Joint weighted least squares for normal decomposition of 3D measurement surface

3D optical and laser measurement devices can obtain the digital representation of physical objects by boundary surface meshes. Such a representation, however, has no semantic information to describe the object's basic shape and its geometric details individually. Meanwhile, existing mesh filters, which process surface normals as signals defined on the Gauss sphere, mainly deal with noise corrupted by measurement and computational errors. While useful in that they preserve geometric structures, they are not intended for filtering out geometric details whose scales are much larger than that of noise. We assume that a 3D surface contains three geometric properties, i.e. geometric detail, structural pattern, and smooth-varying shape, and consider normals as surface signals defined over both the input mesh and the underlying surface of this mesh. We propose a joint weighted least squares (JWLS) to solve the challenging problem of how to filter out the detailed appearance (geometric details) and preserve intrinsic geometric properties (structural patterns) of any measurement surface simultaneously. Specifically, we first suppress high-contrast detail normals, and then detect salient feature normals to produce a feature-guided normal field, and finally jointly fit the original shape. We have shown that a variety of geometric processing tasks benefit from our JWLS, e.g. detail-preserving bas-relief modeling, detail-free mesh smoothing, and detail-enhancing Laplacian coating.