参数化形函数的亚像素匹配方法

Sub-Pixel Matching Method for Parametelrized Shape Function

数字图像相关法的亚像素匹配误差与散斑图像和形函数有关,对于无迭代运算的梯度法和曲线拟合法等,形函数很难适应不同散斑图像的亚像素分布规律,为使形函数能够匹配不同的散斑图像,提出了一种基于参数化形函数的亚像素匹配方法。研究了参数化形函数中的指数变量和背景变量等参数对亚像素匹配误差的调节规律。研究结果表明,对于不同散斑图像,均可以通过对形函数参数的标定得到与散斑图像匹配的最优形函数。以散斑直径为2~20 pixel的高斯散斑图像为例,分别在x方向生成位移为0.1~0.9 pixel的10幅图像,对所提匹配方法进行了验证。验证结果表明,标定后的形函数能使不同散斑图像的亚像素匹配误差减小到0.001 pixel以内。最后,对DIC Challenge提供的实际位移散斑图像进行了验证,同样也证明了所提匹配方法的有效性。

Objective In digital image correlation methods,the sub-pixel matching error is related to the speckle image and shape function.For the gradient algorithm and curve fitting algorithm without iterative operation,the shape function is difficult to adapt to the sub-pixel distribution law of different speckle images.Although the calculation time is short,the sub-pixel matching error is large.For the Newton-Raphson algorithm with an iterative operation,the sub-pixel matching error can be greatly reduced through the infinite approximation of the target image to the original image or the original image to the target image,but the calculation is time-consuming.Generally,in the displacement range of o.1-0.9 pixel,the sub-pixel error is mainly S-shaped,and the S-shaped error is related to the image speckle diameter.The S-shaped error is much more different for different speckle diameters.In the field of displacement measurement,the speckle image is fixed and determined,and how to select an appropriate shape function matching the known speckle image to shorten the sub-pixel matching time and improve the sub-pixel matching accuracy has become the focus of this paper.Methods In order to reduce sub-pixel matching error,this paper proposes a sub-pixel matching method based on parameterized shape function with an exponential variable and background variable,and the core of the method is to decompose the 3X3 correlation coefficient C(i,j)into the 3X1 correlation coefficient A(i)in the direction and the 1X3 correlation coefficient B(i)in the y direction.Specifically,i and j vary in the set of-1,O,and 1,and then the 3X1 correlation coefficient A(i)and the 1X3 correlation coefficient B(j)with the exponential variable and background variable are weighted.In the paper,the difference between the absolute displacement and the sum of relative displacement is defined as a sub-pixel matching error,which includes linear and S-shaped errors.The shape function parameters are calibrated by using different regulation rules of the shape function parameters of the exponential variable and background variable on the sub-pixel matching error so that the proposed method features short sub-pixel matching time and small matching error.Results and Discussions The experiment takes the Gaussian speckle pattern with a speckle diameter of 2 pixel,10 pixel,and 20 pixel as an example,and 10 images with the displacement of 0.1-0.9 pixel in the direction are generated respectively.The regulation rule of the shape function parameters on the sub-pixel matching error is experimentally studied.The research results show that the exponential variable of the shape function parameter has the primary regulation function to change the slope of the linear error and the secondary regulation function to change the direction of the S-shaped error(Fig.4).The background variable of the shape function parameter has the primary regulation function to change the direction of the S-shaped error and the secondary regulation function to change the slope of the linear error(Fig.5).Under the coordinated regulation of shape function parameters,the sub-pixel matching error of the above speckle image is less than O.001 pixel(Table 1,Table 2,and Table 3).At the same time,the influence of the speckle diameter of the speckle image from 2 pixel to 20 pixel on the shape function parameters is studied(Table 4,Fig.7,and Fig.8).It is found that when the speckle diameter is greater than 6 pixel,the influence of the speckle diameter on the shape function parameters becomes weak,and the influence curve becomes flat,which also lays a good foundation for applying the method in the field of deformation measurement.Finally,according to the actual displacement speckle image provided by DIC Challenge,the proposed method is verified(Table 5).ConclusionsThe sub-pixel matching method described in this paper makes the shape function approximate to the subpixel distribution law of the speckle image by calibrating the shape function parameters to obtain the optimal shape function and greatly reduces the sub-pixel matching error.Since the shape function calculation only involves the addition,subtraction,multiplication,division,and exponential operation of nine correlation coefficients,as well as no more than six cycles of calculation,the sub-pixel matching time can be ignored in the digital image correlation calculation.Compared with the gradient algorithm and curve fitting algorithm without iterative operation,the sub-pixel matching method of parameterized shape function can obtain ideal sub-pixel matching accuracy for speckle images with different speckle diameters,which cannot be achieved by gradient algorithm and curve fitting algorithm.Compared with the Newton-Raphson algorithm with the iterative operation,the proposed method has comparable sub-pixel matching accuracy in the field of displacement measurement and is more suitable for online displacement measurement due to the short matching time.However,in the field of deformation measurement,there are still some problems to be solved and further studied,such as the influence of the equivalent speckle diameter change of speckle image under deformation conditions on the shape function,as well as the dynamic calibration for shape function parameters.