Collaborative Proposal: A Geometric Method for Image Registration

提出了一种新的图像配准计算方法。配准是指对通过CT（计算机断层扫描）、MR（磁共振）、超声波等技术获得的一对图像进行对齐，以便对它们进行定性和定量比较的任务。这是从遥感到医学等各种应用的一个重要问题。在医学上，成像技术和分析已经成为一种重要的、非侵入性的诊断工具，用于外科和放射治疗计划。尽管这一领域的研究取得了进展，但三维图像配准所带来的挑战仍然是一个悬而未决的问题。一种新的数学方法被开发，优化任何选择的图像的相似性度量，受制于一组微分方程的约束，可以产生任何可微和可逆的变换。该项目的主要智力优点是它大大提高了我们对图像和形状的理解，以及图像配准技术的准确性和效率。新方法的主要特点如下。用于比较图像的相似度量直接优化。该方法对图像之间的大变形具有标记匹配能力。该方法建立在坚实的数学理论基础上；特别地，变换的可容许空间是所有可微可逆变换的集合。该项目使用国家卫生研究院开发的软件Insight Tool Kit进行；该软件为研究活动提供了极好的资源。拟议活动的更广泛影响如下：本科和研究生接受的教育和训练是将强大的数学技术应用于医学和其他图像处理问题。这种新方法将影响计算科学的其他领域。研究结果将在会议上提出，并在科学杂志上发表，并通过面向科学家和一般大众的大众传播媒介发表。医生、生物医学工程师和数学家之间建立了新的伙伴关系，有助于为进一步开展旨在改善我国公民健康的研究创造有利的环境。

A new computational method for image registration is formulated. Registration refers to the task of aligning a pair of images obtained by CT (computed tomography), MR (magnetic resonance), ultra-sound, and other techniques, so that they can be compared both qualitatively and quantitatively. This is an important problem with applications ranging from remote sensing to medicine. In medicine, imaging techniques and analysis have become an important, non-invasive tool for diagnosis and for surgical and radiation treatment planning. Despite advances in this area of research, the challenges posed by registration for three-dimensional images remains an open problem. A new mathematical approach is developed that optimizes any chosen similarity measure of the images, subject to the constraint of a set of differential equations that can generate any differentiable and invertible transformation.The main intellectual merit of the project is that it significantly enhances our understanding of imagery and shapes and also the accuracy and efficiency of image registration techniques. The main features of the new method are as follows.1. Similarity measures used to compare images are directly optimized.2. The method has a landmark matching capacity for large deformations between images.3. The method is founded on solid mathematical theory; in particular, the admissible space of transformations is the set of all differentiable and invertible transformations.4. The project is carried out with the use of the software Insight Tool Kit developed by the National Institutes of Health; that software provides an excellent resource for the research activity.The broader impacts of the proposed activity are as follows.1. Undergraduate and graduate students are educated and trained to apply powerful mathematical techniques to medical and other image processing problems.2. The new method will impact other areas of the computational sciences. Results are to be presented at conferences and published in scientific journals and through the mass media directed at scientists and the general population as well.3. New partnerships between medical doctors, biomedical engineers, and mathematicians are established, helping create a favorable environment for further research aimed at improving the health of our citizens.