Algorithmic Riemannian Geometry for a Statistical Analysis of Images

用于图像统计分析的算法黎曼几何

• 批准号: 0514743
• 负责人: Washington Mio
• 金额: $ 30.04万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2005
• 资助国家: 美国
• 起止时间: 2005-07-15 至 2009-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0514743&HistoricalAwards=false
• 关键词: Algorithmic; Riemannian; Geometry; Statistical; Analysis

ALGORITHMIC RIEMANNIAN GEOMETRY FOR A STATISTICALANALYSIS OF IMAGESAbstractThis project is concerned with the investigation of novel algorithmic representations of images and geometrical signal processing techniques for the automated analysis of image content. The investigators develop a new framework for an appearance-based analysis of imaged objects in terms of their shapes and textures using methods and tools derived from differential geometry and statistics. A statistical formulation is of the essence due to the large variability of shapes and textures frequently encountered in imagery of interest. The use of differential geometric methods in image processing is still incipient, but very promising, as solid evidence exists that such methodology is particularly well suited for the study of multidimensional, nonlinear features such as shapes and textures.In recent years, the investigators have developed a statistical shape analysis program; shapes are viewed as elements of a shape space whose geometry is exploited for shape analysis. The investigators treat textures in a similar manner by creating a Riemannian manifold of textures and integrate both representations into a single shape-texture model for the algorithmic analysis of image content. Images are decomposed into their spectral components and local spectral histograms are treated as elements of an infinite-dimensional statistical manifold equipped with a geometric structure induced by non-parametric Fisher information. Differential geometric constructs are utilized to develop algorithms for: (i) statistical inferences and learning of shape-texture features; (ii) Bayesian detection and recognition of objects using shape-texture priors; (iii) dimensionality reduction techniques for efficient processing.

图像统计分析的算法黎曼几何摘要这个项目关注的是研究图像的新算法表示和用于图像内容自动分析的几何信号处理技术。 研究人员开发了一个新的框架，用于使用微分几何和统计学中的方法和工具对成像对象的形状和纹理进行基于外观的分析。 由于感兴趣的图像中经常遇到的形状和纹理的变化很大，统计公式是至关重要的。 微分几何方法在图像处理中的应用尚处于起步阶段，但前景广阔，因为有确凿的证据表明，这种方法特别适合于研究多维非线性特征，如形状和纹理，近年来，研究人员已经开发出一种统计形状分析程序，形状被视为形状空间的元素，其几何形状被用于形状分析。 研究人员通过创建纹理的黎曼流形以类似的方式处理纹理，并将两种表示集成到单个形状纹理模型中，用于图像内容的算法分析。 图像被分解成它们的光谱分量和局部谱直方图被视为一个无限维的统计流形的元素配备了由非参数Fisher信息引起的几何结构。 微分几何构造用于开发以下算法：（i）形状纹理特征的统计推断和学习;（ii）使用形状纹理先验知识进行物体的贝叶斯检测和识别;（iii）用于高效处理的降维技术。