Effiziente Modellierung geometrischer Strukturen in digitalen Bildern Entwurf und Analyse neuer Algorithmen

数字图像中几何结构的有效建模新算法的设计和分析。

• 批准号: 18448685
• 负责人: Professor Dr. Hartmut Führ
• 金额: --
• 依托单位: Lehrstuhl A für Mathematik (Analysis und Zahlentheorie)
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2006
• 资助国家: 德国
• 起止时间: 2005-12-31 至 2008-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/18448685?language=en
• 关键词: Effiziente; Modellierung; geometrischer; Strukturen; digitalen

The Institute of Biomathematics and Biometry has recently developed new fast algorithms for the rapid computation of geometry-based adaptive image approximation schemes such as wedgelets, resulting in a speedup for wedgelet approximation of the order 103. Besides speed, an attractive new feature of our implementation is the fact that the algorithms provide instantaneous access to a whole scale of such approximations, from coarse to fine, allowing the development of a new generation of algorithms that use the multiscale information inherent in the scale of approximations. The proposed project has two aims: One is the further development and extension of our techniques to include more diverse local approximation models and geometries. The result will be approximation schemes that rely on a combination of geometric partitioning of the image domain and local regression. The project addresses the specification and mathematical analysis of such algorithms for the adaptive approximation of geometrical image features. The second aim is the development and mathematical analysis of multiscale algorithms that exploit the instantaneous access to the full scale of minimizers. As possible application of these methods we mention image-processing problems such as feature-oriented denoising, compression, pattern recognition or interpolation/resampling problems. Applications to real-life problems dealing with biomedical data and images will also be addressed.

生物数学和生物统计学研究所最近开发了新的快速算法，用于快速计算基于几何的自适应图像近似方案，如楔形波，导致楔形波近似的阶数为103。除了速度，一个有吸引力的新功能，我们的实施是这样一个事实，即算法提供了瞬时访问整个规模的这种近似，从粗到细，允许开发新一代的算法，使用固有的多尺度信息的规模近似。拟议的项目有两个目标：一是进一步开发和扩展我们的技术，以包括更多样化的局部逼近模型和几何形状。结果将是依赖于图像域的几何分区和局部回归的组合的近似方案。该项目的地址规格和数学分析的这种算法的几何图像特征的自适应近似。第二个目标是开发和数学分析的多尺度算法，利用瞬时访问满量程的极小。作为这些方法的可能应用，我们提到图像处理问题，如面向特征的去噪，压缩，模式识别或插值/恢复问题。还将讨论处理生物医学数据和图像的实际问题的应用。