CHS: Small: Novel Method for Vectorization of Arbitrary Natural Images and Its Applications

CHS：Small：任意自然图像矢量化的新方法及其应用

• 批准号: 1715985
• 负责人: Hong Qin
• 金额: $ 50万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2021-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1715985&HistoricalAwards=false
• 关键词: CHS; Small; Novel; Method; Vectorization

Vector graphics offers a compact and lossless image representation with advantages such as geometric editability, resolution independence, significant saving in storage and in network bandwidth, image display at drastically varying resolutions, and ease of animation. This research aims to significantly advance the traditional boundary of image vectorization based on partial differential equations (PDEs) and their intrinsic connection with Green's functions and harmonic B-splines (serving as fundamental solutions for PDEs), which has not yet been explored for vector graphics, image modeling, image data fitting, and analysis. If successful, project outcomes will include a novel vector image modeling methodology and its application for image vectorization and authoring as well as solid texture and animation. At the core of this project's theoretical foundation are PDEs and their meshless closed-form solvers based on fundamental solutions. The novel representation is expected to outperform the conventional diffusion curve based and gradient mesh based representations. The new modeling scheme will be capable in theory of expressing arbitrary images with arbitrary discontinuities. Consequently, this research will advance the state of the art in both the theory and practice of vector graphics. Beyond the conventional frontier of visual computing, since this research is solely built upon PDEs and their fundamental solutions, it is anticipated that other disciplines such as applied mathematics, the physical sciences, mechanical engineering, and the earth/space sciences will directly benefit from project outcomes.This project will explore a novel image vectorization modeling scheme: Poisson Vector graphics (PVG), which computes complex color gradients via a sparse set of geometric primitives and color constraints. Detailed research activities include: (1) articulation of a sound theoretic foundation for PVG with non-zero Laplacians, the methodology to be founded upon PDEs and their meshless closed-form solvers by taking advantage of Green's functions serving as their fundamental solutions; (2) derivation of a closed-form solution for Poisson equations based on the intrinsic connection between Green's function and harmonic B-splines; (3) development of a method for vectorization of arbitrary natural images by PVG based on numerical optimization, so that they can be represented with high precision; (4) design of an authoring tool for PVG with new Poisson curve and Poisson region metaphors, so that users will be able to design vector images with much more flexibility than conventional first or second order diffusion curves; and (5) demonstration that the novel PVG is applicable to animation. Comprehensive qualitative and quantitative comparison with the current state-of-the-art will be carried out to showcase the new framework's superiority. Ultimately, this project's integrated approach combines the merits of diffusion curve and gradient mesh, which is capable of drastically expanding the applied scope of vector graphics to visual information modeling, analysis, and processing, where numerical measurements are prevalent.

向量图形提供了一个紧凑而无损的图像表示形式，其优点，例如几何编辑性，分辨率独立性，存储和网络带宽的大量节省，图像在巨大变化的分辨率上显示以及动画的易用性。 这项研究的目的是根据偏微分方程（PDE）及其与Green的功能和谐波B-Splines（用作PDE的基本解决方案）的固有联系，以显着提高图像矢量化的传统边界，尚未探索用于矢量图形，图像模型，图像数据拟合和分析的矢量图形图形。 如果成功，项目成果将包括一种新颖的矢量图像建模方法及其在图像矢量化和创作以及固体纹理和动画中的应用。 该项目理论基础的核心是PDE及其基于基本解决方案的无网封闭式求解器。 预期新型表示将胜过基于常规扩散曲线和基于梯度网格的表示。 新的建模方案将在理论上能够以任意不连续性表达任意图像。 因此，这项研究将在矢量图形的理论和实践中推进最新的现状。 Beyond the conventional frontier of visual computing, since this research is solely built upon PDEs and their fundamental solutions, it is anticipated that other disciplines such as applied mathematics, the physical sciences, mechanical engineering, and the earth/space sciences will directly benefit from project outcomes.This project will explore a novel image vectorization modeling scheme: Poisson Vector graphics (PVG), which computes complex color gradients via a sparse set of几何原语和颜色约束。 详细的研究活动包括：（1）通过非零的laplacians阐明PVG的合理理论基础，该方法是通过利用Green用作其基本解决方案的Green功能来建立在PDE及其无网状的封闭式求解器的方法； （2）基于Green功能与谐波B-Splines之间固有连接的泊松方程的封闭形式解决方案的推导； （3）开发基于数值优化的PVG对矢量化矢量化的方法，以便可以高精度地表示它们； （4）设计具有新的泊松曲线和泊松区域的PVG的创作工具，以便用户能够比传统的第一阶或二阶扩散曲线更灵活地设计矢量图像； （5）演示新颖的PVG适用于动画。 将进行全面的定性和定量比较与当前的最新技术，以展示新框架的优势。 最终，该项目的集成方法结合了扩散曲线和梯度网格的优点，该方法能够将矢量图形的应用范围大幅扩展到视觉信息建模，分析和处理，其中数值测量很普遍。

项目成果

Multi-Label Visual Feature Learning with Attentional Aggregation

• DOI: 10.1109/wacv45572.2020.9093311
• 发表时间: 2020-03
• 期刊: 2020 IEEE Winter Conference on Applications of Computer Vision (WACV)
• 作者: Ziqiao Guan;K. Yager;Dantong Yu;Hong Qin

Accelerating Liquid Simulation With an Improved Data‐Driven Method

• DOI: 10.1111/cgf.14010
• 发表时间: 2020-05
• 期刊: Computer Graphics Forum
• 影响因子: 2.5
• 作者: Yang Gao;Quancheng Zhang;Shuai Li;A. Hao;Hong Qin

Structure Correction for Robust Volume Segmentation in Presence of Tumors

• DOI: 10.1109/jbhi.2020.3004296
• 发表时间: 2021-04-01
• 期刊: IEEE JOURNAL OF BIOMEDICAL AND HEALTH INFORMATICS
• 影响因子: 7.7
• 作者: Sahu, Pranjal;Zhao, Yiyuan;Qin, Hong
• 通讯作者: Qin, Hong

Using Virtual Digital Breast Tomosynthesis for De-Noising of Low-Dose Projection Images

• DOI: 10.1109/isbi.2019.8759408
• 发表时间: 2019-04
• 期刊: 2019 IEEE 16th International Symposium on Biomedical Imaging (ISBI 2019)
• 作者: Pranjal Sahu;Hailiang Huang;Wei Zhao;Hong Qin

In-Operando Tracking and Prediction of Transition in Material System using LSTM

使用 LSTM 对材料系统中的转变进行操作中跟踪和预测

• DOI: 10.1145/3217197.3217204
• 发表时间: 2018
• 期刊: AI-Science'18: Proceedings of the 1st International Workshop on Autonomous Infrastructure for Science
• 作者: Sahu, Pranjal;Yu, Dantong;Yager, Kevin;Dasari, Mallesham;Qin, Hong
• 通讯作者: Qin, Hong