Structure-guided shape-preserving mesh texture smoothing via joint low-rank matrix recovery

Mesh texture smoothing (MTS) seeks to smooth out the detailed appearances in noise-free surfaces, while preserving the intrinsic geometric properties. However, the intricacy of mesh texture patterns commonly results in side-effects, including remnant textures, improperly-smoothed structures and distorted shapes. We propose a new joint low-rank matrix recovery (J-LRMR) model to the problem of MTS with the properties of texture smoothing, structure preservation, and shape fitting. J-LRMR benefits from our three key observations: (1) local surface patches sharing approximate geometric properties always exist within an original surface (OS); (2) the OS comprises three geometric properties, i.e., details, structures, and the smooth-varying shape, where the structures construct the step-edge surface (SS), but more importantly the later two components contribute to forming the underlying surface (US); (3) the US normals can be defined as signals over both the OS and SS. By exploring the three observations, we first collect similar patches together by the local iterative closest point technique on the OS, and concurrently optimize the OS to produce the SS by ℓ₀ normal minimization. Second, we pack the normals on the similar patches of both the OS and SS into the patch-group matrix (PGM) for rank analysis. The rank of sub-PGM from the OS is high due to suffering from details (textures), while the rank of sub-PGM from the SS is low but does not have a smooth shape. Third, we formulate a structure-guided shape-preserving optimization framework by non-local low-rank matrix recovery to produce the normals of US containing both the structures and the smooth-varying shape. Finally, we update the vertex positions of OS to fit the recovered normals of US by Poisson reconstruction. We have verified our method on a variety of surfaces with abundant details, and compared it with several state-of-the-art methods. Both visual and quantitative comparisons show that our method can better remove mesh textures with a minimal disturbance of the underlying surface.