Surface reconstructionAnimationSurface retouchingImage InpaintingMetamorphosisSurface blendingSketchingSmoothing


The result of the reconstruction by CSRBF from the 6719 points taken on the surface of the Venus model, processed in 45 sec.

If initially a set of N scattered data points in 3D are given and our goal is to reconstruct a surface based on this data. Using CSRBF we create a spline implicit function f(x,y,z)=0 (surface) or f(x,y,z)<=0 (volume).

There are two approaches to the reconstruction problem using RBF splines:

In practice, the problem of reconstruction with RBFs consists of the following steps: sorting the data, constructing the system of linear algebraic equations (SLAE), solving the SLAE, and evaluating the functions. In fact, while the solution of the system is the limiting step, constructing the matrix and evaluating the functions to extract the isosurface may also be computationally expensive.

We use CSRBF splines instead of RBF for both approaches which leads to a sparce matrix of size N+4*N+4 in SLAE. We have created a special algorithm based on octal tree subdivision of the intial space, which sorts initial data points in such a way that the resulting matrix is band-diagonal, which enables us to store it very compactly and solve it by using fast and easy direct solver. Later the octal tree is also used in the process of the surface extraction to accelerate the computation of the implicit function f(x,y,z).


Examples (sphere as a carrier function)

Examples (both-sides approach)

Demo software