Analysis of images to detect and quantify spatial variations in deformation is important for understanding the health and disposition of, for example, materials, structures, and tissues. A standard approach for such analysis involves estimating displacement fields inferred by comparing images of the sample taken at different times or under different conditions. Displacement field, as used herein, refers to a spatial distribution of displacements of locations within a sample between a first image and a second image. The most broadly used method involves matching image intensities over a grid of regions of a sample before and after the sample is deformed, 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 algorithm that applies and optimizes a warping function to the undeformed image before matching it to a deformed image; this may also be achieved by applying the Lucas-Kanade algorithm in the reverse direction by optimizing a warping function to the deformed image before matching it to the undeformed image. Strain tensors estimated through these optical approaches underlie much of quantitative cell mechanics, 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. Similar approaches have been used to study collective cell motion, tissue morphogenesis, and tissue mechanics. More generally, these tools are standard in the non-destructive evaluation of materials, structures, and tissues using optical techniques.
However, these methods are subject to large errors when strain is high or localized. Specifically, small inaccuracies in displacement estimation become amplified through the numerical differentiation needed to estimate strain tensors. Minor mis-tracking of a single displacement can lead to an artifact that is typically indistinguishable from a region of concentrated strain. Although accuracy can be improved by incorporating into the image matching algorithm a mathematical model that describes how a specific tissue deforms, such techniques cannot be applied to a tissue whose properties are not known a priori.