Xiaohai Xu

Fourier-based interpolation bias prediction in digital image correlation.

Based on the Fourier method, this paper deduces analytic formulae for interpolation bias in digital image correlation, explains the well-known sinusoidal-shaped curves of interpolation bias, and introduces the concept of interpolation bias kernel, which characterizes the frequency response of the interpolation bias and thus provides a measure of the subset matching quality of the interpolation algorithm. The interpolation bias kernel attributes the interpolation bias to aliasing effect of interpolation and indicates that high-frequency components are the major source of interpolation bias. Based on our theoretical results, a simple and effective interpolation bias prediction approach, which exploits the speckle spectrum and the interpolation transfer function, is proposed. Significant acceleration is attained, the effect of subset size is analyzed, and both numerical simulations and experimental results are found to agree with theoretical predictions. During the experiment, a novel experimental translation technique was developed that implements subpixel translation of a captured image through integer pixel translation on a computer screen. Owing to this remarkable technique, the influences of mechanical error and out-of-plane motion are eliminated, and complete interpolation bias curves as accurate as 0.01 pixel are attained by subpixel translation experiments.

Noise-induced bias for convolution-based interpolation in digital image correlation.

In digital image correlation (DIC), the noise-induced bias is significant if the noise level is high or the contrast of the image is low. However, existing methods for the estimation of the noise-induced bias are merely applicable to traditional interpolation methods such as linear and cubic interpolation, but are not applicable to generalized interpolation methods such as BSpline and OMOMS. Both traditional interpolation and generalized interpolation belong to convolution-based interpolation. Considering the widely use of generalized interpolation, this paper presents a theoretical analysis of noise-induced bias for convolution-based interpolation. A sinusoidal approximate formula for noise-induced bias is derived; this formula motivates an estimating strategy which is with speed, ease, and accuracy; furthermore, based on this formula, the mechanism of sophisticated interpolation methods generally reducing noise-induced bias is revealed. The validity of the theoretical analysis is established by both numerical simulations and actual subpixel translation experiment. Compared to existing methods, formulae provided by this paper are simpler, briefer, and more general. In addition, a more intuitionistic explanation of the cause of noise-induced bias is provided by quantitatively characterized the position-dependence of noise variability in the spatial domain.