Optimal Image Registration

描述（由申请人提供）：对准图像以使对应特征相关的过程称为图像配准。图像配准是医学图像分析中的主要问题之一，二十多年来一直受到广泛关注。许多建议的图像配准方法尚未被证明是最佳的任何措施，他们遭受一个共同的问题：特设的假设。此外，通常它们依赖于目标函数的优化，这固有地遭受局部最小值的问题并且需要初始化。由于这些原因，文献中提出的图像配准方法仅在特殊条件下工作，并且任何偏离这些条件的情况都会导致方法失败。然而，图像配准是一个数学问题，如果定义正确，可以有一个最佳的解决方案。数学上保证的最佳图像配准可以对医学和几乎任何科学和工程领域产生相当大的影响。该项目的总体目标是获得与应用无关的最佳图像配准的显式表达式，这将避免局部极小值和初始化的问题。为实现这一目标，确定了以下具体目标。目的1：识别图像配准算子的性质，并定义最佳图像配准算子。目标2：确定可实现的最小图像配准误差（图像配准的基本极限）。目的3：推导出最佳图像配准算子的显式表达式。目标4：为了实现最佳图像配准方法，将其应用于不同模态的许多图像，并使用多项研究对其进行验证。

DESCRIPTION (provided by applicant): The process of aligning images so that the corresponding features are related is called image registration. Image registration is one of the main problems in medical image analysis and it has received considerable attention for more than two decades. The numerous proposed image registration methods have not been shown to be optimal by any measure and they suffer from a common problem: ad-hoc assumptions. Furthermore, typically they rely on the optimization of an objective function, which inherently suffers from the problem of local minima and requires initialization. For these reasons the image registration methods proposed in the literature work only under special conditions and any deviation from these conditions causes the methods to fail. However, image registration is a mathematical problem that, if defined properly, can have an optimal solution. Mathematically guaranteed optimal image registration could have a considerable impact on medicine and almost any science and engineering field. The overall objective of this project is to obtain an explicit expression for the application-independent optimal image registration, which would avoid the problem of local minima and initialization. To achieve this objective the following specific aims are set. Aim 1: To identify the properties of image registration operators and define the optimal image registration operator. Aim 2: To determine the minimal achievable image registration error (the fundamental limit of image registration). Aim 3: To derive an explicit expression for the optimal image registration operator. Aim 4: To implement the optimal image registration method, apply it to a number of images of different modalities, and validate it using several studies.