A General and Efficient Framework for Computational Shape Analysis Through Geometric Distributions

通过几何分布进行计算形状分析的通用且有效的框架

基本信息

批准号：
1819131
负责人：
Nicolas Charon
金额：
$ 21.5万
依托单位：
Johns Hopkins University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2020-10-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1819131&HistoricalAwards=false
关键词：
General Efficient Framework Computational Shape

项目摘要

The analysis of shapes and their variability has become an increasingly central problem in multiple areas of data science. In the field of computer vision, shape recognition and classification is often a crucial component of machine learning systems such as self-driving cars. In natural sciences, the recent development of computational anatomy, that is the automatic analysis of anatomical structures by numerical algorithms, provides a fruitful approach in understanding and diagnosing a wide range of pathologies and disorders. Along these different scientific questions, the amount and variety of available data has never ceased to grow. As a result, the concept of shape itself has considerably expanded and may refer to various types of geometric objects, which poses the important challenge of constructing and computing relevant similarity metrics between shapes across all these different modalities. The purpose of this research project is to develop an integrated mathematical model and associated numerical pipeline that allows for morphological analysis of geometric structures in a flexible and efficient way, and explore its possible applications to computational anatomy and computer vision. It will also include a substantial educational component with the training of a graduate student, support for presentations in conferences and workshops, and dissemination of an open-source code to the scientific community.The primal challenge of statistical shape analysis is the rather non-standard and disparate mathematical spaces in which objects belong, whether the shapes in question are raw images, manually or automatically extracted landmarks, curves, surfaces, vector fields or multi-modal objects. While the seminal model proposed by Grenander introduced the idea of comparing any two shapes through the estimation of an optimal deformation (measured by a metric on a certain diffeomorphism group), this model's generality falls short in many real applications where a certain amount of residual dissimilarity is necessary to account for other sources of variability (like noise). This project intends to fill this current gap by introducing a flexible approach to quantify shape similarity which relies on a unified embedding of shape spaces as generalized distributions, following the principles of geometric measure theory. Beyond the past success of these representations for curve and surface registration problems, the objective will be to demonstrate on a mathematical and computational level how it extends to a much wider class of geometric data structures and allows for cross-modality analysis, while pushing the scope of applications to other problems like clustering, classification and sparse representations on shapes. Fast numerical methods for this new framework is also an important aspect of the project, with the objective of making implementations scalable to the current dimensionality of datasets e.g. in medical imaging.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.

形状及其变异性的分析已成为数据科学多个领域中日益核心的问题。在计算机视觉领域，形状识别和分类通常是自动驾驶汽车等机器学习系统的重要组成部分。在自然科学中，计算解剖学的最新发展，即通过数值算法对解剖结构进行自动分析，为理解和诊断各种病理和疾病提供了一种富有成效的方法。沿着这些不同的科学问题，可用数据的数量和种类从未停止增长。因此，形状本身的概念已经大大扩展，并且可以指代各种类型的几何对象，这对跨所有这些不同模态构建和计算形状之间的相关相似性度量提出了重要挑战。该研究项目的目的是开发一个集成的数学模型和相关的数值管道，以灵活有效的方式对几何结构进行形态学分析，并探索其在计算解剖学和计算机视觉中的可能应用。它还将包括实质性的教育内容，包括培训研究生、支持会议和研讨会上的演讲以及向科学界传播开源代码。统计形状分析的主要挑战是相当不标准的数据分析。以及对象所属的不同数学空间，无论所讨论的形状是原始图像、手动或自动提取的地标、曲线、曲面、矢量场还是多模态对象。虽然 Grenander 提出的开创性模型引入了通过估计最佳变形（通过某个微分同胚组上的度量来测量）来比较任意两个形状的想法，但该模型的通用性在许多实际应用中存在一定程度的残余相异性。有必要考虑其他变异源（如噪声）。该项目旨在通过引入一种灵活的方法来量化形状相似性，该方法依赖于形状空间作为广义分布的统一嵌入，遵循几何测度理论的原理，来填补当前的空白。除了过去这些曲线和曲面配准问题的表示的成功之外，目标将是在数学和计算层面上演示它如何扩展到更广泛的几何数据结构类别并允许跨模态分析，同时扩大范围应用于其他问题，如聚类、分类和形状的稀疏表示。这个新框架的快速数值方法也是该项目的一个重要方面，其目标是使实现可扩展到数据集的当前维度，例如该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

期刊论文数量（6）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

An inexact matching approach for the comparison of plane curves with general elastic metrics

平面曲线与一般弹性度量比较的不精确匹配方法

DOI：
10.1109/ieeeconf44664.2019.9049031
发表时间：
2020
期刊：
and Computers
影响因子：
0
作者：
Sukurdeep, Yashil;Bauer, Martin;Charon, Nicolas
通讯作者：
Charon, Nicolas

Inexact Elastic Shape Matching in the Square Root Normal Field Framework

平方根法向场框架中的不精确弹性形状匹配

DOI：
10.1007/978-3-030-26980-7_2
发表时间：
2019
期刊：
International Conference on Geometric Science of Information
影响因子：
0
作者：
Bauer, Martin;Charon, Nicolas;Harms, Philipp
通讯作者：
Harms, Philipp

Diffeomorphic Registration of Discrete Geometric Distributions

DOI：
10.1142/9789811200137_0003
发表时间：
2018-01
期刊：
Lecture Notes Series, Institute for Mathematical Sciences, National University of Singapore
影响因子：
0
作者：
Hsi-Wei Hsieh;N. Charon
通讯作者：
Hsi-Wei Hsieh;N. Charon

A relaxed approach for curve matching with elastic metrics