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The properties of the human visual system are taken into account, along with the geometric aspects of an object, in a new surface remeshing algorithm and a new mesh simplification algorithm. Both algorithms have a preprocessing step and are followed by the remeshing or mesh simplification steps. The preprocessing step computes an importance map that indicates the visual masking potential of the visual patterns on the surface. The importance map is then used to guide the remeshing or mesh simplification algorithms. Two different methods are proposed for computing an importance map that indicates the masking potential of the visual patterns on the surface. The first one is based on the Sarnoff visual discrimination metric, and the second one is inspired by the visual masking tool available in the current JPEG2000 standard. Given an importance map, the surface remeshing algorithm automatically distributes few samples to surface regions with strong visual masking properties due to surface texturing, lighting variations, bump mapping, surface reflectance and inter-reflections. Similarly, the mesh simplification algorithm simplifies more aggressively where the light field of an object can hide more geometric artifacts.