Image registration is one of today's challenging image processing problems. Given two images, one attempts to find a reasonable transformation to deform one image into the other. Image registration is applied whenever images resulting from different times and devices need to be compared or integrated. It is often used in radiation therapy and surgery planing. Image registration is a highly ill-posed problem. To reduce the level of non-uniqueness, it is possible to use additional constraints such as rigidity of bones. This research deals with the numerical treatment of image-based constraints. While it is possible to formulate constrained image registration problems, such problems can be very difficult to solve. This project develops and experiments with inexact adaptive multilevel inexact Sequential Quadratic Programming methods that allow inaccurate solutions of the subproblem at each iteration.
Intellectual Merit: The challenges in this work are composed of two parts. First, constrained image registration problems are formulated in a way that yields continuously differentiable objective functions. Second, constrained optimization techniques are develop. This involves SQP, multigrid and adaptive mesh refinement methods. Broad Impact: Image registration is routinely used for clinical procedures. Nevertheless a vast majority of registration problems use either rigid or affine linear transformations. This is because fully nonlinear registration tends to be unreliable. Using image-based constraints will generate realistic deformations and thus expand the use of image registration algorithms to much more complicated problems. This can directly impact clinical procedures such as radiation planning and tumor tracking.
