Image and Complex Correlation Near Discontinuities

Abstract

Abstract: In this paper, the effect of imposing continuity constraints in real and complex image correlation has been investigated. It is found that in regions where continuity can be assumed a second-order spline expansion of the underlying deformation field provides a globally smooth estimate of the deformation field. In general, only an estimate of the deformation at the subinterval centres needs to be provided from local correlation. If the assumption of continuity is violated multiple peaks in the correlation function are introduced. If the discontinuity exceeds one speckle diameter the correlation peaks will be separated, but with reduced correlation values. Otherwise, the different peaks will blend resulting in a deformed correlation function and a correlation value that approaches unity for small discontinuities. In this case, the Hessian is shown to provide a good estimate of the position of a discontinuity. Furthermore, a methodology to perform automatic remeshing is sketched. A subinterval edge is placed at the position of the detected discontinuity, the surrounding subintervals are reduced in size and the continuity constraint is relaxed. The methodology has proven successful on one-dimensional images but it can be transferred with reasonable effort to multi-dimensional images.