Abstract
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.
Highlights
Computer vision techniques for motion extraction are widely developed in a huge variety of applications, including motion tracking, motion compensation, image registration [1], remote sensing [2], biomedicine [3], satellite imagery [4] and vibration analysis [5]
Various variants of digital image correlation (DIC) exist in the literature, for example, phase-only correlation (POC) [2], upsampling cross-correlation (UCC) [6], Fourier-based correlation [1] and virtual image correlation [7]
Three examples with either synthetic or real-world images are presented below to show that the quadratic surface fitted in the quadratic surface fitting (QSF) method does not always have a maximum in the close vicinity of the pixel-level cross-correlation peak
Summary
Computer vision techniques for motion extraction are widely developed in a huge variety of applications, including motion tracking, motion compensation, image registration [1], remote sensing [2], biomedicine [3], satellite imagery [4] and vibration analysis [5]. Displacement estimation is refined in the vicinity of the cross-correlation peak Among such refinement methods, quadratic surface fitting (QSF) provides a good trade-off between accuracy and computational burden, suitable for video-based SHM, as reported in [9]. Quadratic surface fitting (QSF) provides a good trade-off between accuracy and computational burden, suitable for video-based SHM, as reported in [9] This method and its variant forms have been investigated in [1,2,10,11,12,13,14]. Solutions will be proposed to handle the failures cases of the QSF method by constrained optimization ensuring that the estimated subpixel displacement is within one pixel.
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