Anisotropic diffusion in vector field visualization on Euclidean domains and surfaces

Vector field visualization is an important topic in scientific visualization. Its aim is to graphically represent field data on two and three-dimensional domains and on surfaces in an intuitively understandable way. Here, a new approach based on anisotropic nonlinear diffusion is introduced. It enables an easy perception of vector field data and serves as an appropriate scale space method for the visualization of complicated flow pattern. The approach is closely related to nonlinear diffusion methods in image analysis where images are smoothed while still retaining and enhancing edges. Here, an initial noisy image intensity is smoothed along integral lines, whereas the image is sharpened in the orthogonal direction. The method is based on a continuous model and requires the solution of a parabolic PDE problem. It is discretized only in the final implementational step. Therefore, many important qualitative aspects can already be discussed on a continuous level. Applications are shown for flow fields in 2D and 3D, as well as for principal directions of curvature on general triangulated surfaces. Furthermore, the provisions for flow segmentation are outlined.