Data Mining for Large Data Sets of Shapes Deformations

该项目旨在重建和量化临床医生或研究人员在医学影像数据中经常观察到的软组织形状的动态变形。我们的数学和计算方法可以潜在地影响许多领域，从计算机辅助医疗诊断到计算机视觉中的自动形状识别，以及生物医学图像序列的自动聚类、分类和快速检索。我们将研究记录三维生物医学形状动力学的电影，例如在患者心脏跳动的实时超声心动图成像中。我们将通过计算可变形形状之间的“弹性距离”和评估组织局部变形的大量“应变值”来量化形状变形。反过来，这些变形特征使得能够使用人工神经网络对可变形形状进行自动分类和聚类。我们的工作是受到越来越多的大型电影数据库的推动，这些数据库以3D的形式记录了像人体器官这样的“软”形状的动态变形。我们的目标是在任何一对记录相似生物医学形状的动态变形的电影之间产生量化的比较，例如心脏病患者的二尖瓣。我们将使用二尖瓣动力学的实际回声心动图的一个大种子集来生成N=1000个随机微分同胚3D表面变形的大集合。在计算解剖学的精神下，对于每一部这样的电影，我们将计算连续帧的依赖于时间的微分同胚配准，并提取相关的详细应变图。对于每一对电影M1和M2，经过时间登记后，我们将在相应的关键时间帧M1和M2之间实现微分同胚登记。这涉及到通过创新的快速非线性最优控制来数值求解高维变分问题。从所有这些微分同胚的配准中，我们将提取每一部电影的多个特征以及电影对之间的定量“相似性”。在这一阶段，强大的数据挖掘技术，如支持向量机和人工神经网络，将成为可实现的多尺度聚类以及形状变形的分类。为了应对繁重的计算挑战，我们将在远程高功率计算资源上实施高度并行的计算方案。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

This project aims to reconstruct and quantify the dynamic deformations of soft organ shapes which are routinely observed by clinicians or researchers in medical imaging data. Our mathematical and computational approaches can potentially impact many domains, ranging from computer aided medical diagnosis, to automatic shape recognition in computer vision, as well as automated clustering, classification, and fast retrieval of biomedical image sequences. We will study movies recording dynamics of three dimensional biomedical shapes, for instance in live echo-cardiographic imaging of patients beating hearts. We will quantify shape distortions by computing "elastic distances" between deformable shapes and by large numbers of "strain values" evaluating local deformation of tissues. In turn these deformations characteristics enable the use of artificial neural networks for automatic classification and clustering of deformable shapes. Our work is motivated by the increasing availability of large databases of movies recording in 3D the dynamic deformations of "soft" shapes, such as human organs. We aim to generate quantified comparison between any pairs of movies recording the dynamic deformations of similar biomedical shapes, such as the mitral valves of cardiology patients. We will use one large seed set of actual echo-cardiographies of mitral valves dynamics to generate a large set of N = 1000 random diffeomorphic 3D surfaces deformations. In the spirit of computational anatomy, for each such movie, we will compute a time dependent diffeomorphic registration of successive frames, and extract an associated detailed strain map. For each pair of movies M1 and M2, after time registration, we will implement diffeomorphic registrations between corresponding key time frames of M1 and M2. This involves the numerical solving of a high dimensional variational calculus problems by innovative fast non-linear optimal control. From all these diffeomorphic registrations, we will extract multiple characteristics of each movie as well as quantitative "similarities" between pairs of movies. At this stage, powerful data mining techniques such as support vector machines and artificial neural networks will become implementable to generate multi-scale clustering as well as classification of shapes deformations. To handle the heavy computing challenges, we will implement highly parallelized computational schemes on remote high power computing resources.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.