Laplacian-Based Feature Preserving Mesh Simplification

We introduce a novel approach for feature preserving mesh simplification based on vertex Laplacians, specifically, the uniformly weighted Laplacian. Our approach is unique in three aspects: 1) a Laplacian based shape descriptor to quantize the local geometric feature sensitivity; 2) a Laplacian weighted cost function that is capable of providing different retaining rates of the geometric features; and 3) an optimal clustering technique which combines K-means and the Laplacian based shape descriptor to implement vertex classification. During simplification, the Laplacian based shape descriptors are firstly computed, and then a chosen error function to be optimized is penalized by our Laplacian weighted cost function, leading it to feature preserving. By applying the clustering technique, different simplification operators may be applied to different vertex groups for different purposes. Different error functions have been implemented to demonstrate the effectiveness, applicability and flexibility of the approach. Experiments conducted on various models including those of natural objects and CAD ones, show superior results.