Sharp Ridge Structures in Flow Visualization

脊线是一种被广泛研究的结构，在图像和形状分析以及科学可视化中有着广泛的应用。山脊有许多不同的定义，每一种定义都有其优缺点。事实上，对于每个脊线概念的数值提取算法都有活跃的研究。在流动可视化中，许多现代分析技术都是基于集成的，即通过在一定的有限积分时间内平流和集成信息来创建新的场。在可视化或图像处理中经常出现的脊线有一些根本的不同：它们往往非常尖锐，这使得传统的脊线提取器不适用于较大的积分时间。该项目试图对基于积分的脊线的锐度进行形式化分析，表明即使在考虑自适应网格细化的情况下，标准脊线提取工具的适用性也是有限的。为了克服这一问题，提出了一种新的提取尖锐脊线的方法，该方法基于对先前非尖锐脊线的跟踪。对于尖锐的脊线，将引入简化的提取算法以及新的体绘制方法。尖脊提取装置用于提取FTLE、FSLE、条纹线场和时间线场中的脊线，以及提取冲击波。

Ridges are well-studied structures with a variety of applications in image and shape analysis as well as in scientific visualization. There are many different definitions for ridges, each of them having its advantages and disadvantages. In fact, there is an active research on numerical extraction algorithms for each of the ridge concepts. In flow visualization, a number of modern analysis techniques are integration-based, i.e., new fields are created by advecting and integrating information over certain finite integration times. There are fundamental differences to ridges that usually occur in visualization or image processing: they tend to be extremely sharp, making conventional ridge extractors not applicable for larger integration times. The project attempts to give a formal analysis of the sharpness of integration-based ridges, showing that standard ridge extractors have a limited applicability even under consideration of adaptive mesh refinement. To overcome this, a new approach for the extraction of sharp ridges is proposed, which is based on a tracking of previously non-sharp ridges. For sharp ridges, simplified extraction algorithms as well as new volume rendering approaches will be introduced. Sharp ridge extractors are applied to extract ridges in FTLE, FSLE, streak line and time line fields as well as for extracting shock waves.