Collaborative Proposal: A Geometric Method for Image Registration

提出了一种新的图像配准计算方法。配准是指将通过CT(计算机断层摄影)、MR(磁共振)、超声和其他技术获得的一对图像进行配准，以便可以进行定性和定量比较。对于从遥感到医学的各种应用，这是一个重要的问题。在医学上，成像技术和分析已经成为诊断以及外科和放射治疗计划的一种重要的非侵入性工具。尽管在这一研究领域取得了进展，但三维图像配准带来的挑战仍然是一个悬而未决的问题。开发了一种新的数学方法，在一组可以产生任何可微和可逆变换的微分方程的约束下，优化图像的任何选定的相似性度量。该项目的主要智力优点是它显著地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。新方法的主要特点有以下几个方面。对用于图像比较的相似性度量进行了直接优化。该方法对图像间的大变形具有标志性的匹配能力。该方法建立在坚实的数学理论基础上，特别地，可容许变换空间是所有可微和可逆变换的集合。该项目是利用美国国立卫生研究院开发的软件洞察工具包进行的；该软件为研究活动提供了极好的资源。本科生和研究生接受教育和培训，以便将强大的数学技术应用于医学和其他图像处理问题。新方法将影响计算科学的其他领域。结果将在会议上提出，并在科学期刊上发表，并通过面向科学家和普通民众的大众媒体发表。医生、生物医学工程师和数学家之间建立了新的合作伙伴关系，有助于为旨在改善我国公民健康的进一步研究创造良好的环境。

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.