarm algorithm-based sub-pixel positioning method according to claim 1, wherein: the radius of the sample sub-area selected in the target map in step S2 is 10 pixels.
3. The particle swarm algorithm-based sub-pixel positioning method according to claim 1, wherein: the particle swarm algorithm in the step S3 has an initial population size of 400, the coordinates of the start point of each particle are initialized randomly, the flying speed is initialized randomly, the number of iterations is 150, and the search is stopped after the algorithm converges.
4. The particle swarm algorithm-based sub-pixel positioning method according to claim 1, wherein: in step S4, the interpolating the region to be interpolated by the bicubic interpolation algorithm includes: and performing cubic interpolation once in the x direction and the y direction of the region respectively to obtain bicubic interpolation, and performing gray level interpolation by adopting a sinc function in the image interpolation process.
5. The particle swarm algorithm-based sub-pixel positioning method according to claim 1, wherein: in step S4, a bicubic interpolation algorithm is used to select 16 points around the target point as stagnation points, then the interpolation area is enlarged by 20 times, and a particle swarm algorithm is used to find the point with the largest correlation coefficient in the enlarged sub-area.
6. The particle swarm algorithm-based sub-pixel positioning method according to claim 1, wherein: in step S5, after the coordinates of the integer pixel in the target map are obtained, 8 points around the point are used to calculate the parameters in the bivariate polynomial fitting, where the coordinates of the 8 points are (x) respectively0,y0)、(x0,y1)、(x0,y2)、(x1,y0)、(x2,y0)、(x1,y1)、(x1,y2)、(x2,y1)、(x2,y2) For the coordinates found after fitting, the calculated displacement is divided by 20 to obtain the final sub-pixel displacement.
7. The particle swarm algorithm-based sub-pixel positioning method of claim 6, wherein: the fitting function in the bivariate polynomial is:
f(x,y)＝a00+a10x+a01y+a20x2+a11xy+a02y2
taking a 3 × 3 fitting window, there are:
f(x0,y0)＝a00+a10x0+a01y0+a20x0 2+a11x0y0+a02y0 2
f(x0,y1)＝a00+a10x0+a01y1+a20x0 2+a11x0y1+a02y1 2
f(x0,y2)＝a00+a10x0+a01y2+a20x0 2+a11x0y2+a02y2 2
f(x1,y0)＝a00+a10x1+a01y0+a20x1 2+a11x1y0+a02y0 2
f(x2,y0)＝a00+a10x2+a01y0+a20x2 2+a11x2y0+a02y0 2
f(x1,y1)＝a00+a10x1+a01y1+a20x1 2+a11x1y1+a02y1 2
f(x1,y2)＝a00+a10x1+a01y2+a20x1 2+a11x1y2+a02y2 2
f(x2,y1)＝a00+a10x2+a01y1+a20x2 2+a11x2y1+a02y1 2
f(x2,y2)＝a00+a10x2+a01y2+a20x2 2+a11x2y2+a02y2 2
wherein, a00、a01、a10、a20、a11、a02For the coefficient to be solved, 6 coefficients in the equation set are obtained by using a least square method, and at the extreme point of the fitted surface, the following conditions are satisfied:
solving to obtain sub-pixel coordinates:
the sub-pixel displacement can be obtained from the obtained sub-pixel coordinates.
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| 孙娇: "数字散斑相关测量方法研究", 《中国优秀硕士论文电子期刊网 信息科技辑》 * |
Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN114283736A (en) * | 2022-03-03 | 2022-04-05 | 武汉精立电子技术有限公司 | Method, device and equipment for correcting positioning coordinates of sub-pixels and readable storage medium |
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