Application of an improved subpixel registration algorithm on digital speckle correlation measurement
Introduction
In the modern optical metrology, a variety of techniques have been applied to the deformation measurement due to the advantages of automatic, non-contact, full field and real time [1]. The digital speckle correlation method, introduced by Peters and Ranson [2], has found valuable and widespread use in many research and engineering applications [3], [4], [5]. By means of this technique, speckle patterns can be obtained under white light illumination and the heavy dependence on the test environment is then reduced [6]. It also avoids the difficulties of dealing with the tedious phase information and fringe analysis. To enhance the sensitivity and the accuracy of the measurement further, subpixel algorithms are required.
Various techniques have been proposed that are used to determine the subpixel registration such as interpolation [7], [8], [9], [10], differential iteration [11], double Fourier transform [12], [13] and gradient-based methods [14], [15]. However, one challenge as to how to obtain high accuracy with far less computation complexity is offered in real applications. Interpolations used in the subpixel registration usually include phase correlation interpolation [7], intensity interpolation [8] and correlation function interpolation [9], [10]. The phase correlation interpolation method is suitable for the images seriously distorted, however, the accuracy of which is the lowest among the three [16]. While the intensity interpolation has been less adopted for its immense computation consumption, the correlation function interpolation is generally considered due to its lower computation and better noise-proof feature [17]. Nevertheless, an obvious weakness of the interpolation algorithm is that the sensitivity is limited by the computation step because of the systematic error of the algorithm [17]. Moreover, the Peak Locking or Bias Error phenomenon occurs while using the interpolation methods to determine the subpixel registration [18]. Both the disadvantages will limit the improvement of the subpixel accuracy. Differential iterative method can be performed to determine multiple deformation parameters simultaneously [11]. However, this algorithm depends on the calculation of prediction and correction terms and often requires the calculation of second-order spatial derivations; the computation complexity will be increased. The methods by Double Fourier Transform, without the multiplication in the spectral space and the inverse Fourier transform, are performed by a two-step Fourier transform and faster than phase correlation methods. However, to obtain subpixel resolution, the methods must be supplemented by the interpolation-based oversampling technique [12] or the recursive iteration method [13] based on the discrete spectrum and the above-mentioned disadvantages are still there. The classical gradient-based algorithm used for the subpixel registration is to relate the difference between two successive frames to the spatial intensity gradient of the first image, with the expression given as [14]where f1(x,y) and f2(x,y) are the two successive images and Dx, Dy are the translations of an object centered at (x0,y0) of image 1 with respect to image 2 in the X and Y directions, respectively. Based on an optical flow method developed by Davis and Freeman [19], another gradient-based algorithm that considered the effect of intensity gradients of both images before and after deformation was presented [15]. The two gradient-based algorithms are faster than the other three kinds of methods described above. And yet, in these two methods, only the simple difference between the gray values of two images was considered and the important information of the statistics property was lost. In addition, the sensitivities and accuracies reported in many previous studies vary within orders of magnitude from 0.5 to 0.01 pixel [11], [15], [16], [20], [21]. However, while numerous studies of subpixel registration algorithms exist, relatively few reported quantitative results and tried to solve the discrepancy.
In this paper, a spatial-gradient-based algorithm considering the statistical characterization of the subset region is developed to determine the subpixel registration. With this method, only the first-order partial derivatives of the given functional are required to calculate in a subset region with far less computation time. Four different modes of the algorithm are given and compared with computation time, optimal subset-region size (SRS) and sensitivity using computer-simulated images. Furthermore, the influences of the size and the density of speckle granules on accuracy are studied based on the optimal mode. Finally, practical deformation measurements are performed to validate the feasibility and the validity of the algorithm.
Section snippets
Basic principle of the digital speckle correlation method (DSCM)
The basic principle of DSCM is to match two speckle patterns before and after deformation. Based on the predefined correlation function, the matching procedure is completed through searching the peak position of the distribution of correlation coefficients, which indicates the similarity of the two speckle patterns. Finally, the displacement will be extracted by the peak position. A better and commonly used cross-correlation function is defined as below [22]:
Generation of simulated images
Computer-simulated images are used for the verification of the algorithm due to the well-controlled image features and information of deformation. For the purpose of this research, the two main variables of the digitization process were chosen to be 128×128 for the resolution and 8-bit per pixel for the pixel depth (256 gray levels). While this resolution is low, the 128×128 image can be considered without any loss of generality to be a subset of an image digitized with higher resolution.
The
Verification of algorithm using simulated images
More general simulated images are studied and the results pooled from more than 2000 simulations are reported. For every image pair, the total number of calculated points with fixed positions in the original image is 169. All the computations are completed under the same conditions of PIII550 mainframe with 128M memory.
Rigid body translation and rotation
Fig. 9 shows the experimental verification of the algorithm in Mode 4 with SRS=51×51 pixels. The specimen is sprayed with white paint onto its black surface and then attached to a manual two-axis stage with a translation in increments of and a single stage with a rotation accuracy of 0.0174 radians. Speckle patterns are captured with a CCD camera with the magnification of . The feasibility and validity of the algorithm are clearly verified by the deformation measurements of
Conclusions
In this paper, an improved gradient-based algorithm is developed to determine the subpixel registration of DSCM. Computer-simulated images are used to verify the algorithm with four modes through comparisons of computation time, optimal subset-region size and sensitivity. Based on the simulations, the optimal subset size is suggested to be 31×31 to 51×51 pixels and a high accuracy is obtained with the error less than 0.001, 0.003 and 0.01 pixel for measuring the subpixel displacements in the
Acknowledgements
The authors would like to acknowledge the NSFC 19972033 and the Fund of Tsinghua University GC 2001031 for this research work.
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