A Digital Volume Correlation Technique for 3-D Deformation Measurements of Soft Gels

Abstract

This paper develops a set of digital volume correlation (DVC) algorithms to address 3-D deformation measurements of soft gels with the aid of laser-scanning confocal microscopy. As an extension of the well-developed digital image correlation (DIC) method, the present DVC approach adopts a three-dimensional zero-normalized cross-correlation criterion (3-D ZNCC) to perform volume correlation calculations. Based on a 3-D sum-table scheme and the fast Fourier transform technique, a fast algorithm is first proposed to accelerate the integer-voxel correlation computations. Subsequently, two kinds of sub-voxel registration algorithms, i.e., 3-D gradient-based algorithm and 3-D Newton–Raphson algorithm, are presented to obtain the sub-voxel displacement and strain fields of volume images before and after deformation. Both a series of computer-simulated digital volume images and an actual agarose gel sample randomly embedded with fluorescent particles are employed to verify the 3-D deformation measurement capability of the proposed DVC algorithms, which indicates that they are competent to acquire 3-D displacement and strain fields of soft gels.

Full-field mapping of internal strain distribution in red sandstone specimen under compression using digital volumetric speckle photography and X-ray computed tomography

“…However, creating a 3D volumetric speckle pattern is a much more complicated endeavor. One can either artificially introduce markers into the studied material (Huang et al, 2011), or just use the material's internal microstructure itself as the speckle pattern (Bay et al, 1999;Lenoir et al, 2007;Hall et al, 2010a, b;Charalampidou et al, 2011Charalampidou et al, , 2014. In this study, we use the natural microstructure of red sandstone as the volumetric speckle pattern.…”

Challenges in imaging and predictive modeling of rhizosphere processes

“…Bay et al (1999) were the first to extend the DIC approach to 3D data acquired using a bench-top CT scanner, applying the technique to samples of trabecular bone in simple uniaxial compression. Since this first demonstration, in which sub-voxel precision in displacement measurement was achieved, variations of the method have been applied to study a diverse range of materials including sand (Hall et al 2010), woods (Forsberg et al 2008), sugar (Forsberg and Siviour 2009), metals (Morgeneyer et al 2013), gels (Huang et al 2011), rock (Lenoir et al 2007), engineering composites (Brault et al 2013), and foams (Roux et al 2008). Because DVC and DIC provide full-field deformation information and are physically non-invasive, they are highly promising techniques for investigating the mechanics of soil and root systems whose opacity, heterogeneity and complexity make other strain measurement approaches unfeasible.…”

GPU Accelerated Digital Volume Correlation

“…This technique can be considered as a straightforward extension of the well-established digital image correlation (DIC) [3,4] and shares its simplicity in principles and effectiveness in applications. Nowadays, it has been extensively applied in the characterization of various materials including bones [1,5], soft materials [6,7], wood [8] and sand [9]. Compared with DIC, the computational burden of DVC is much heavier.…”

“…For integer-voxel displacement estimation, fast Fourier transform based crosscorrelation (FFT-CC) algorithm [6,10] is widely used as a classic method, which benefits from the fact that crosscorrelation operation in space domain is equivalent to pointwise multiplication in frequency domain. The algorithm can be further accelerated by combining a fast sum-table approach [7]. To achieve a sub-voxel level accuracy, various sub-voxel registration algorithms have been developed, including the iterative algorithms derive from Newton's minimization method, e.g., Levenberg-Marquardt algorithm [1], BroydenFletcher-Goldfarb-Shanno (BFGS) algorithm [2,11,10], Newton-Raphson algorithm [7] and iterative least-squares algorithm [12], and non-iterative algorithms such as the correlation coefficients curve-fitting algorithm [6] and the gradientbased algorithm [7].…”

“…The algorithm can be further accelerated by combining a fast sum-table approach [7]. To achieve a sub-voxel level accuracy, various sub-voxel registration algorithms have been developed, including the iterative algorithms derive from Newton's minimization method, e.g., Levenberg-Marquardt algorithm [1], BroydenFletcher-Goldfarb-Shanno (BFGS) algorithm [2,11,10], Newton-Raphson algorithm [7] and iterative least-squares algorithm [12], and non-iterative algorithms such as the correlation coefficients curve-fitting algorithm [6] and the gradientbased algorithm [7]. Recently, Pan et al introduced three ideas to accelerate the computation of DVC effectively [13] : (1) an inverse compositional Gauss-Newton (ICGN) algorithm [14] was introduced to replace the conventional forward additive Newton-Raphson algorithm for sub-voxel registration.…”