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

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逼近方案，例如楔形图案，从而使楔形图案逼近的速度提高到103量级。除了速度之外，我们实现的一个吸引人的新特征是，这些算法提供了从粗略到精细的整个尺度的即时访问，允许开发使用近似尺度中固有的多尺度信息的新一代算法。提出的项目有两个目标：一是进一步发展和扩展我们的技术，包括更多不同的局部逼近模型和几何。其结果将是依赖于图像域的几何划分和局部回归的组合的近似方案。该项目致力于几何图像特征的自适应近似的这种算法的规范和数学分析。第二个目标是多尺度算法的开发和数学分析，这些算法利用瞬时访问全尺度的最小化。作为这些方法的可能应用，我们提到图像处理问题，例如面向特征的去噪、压缩、模式识别或内插/重采样问题。还将讨论如何应用于处理生物医学数据和图像的实际问题。

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.