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（计算机断层扫描）、MR（磁共振）、超声和其他技术获得的一对图像对齐，以便可以定性和定量地比较它们的任务。这是从遥感到医学等应用领域的一个重要问题。在医学中，成像技术和分析已成为诊断和手术及放射治疗计划的重要非侵入性工具。 尽管在这一领域的研究取得了进展，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，优化任何选择的图像相似性度量，受一组微分方程的约束，可以产生任何可微和可逆transformation. Main智力项目的优点是，它显着提高了我们的理解图像和形状，也图像配准技术的准确性和效率。新方法的主要特点如下：1.直接优化用于图像比较的相似性度量.该方法对图像间的大变形具有较强的特征点匹配能力.该方法是建立在坚实的数学理论;特别是，可容许的空间的转换是所有可微和可逆的转换的集合。4.该项目是利用美国国立卫生研究院开发的Insight Tool Kit软件进行的，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，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。研究结果将在会议上提出，并在科学期刊上发表，并通过大众媒体向科学家和一般民众公布。医生，生物医学工程师和数学家之间建立了新的伙伴关系，有助于为旨在改善我们公民健康的进一步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.