Numerical methods for geometric partial differential equations: applications to freeform deformations in animation and nonrigid medical image registration
几何偏微分方程的数值方法:在动画和非刚性医学图像配准中自由变形的应用
基本信息
- 批准号:312489-2011
- 负责人:
- 金额:$ 1.89万
- 依托单位:
- 依托单位国家:加拿大
- 项目类别:Discovery Grants Program - Individual
- 财政年份:2015
- 资助国家:加拿大
- 起止时间:2015-01-01 至 2016-12-31
- 项目状态:已结题
- 来源:
- 关键词:
项目摘要
Shapes may be described by using the familiar geometric notions of length, area, volume, angle and curvature. Changing shapes may be described by Geometric Partial Differential Equations: stretching or bending, smoothing rough edges, or mapping one onto another.
The proposed research will build new tools for manipulating three dimensional shapes. To do this, we need to be able to numerically solve the equations which describe the transformations. This task is made difficult by the complexity of the equations and the large amounts of data. To date, simplified equations have been used which neglect some geometric detail. My research has found new representations of these equations which have overcome some of these difficulties. This work will allow for geometric detail to be preserved in shape manipulation.
The proposal will allow for better geometric fidelity in three dimensional tools used in the following important applications:
Freeform deformations in computer animation allow the artist to move an animated image by manipulating a simpler skeleton or cage. The geometric equations extrapolate the motion to the shape while preserving fine features. This saves considerable time and effort in animation.
Nonrigid image registration tools are used to compare images of organs taken at successive times. For example, after a surgeon removes a tumour from a patient's brain, three dimensional images are taken of the brain immediately after surgery and at later times. In order to determine if the growth has stopped, the images are compared by mapping (warping) the later images onto the first one.
可使用长度、面积、体积、角度和曲率等熟悉的几何概念来描述曲率。 改变形状可以用几何偏微分方程来描述:拉伸或弯曲,平滑粗糙的边缘,或将一个映射到另一个。
拟议的研究将建立新的工具来操纵三维形状。 要做到这一点,我们需要能够数值求解描述变换的方程。 由于方程的复杂性和大量的数据,这项任务变得困难。 到目前为止,已经使用简化的方程,忽略了一些几何细节。 我的研究发现了这些方程的新表示,克服了其中的一些困难。 这项工作将允许几何细节被保存在形状操作。
该提案将允许在以下重要应用中使用的三维工具中实现更好的几何保真度:
计算机动画中的自由变形允许艺术家通过操纵更简单的骨架或笼子来移动动画图像。几何方程将运动外推到形状,同时保留精细特征。 这节省了大量的时间和精力在动画。
非刚性图像配准工具用于比较连续时间拍摄的器官图像。 例如,在外科医生从患者的大脑中移除肿瘤之后,立即在手术之后以及在稍后的时间拍摄大脑的三维图像。 为了确定生长是否已经停止,通过将后面的图像映射(扭曲)到第一个图像上来比较图像。
项目成果
期刊论文数量(0)
专著数量(0)
科研奖励数量(0)
会议论文数量(0)
专利数量(0)
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Oberman, Adam其他文献
Deep relaxation: partial differential equations for optimizing deep neural networks
- DOI:
10.1007/s40687-018-0148-y - 发表时间:
2018-06-28 - 期刊:
- 影响因子:1.2
- 作者:
Chaudhari, Pratik;Oberman, Adam;Carlier, Guillaume - 通讯作者:
Carlier, Guillaume
ANISOTROPIC TOTAL VARIATION REGULARIZED L1 APPROXIMATION AND DENOISING/DEBLURRING OF 2D BAR CODES
- DOI:
10.3934/ipi.2011.5.591 - 发表时间:
2011-08-01 - 期刊:
- 影响因子:1.3
- 作者:
Choksi, Rustum;van Gennip, Yves;Oberman, Adam - 通讯作者:
Oberman, Adam
NUMERICAL METHODS FOR MATCHING FOR TEAMS AND WASSERSTEIN BARYCENTERS
- DOI:
10.1051/m2an/2015033 - 发表时间:
2015-11-01 - 期刊:
- 影响因子:0
- 作者:
Carlier, Guillaume;Oberman, Adam;Oudet, Edouard - 通讯作者:
Oudet, Edouard
A REGULARIZATION INTERPRETATION OF THE PROXIMAL POINT METHOD FOR WEAKLY CONVEX FUNCTIONS
- DOI:
10.3934/jdg.2020005 - 发表时间:
2020-01-01 - 期刊:
- 影响因子:0.9
- 作者:
Hoheisel, Tim;Laborde, Maxime;Oberman, Adam - 通讯作者:
Oberman, Adam
Oberman, Adam的其他文献
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{{ truncateString('Oberman, Adam', 18)}}的其他基金
Principled approaches to deep learning: generalization under distribution shift and predictive uncertainty
深度学习的原则方法:分布变化和预测不确定性下的泛化
- 批准号:
RGPIN-2022-03609 - 财政年份:2022
- 资助金额:
$ 1.89万 - 项目类别:
Discovery Grants Program - Individual
Numerical Methods for Nonlinear Partial Differential Equations, with applications to Optimal Transportation, and Geometric Data Reduction
非线性偏微分方程的数值方法,及其在最优运输和几何数据简化中的应用
- 批准号:
RGPIN-2016-03922 - 财政年份:2021
- 资助金额:
$ 1.89万 - 项目类别:
Discovery Grants Program - Individual
Numerical Methods for Nonlinear Partial Differential Equations, with applications to Optimal Transportation, and Geometric Data Reduction
非线性偏微分方程的数值方法,及其在最优运输和几何数据简化中的应用
- 批准号:
RGPIN-2016-03922 - 财政年份:2020
- 资助金额:
$ 1.89万 - 项目类别:
Discovery Grants Program - Individual
Numerical Methods for Nonlinear Partial Differential Equations, with applications to Optimal Transportation, and Geometric Data Reduction
非线性偏微分方程的数值方法,及其在最优运输和几何数据简化中的应用
- 批准号:
RGPIN-2016-03922 - 财政年份:2019
- 资助金额:
$ 1.89万 - 项目类别:
Discovery Grants Program - Individual
Numerical Methods for Nonlinear Partial Differential Equations, with applications to Optimal Transportation, and Geometric Data Reduction
非线性偏微分方程的数值方法,及其在最优运输和几何数据简化中的应用
- 批准号:
RGPIN-2016-03922 - 财政年份:2018
- 资助金额:
$ 1.89万 - 项目类别:
Discovery Grants Program - Individual
Numerical Methods for Nonlinear Partial Differential Equations, with applications to Optimal Transportation, and Geometric Data Reduction
非线性偏微分方程的数值方法,及其在最优运输和几何数据简化中的应用
- 批准号:
RGPIN-2016-03922 - 财政年份:2017
- 资助金额:
$ 1.89万 - 项目类别:
Discovery Grants Program - Individual
Numerical Methods for Nonlinear Partial Differential Equations, with applications to Optimal Transportation, and Geometric Data Reduction
非线性偏微分方程的数值方法,及其在最优运输和几何数据简化中的应用
- 批准号:
RGPIN-2016-03922 - 财政年份:2016
- 资助金额:
$ 1.89万 - 项目类别:
Discovery Grants Program - Individual
High Dimensional Data Reduction using approximate Convex Hulls
使用近似凸包进行高维数据缩减
- 批准号:
486596-2015 - 财政年份:2015
- 资助金额:
$ 1.89万 - 项目类别:
Engage Grants Program
Numerical methods for geometric partial differential equations: applications to freeform deformations in animation and nonrigid medical image registration
几何偏微分方程的数值方法:在动画和非刚性医学图像配准中自由变形的应用
- 批准号:
312489-2011 - 财政年份:2014
- 资助金额:
$ 1.89万 - 项目类别:
Discovery Grants Program - Individual
Numerical methods for fully nonlinear and degenerate elliptic partial differential equations
全非线性和简并椭圆偏微分方程的数值方法
- 批准号:
411943-2011 - 财政年份:2013
- 资助金额:
$ 1.89万 - 项目类别:
Discovery Grants Program - Accelerator Supplements
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- 资助金额:28.0 万元
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