Hermite variational implicit surface reconstruction

Abstract

We propose a new technique for reconstructing surfaces from a large set of unorganized 3D data points and their associated normal vectors. The surface is represented as the zero level set of an implicit volume model which fits the data points and normal constraints. Compared with variational implicit surfaces, we make use of surface normal vectors at data points directly in the implicit model and avoid of introducing manufactured off-surface points. Given n surface point/normal pairs, the proposed method only needs to solve an n×n positive definite linear system. It allows fitting large datasets effectively and robustly. We demonstrate the performance of the proposed method with both globally supported and compactly supported radial basis functions on several datasets. implicit surfaces, radial basis functions, regularized regression, variational implicit surface

Hermite Radial Basis Functions Implicits

“…[WSC06], we were able to enhance the flexibility of both schemes by ensuring well posedness of an interesting combined interpolation/regularization approach. Similar insights come up by comparing our derivations and results with those from a recent variationally deduced approach [PMW09], allowing a better understanding of the method in that work.…”

“…On the theoretical side, HRBF implicits framework unifies recently introduced surface reconstruction methods based on RBF which incorporate normals directly in their problem formulation (see [PMW09, WSC06]).…”

“…The offset requirement was avoided in posterior works deduced from a statistical‐learning perspective [PMW09, WSC06], where normals were directly used in the variational problem. Pan et al .…”

“…Pan et al . [PMW09] incorporate normals directly in their regularized variational problem, where the reasoning is to consider the alignment of the gradient of the surface with the normals at the sample points. This amounts to solving an linear system for N point/normal pairs.…”

“…HRBF implicits compute desirable reconstructions even in the presence of very non‐uniform data distributions. Systematic comparisons with previous methods [PMW09, CBC*01] suggest its effectiveness.…”