Numerical Optimization For Image-Based Constrained Registration

图像配准是当今具有挑战性的图像处理问题之一，给定两幅图像，其中一幅试图找到一个合理的变换来将一幅图像变形为另一幅图像。图像配准是一个高度不适定的问题。为了降低非唯一性的水平，可以使用额外的约束，例如骨骼的刚度。本研究主要探讨以影像为基础之限制条件的数值处理，虽然有可能以公式化的方式表达限制条件下的影像配准问题，但这类问题可能很难解决。 这个项目开发和实验不精确自适应多级不精确序列二次规划方法，允许不准确的解决方案的子问题在每个iteration.Intellectual优点：在这项工作中的挑战是由两部分组成。首先，约束图像配准问题制定的方式，产生连续可微的目标函数。 第二，发展了约束优化技术。这涉及SQP、多重网格和自适应网格细化方法。广泛影响：图像配准通常用于临床程序。然而，绝大多数配准问题使用刚性或仿射线性变换。这是因为完全非线性配准往往不可靠。使用基于图像的约束将产生逼真的变形，从而将图像配准算法的使用扩展到更复杂的问题。这可能直接影响临床程序，如放射计划和肿瘤跟踪。

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 willgenerate 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.