Visualization of Principal Curvature Directions by Anisotropic Diffusion

Anisotropic diffusion is known to be a powerful tool in image processing. It enables the smoothing of initially noisy images while still retaining, respectively sharpening edges and enhancing features. Here recent results in the context of vector field visualization are expanded to non Euclidean domains. The aim is to graphically represent vector field data on two dimensional surfaces in an intuitively understandable way. Furthermore the multiscale properties of the approach support a scale of resolutions, ranging from detailed flow representation to a coarse overview of field data. Here an initial noisy image intensity is smoothed along integral lines, whereas the image is mainly sharpened in the orthogonal direction. The method is based on a continuous model and requires the solution of a parabolic PDE problem on manifolds. It is discretized by finite elements on surface triangulations only in the final implementational step. Applications are shown for principal directions of curvature on general surfaces.