Formulation of Lucas–Kanade Digital Image Correlation Algorithms for Non‐contact Deformation Measurements: A Review

Abstract

Digital image correlation (DIC) metrology has been increasingly used in a wide range of experimental mechanics research and applications. The DIC algorithm used so far is however limited mostly to the classic forward additive Lucas–Kanade type. In this paper, a survey is given about the formulation of other types of Lucas–Kanade DIC algorithms that have been appeared in computer vision, robotics, medical image analysis literature and so on. Concise notations consistent with the finite deformation kinematics analysis in continuum mechanics are used to describe all Lucas–Kanade DIC algorithms. An intermediate image is introduced as a frame of reference to clarify the so‐called compositional algorithms in a two‐frame DIC analysis. Explicit examples about the additive and compositional updating of deformation parameters are given for affine deformation mapping. Extensions of these algorithms to the so‐called consistent or symmetric types are also presented. The equivalency of final numerical solutions using additive, compositional and inverse compositional algorithms is shown analytically for the case of affine deformation mapping. In particular, the inverse compositional algorithm for affine image subset deformation is highlighted for its superior computational efficiency. While computationally less efficient, consistent and symmetric algorithms may be more robust and less biased and their potentials in experimental mechanics applications remain to be explored. The unified formulation of these Lucas–Kanade DIC algorithms collected all together in this paper can serve as a useful guide for researchers in experimental mechanics to further evaluate the merits as well as limitations of these non‐classic algorithms for image‐based precision displacement measurement applications.

Simple and accurate methods for quantifying deformation, disruption, and development in biological tissues

“…Although not widely used in the biomedical and engineering communities, the LK method is broadly applied in computer vision to improve region-matching (figure 1a,c) [7,8,10,11]. Rather than matching regions of identical size and shape, the LK method optimizes a warping function for each region to improve the matching.…”

“…Specifically, small inaccuracies in displacement estimation become amplified through the numerical differentiation needed to estimate strain fields [7][8][9]. Minor mistracking of a single displacement can lead to an artefact that is typically indistinguishable from a region of concentrated strain.…”

“…A standard approach for such analysis involves estimating displacement fields inferred by comparing images of the same system taken at different times or under different conditions [7,8]. The most broadly used technique involves matching image intensities over a grid of regions of a sample before and after the sample is deformed [8,9], then differentiating the resulting displacement fields numerically to estimate the tensor of strains that describes the spatial distribution of deformation.…”

“…The most broadly used technique involves matching image intensities over a grid of regions of a sample before and after the sample is deformed [8,9], then differentiating the resulting displacement fields numerically to estimate the tensor of strains that describes the spatial distribution of deformation. Displacement field estimation can be improved dramatically for large deformations through the Lucas-Kanade (LK) algorithm that applies and optimizes a 'warping function' to the undeformed image before matching it to an undeformed image [7,[10][11][12]. Strain fields estimated through these approaches underlie much of cell mechanics [13][14][15][16], using a technique that compares images of a deformable medium contracted by cells to images of the same medium after deactivation or removal of the cells.…”

Regularised digital-level corrections for infrared image correlation

“…A series of DIC criteria have been proposed with different degrees of robustness (see Refs. [5,8,9] for reviews). The so-called Zero-mean Normalized Sum of Squared Differences (ZNSSD) criterion for instance is popular in local DIC measurements.…”