YaDICs (Yet another Digital Image Correlation software) is a program written to perform digital image correlation on 2D and 3D tomographic images. The program was designed to be both modular (by its plugin strategy) and efficient (by its multithreading strategy). It incorporates different transformations (Global, Elastic, Local), optimization strategies (Gauss-Newton, Steepest descent), as well as various global/local shape-functions (such as rigid-body motions, homogeneous dilatations, flexural, and Brazilian test models).
Theoretical background
Context In solid mechanics, digital image correlation is a tool that allows to identify the displacement field to register a reference image (called herein fixed image) to images during an experiment (the mobile image). For example, it is possible to observe the face of a specimen with a painted speckle on it in order to determine its displacement fields during a tensile test. Before the appearance of such methods, researchers usually used strain gauges to measure the mechanical state of the material but strain gauges only measure the strain on a point and don't allow to understand material with an heterogeneous behavior. One can obtain a full in plane strain tensor by derivation of the displacement fields. Many methods are based upon the optical flow. In fluid mechanics a similar method is used, called Particle Image Velocimetry (PIV); the algorithms are similar to those of DIC but it is impossible to ensure that the optical flow is conserved so a vast majority of the software used the normalized cross correlation metric. In mechanics the displacement or velocity fields are the only concern, registering images is just a side effect. There is another process called image registration using the same algorithms (on monomodal images) but where the goal is to register images and thereby identifying the displacement field is just a side effect. YaDICs uses the general principle of image registration with a particular attention to the displacement fields basis.
Image registration principle YaDICs can be explained using the classical image registration framework:
Image registration general scheme The common idea of image registration and digital image correlation is to find the transformation between a fixed image and a moving one for a given metric using an optimization scheme. While there are many methods to achieve such a goal, Yadics focuses on registering images with the same modality. The idea behind the creation of this software is to be able to process data that comes from a μ-tomograph; i.e.: data cube over 10003 voxels. With such a size it is not possible to use naive approach usually used in a two-dimensional context. In order to get sufficient performances OpenMP parallelism is used and data are not globally stored in memory. As an extensive description of the different algorithms is given in.
Sampling Contrary to image registration, Digital Image Correlation targets the transformation, one wants to extracted the most accurate transformation from the two images and not just match the images. Yadics uses the whole image as a sampling grid: it is thus a total sampling.
Interpolator It is possible to choose between bilinear interpolation and bicubic interpolation for the grey level evaluation at non integer coordinates. The bi-cubic interpolation is the recommended one.
Metrics
Sum of squared differences (SSD) The SSD is also known as mean squared error. The equation below defines the SSD metric:
S S D ( μ , I F , I M ) = 1 | Ω F | ∑ x i ∈ Ω F ( I F ( x i ) − I M ( T μ ( x i ) ) ) 2 , {\displaystyle SSD(\mu ,{\mathcal {I_{F}}},{\mathcal {I_{M}}})={\dfrac {1}{\left|\Omega _{F}\right|}}\sum _{x_{i}\in \Omega _{F}}\left({\mathcal {I_{F}}}(x_{i})-{\mathcal {I_{M}}}({T}_{\mu }(x_{i}))\right)^{2},}
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