RI: Small: Efficient Statistical Computing on Riemannian Manifolds with Applications to Medical Imaging and Computer Vision

RI：小型：黎曼流形的高效统计计算及其在医学成像和计算机视觉中的应用

基本信息

批准号：
1525431
负责人：
Baba Vemuri
金额：
$ 45.52万
依托单位：
University of Florida
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2015
资助国家：
美国
起止时间：
2015-09-01 至 2019-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1525431&HistoricalAwards=false
关键词：
RI Small Efficient Statistical Computing

项目摘要

This project develops efficient incremental algorithms are proposed for computing averages and other statistical quantities of interest from pools of data incrementally acquired. Many existing data acquisition and processing methods have reached a level of sophistication so as to be able to acquire and/or synthesize data that reside in curved spaces such as spheres, hyperboloids etc. As such data have become ubiquitous in many Science and Engineering fields, need for efficient statistical analysis of these data has emerged as an area of significant importance. Further, in this era of massive and continuous streaming data, samples of data are acquired sequentially over time. Hence, from an applications and computational efficiency perspective, the desired averaging algorithm ought to be amenable to incremental updates to accommodate the newly acquired data over time. The developed algorithms can be applied different applications, such as face recognition from videos, action recognition, trajectory averaging and clustering from videos, image and video restoration, pattern clustering and classification, etc. In the context of diagnostic medical imaging, methods developed in this project can be used to automatically discriminate between various disease classes, such as Parkinson's and Essential Tremor which are distinct types of movement disorders.This research investigates a general framework for recursive computation of the intrinsic mean and the principal geodesic analysis on several commonly encountered manifolds such as the manifold of symmetric positive definite matrices, the Grassmann, the Stiefel manifolds, the hypersphere, the manifold of special orthogonal matrices, and several others. The research team applies the developed recursive framework of computing statistics from manifold-valued data to several tasks namely, atlas computation from diffusion MRI in Medical Imaging, inter-class discrimination between sub-types of a neuro-degenerative disorder using diffusion MRI, face and action recognition, image and shape retrieval in Computer Vision applications.

该项目提出了有效的增量算法，以计算从逐步获取的数据池中计算平均值和其他统计量的兴趣数量。许多现有的数据采集和处理方法已经达到了一定程度的复杂水平，以便能够获取和/或合成位于诸如球体，倍或倍或工程领域的弯曲空间中的数据，这些数据在许多科学和工程领域都变得无处不在，需要对这些数据进行有效的统计分析，以使这些数据具有重要的重要性。此外，在这个大规模和连续流数据的时代，随着时间的流逝，数据样本被顺序获取。因此，从应用程序和计算效率的角度来看，所需的平均算法应适合增量更新，以适应新获得的数据。可以应用不同应用的开发算法，例如视频识别，动作识别，轨迹平均和聚类中的视频，图像和视频恢复，图案聚类和分类等。在诊断医学成像的背景下，在该项目中开发的方法可以自动研究各种疾病类型，例如，各种疾病的范围，这些疾病的类型是parkinson's extrants的类型，这些疾病是parkinson's extresss的类型，这些疾病是parkinson's tormers的类型范围。在几种常见的歧管上的固有平均值和主要的大地测量分析的递归计算中，例如对称阳性确定的矩阵的歧管，格拉斯曼，stiefel歧管，超孔，特殊正交矩阵的多种形式，以及其他几个。该研究团队应用了开发的计算统计数据递归框架，从流动价值数据到几个任务，即从医学成像中的扩散MRI进行的地图集计算，使用扩散MRI，面部和动作识别，图像识别，图像识别，图像识别，图像识别，图像识别，计算机视觉应用中的神经分层障碍的子类型之间的类别歧视。