Scale-Space Tracking of Critical Points in 3D Vector Fields

Scale-space techniques are very popular in image processing since they allow for the integrated analysis of image structure. The multi-scale approach enables one to distinguish between important features such as edges and small-scale features such as numerical artifacts or noise. In general, the same properties hold for vector fields such as flow data. Many flow features, e.g. vortices, can be observed on multiple scales of the data and also many features that can be detected are essentially artifacts of the employed interpolation scheme or originate from noise in the data. In this paper, we investigate an approach based on scale-space hierarchies of threedimensional vector fields. Our main interest concerns how vector field singularities can be tracked over multiple spatial scales in order to assess the importance of a critical point to the overall behavior of the underlying flow field.

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