GeoFilter: Geometric Selection of Mesh Filter Parameters

When designing a lowpass filter to eliminate noise in a triangle mesh, the cutoff frequency is typically chosen by a cumbersome trial-and-error process. Therefore, it is important to provide a guideline in selecting filter frequencies. Here, we explore the relation between the frequencies in a mesh filter and the geometric measures of user-selected features. In addition, by combining previously proposed implicit and explicit formulations, we develop a second order filter that can act as lowpass, bandpass, highpass, notch, and band exaggeration/reduction filters. The proposed GeoFilter framework allows the user to choose the frequencies for that filter based on the physical size of a blob (ellipsoid) automatically fit to a user-selected feature in the mesh. For example, the size of a bump in a noisy pattern can be used as a cutoff frequency in a lowpass filter, while the size of a nose may be used to smoothen a face or to exaggerate its features as in a caricature.