Influence of Neighborhood Size and Cross-Correlation Peak-Fitting Method on Location Accuracy

On Quadratic Interpolation of Image Cross-Correlation for Subpixel Motion Extraction

Digital image correlation techniques are well known for motion extraction from video images. Following a two-stage approach, the pixel-level displacement is first estimated by maximizing the cross-correlation between two images, then the estimation is refined in the vicinity of the cross-correlation peak. Among existing subpixel refinement methods, quadratic surface fitting (QSF) provides good performances in terms of accuracy and computational burden. It estimates subpixel displacement by interpolating cross-correlation values with a quadratic surface. The purpose of this paper is to analytically investigate the QSF method. By means of counterexamples, it is first shown in this paper that, contrary to a widespread intuition, the quadratic surface fitted to the pixel-level cross-correlation values in the neighborhood of the cross-correlation peak does not always have a maximum. The main contribution of this paper then consists in establishing the mathematical conditions ensuring the existence of a maximum of this fitted quadratic surface, based on a rigorous analysis. Algorithm modifications for handling the failure cases of the QSF method are also proposed in this paper, in order to consolidate it for subpixel motion extraction. Experimental results based on two typical types of images are also reported.

Influence of Neighborhood Size and Cross-Correlation Peak-Fitting Method on Location Accuracy

A known technique to obtain subpixel resolution by using object tracking through cross-correlation consists of interpolating the obtained correlation function and then refining peak location. Although the technique provides accurate results, peak location is usually biased toward the closest integer coordinate. This effect is known as the peak-locking error and it strongly limits this calculation technique’s experimental accuracy. This error may differ depending on the scene and algorithm used to fit and interpolate the correlation peak, but in general, it may be attributed to a sampling problem and the presence of aliasing. Many studies in the literature analyze this effect in the Fourier domain. Here, we propose an alternative analysis on the spatial domain. According to our interpretation, the peak-locking error may be produced by a non-symmetrical sample distribution, thus provoking a bias in the result. According to this, the peak interpolant function, the size of the local domain and low-pass filters play a relevant role in diminishing the error. Our study explores these effects on different samples taken from the DIC Challenge database, and the results show that, in general, peak fitting with a Gaussian function on a relatively large domain provides the most accurate results.