A Robust Formulation for Optical-Flow/Material Identification Problems

Abstract

The characterization of material properties from image sequences is of paramount importance for the non-destructive assessment of structural integrity. A particular application can be found in the field of biomedical engineering, where anatomical structures, whose material properties are frequently sought, can be observed in-vivo through time. A traditional approach for such task, involves the estimation of the displacement field across the image sequence -usually by means of optical flow techniques- and the subsequent estimation of the material properties through the formulation of an inverse mechanical problem. The decoupled nature of this approach leads to cumulative errors across these stages, caused by the lack of consistency between the recovered optical flow and the displacement field delivered by the underlying mechanical model yet to be identified. In recent years, new approaches were proposed to integrate the optical flow and the material identification problems to render a compatible characterization of the displacement field in the sense that they correspond to a mechanical model whose material properties also undergo an identification process. In the present work, a new numerical method for the simultaneous identification of the optical flow field and the material properties of a mechanical model from a sequence of images is presented. Realistic numerical examples with manufactured solutions are solved, considering different sources of errors (such as pixel errors and interpolation errors). The results obtained allow us to conclude that the proposed method performs robustly even in the presence of noise, and is also efficient in terms of the number of iterations required to achieve convergence.