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成像数据中常规观察到的软器官形状的动态变形。我们的数学和计算方法可能会影响许多领域，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态的电影，例如在患者跳动心脏的实时超声心动图成像中。我们将通过计算变形形状之间的“弹性距离”和大量的“应变值”来评估组织的局部变形来量化形状变形。反过来，这些变形特性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。我们的工作的动机是越来越多的可用性的大型数据库的电影记录在3D的动态变形的“软”的形状，如人体器官。我们的目标是在任何一对记录类似生物医学形状的动态变形的电影之间生成量化的比较，例如心脏病患者的二尖瓣。我们将使用二尖瓣动态的实际超声心动图的一个大种子集来生成N = 1000个随机仿形3D表面变形的大集合。本着计算解剖学的精神，对于每一个这样的电影，我们将计算连续帧的时间依赖性同构配准，并提取相关的详细应变图。对于每对电影M1和M2，在时间配准之后，我们将在M1和M2的对应关键时间帧之间实现同构配准。这涉及到一个高维变分问题的数值求解创新的快速非线性最优控制。 从所有这些同构注册中，我们将提取每个电影的多个特征以及电影对之间的定量“相似性”。 在这个阶段，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，以产生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现高度并行化的计算方案。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值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.