Surface denoising with directional fuzzy vector median filtering

This paper proposes a novel approach for smoothing surfaces represented by triangular meshes. The proposed method is a two-step procedure: surface normal smoothing through fuzzy vector median (FVM) filtering followed by vertex position update based on the least square error criteria. This paper applies the fuzzy ordering theory to the vector based data and introduces the fuzzy vector median. The application of FVM filters to surface normal smoothing yields improved results over previously introduced normal smoothing algorithms. The improved filtering results, coupled with LSE vertex position update, produces surface smoothing that minimizes the effects of noise while simultaneously preserving detail features. Simulation results are presented showing the performance of the proposed method and its advantages over commonly used surface smoothing algorithms. Additionally, optimization procedures for FVM are derived and evaluated.