Direct estimation of surface strain fields from a stereo vision system

Estimating strain on surfaces of deforming three-dimensional (3D) structures is a critical need in experimental mechanics. Although single-camera techniques excel at estimating deformation on a surface parallel to the imaging plane, they are prone to artifact for 3D motion because they cannot distinguish between out-of-plane motion and in-plane dilatation. Multiview (e.g., stereo) camera systems overcome this via a three-step process consisting of: (1) independent surface registration, (2) triangulation to estimate surface displacements, and (3) deformation estimation. However, existing methods are prone to errors associated with numerical differentiation when computing estimating strain fields from displacement fields unless regularization schemes are used. Such regularization schemes can introduce inaccuracy into strain estimation. Inspired by previous work which combined registration and deformation estimation into a single step for 2D images and 3D imaging stacks, we developed a theory for simultaneous image registration, 3D triangulation, and deformation estimation in a multiview system. The deformation estimation does not require numerical differentiation of displacement fields to estimate strain fields. We present here the theoretical foundations and derivation of two related implementations of this approach, and discuss their strengths and weaknesses.