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。给定两个图像，其中一个试图找到一个合理的变换，将一个图像变形为另一个图像。当需要比较或集成来自不同时间和设备的图像时，应用图像配准。它通常用于放射治疗和手术计划。图像配准是一个高度不适定的问题。为了降低非唯一性的程度，可以使用额外的约束，如骨骼的刚性。本研究涉及基于图像的约束的数值处理。虽然有可能制定约束图像配准问题，但此类问题可能很难解决。本项目开发和实验了不精确自适应多级不精确顺序二次规划方法，该方法允许在每次迭代中对子问题进行不准确的解。智力优势：这项工作的挑战由两部分组成。首先，以产生连续可微目标函数的方式制定约束图像配准问题。其次，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的配准往往不可靠。使用基于图像的约束将产生真实的变形，从而将图像配准算法的使用扩展到更复杂的问题。这可以直接影响临床程序，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.