转自：https://stackoverflow.com/questions/838761/robust-algorithm-for-surface-reconstruction-from-3d-point-cloud

I am trying to figure out what algorithms there are to do surface reconstruction from 3D range data. At a first glance, it seems that the *Ball pivoting algorithm* (**BPA**) and *Poisson surface reconstruction* are the more established methods?

- What are the established, more robust algorithm in the field other than BPA and Poisson surface reconstruction algorithm?
- Recommended research publications?
- Is there available source code?

I have been facing this dilemma for some months now, and made exhaustive research.

# Algorithms

Mainly there are 2 categories of algorithms: computation geometry, and implicit surfaces.

## Computation Geometry

They fit the mesh on the existing points.

Probably the most famous algorithm of this group is powercrust, because it is theoretically well-established - it guarantees watertight mesh.

Ball Pivoting is patented by IBM. Also, it is not suitable for pointclouds with varying point density.

## Implicit functions

One fits implicit functions on the pointcloud, then uses a marching-cube-like algorithm to extract the zero-set of the function into a mesh.

Methods in this category differ mainly by the different implicit functions used.

Poisson, Hoppe's, and MPU are the most famous algorithms in this category. If you are new to the topic, i recommend to read Hoppe's thesis, it is very explanatory.

The algorithms of this category usually can be implemented so that they are able to process huge inputs very efficiently, and one can scale their quality<->speed trade-off. They are not disturbed by noise, varying point-density, holes. A disadvantage of them is that they require consistently oriented surface normals at the input points.

# Implementations

You will find small number of free implementations. However it depends on whether You are going to integrate it into free software (in this case GPL license is acceptable for You) or into a commercial software (in this case You need a more liberal license). The latter is very rare.

One is in VTK. I suspect it to be difficult to integrate (no documentation is available for free), it has a strange, over-complicated architecture, and is not designed for high-performance applications. Also has some limitations for the allowed input pointclouds.

Take a look at this Poisson implementation, and after that share your experience about it with me please.

Also: here are a few high-performance algorithms, with surface reconstruction among them.

CGAL is a famous 3d library, but it is free only for free projects.Meshlab is a famous application with GPL.

Also (Added August 2013):The library PCL has a module dedicated to surface reconstruction and is in active development (and is part of Google's Summer of Code). The surface module contains a number of different algorithms for reconstruction. PCL also has the ability to estimate surface normals, incase you do not have them provided with your point data, this functionality can be found in the features module. PCL is released under the terms of the BSD license and is open source software, it is free for commercial and research use.

If you want make some direct experiments with various surface reconstruction algorithms you should try **MeshLab**, the mesh-processing system, it is open source and it contains implementations of many of the previously cited surface reconstruction algorithms, like:

- Poisson Surface Recon
- a couple of MLS based approach,
- a ball pivoting implementation
- a variant of the Curless volume based approach
- Delaunay based techniques (Alpha shapes and Voronoi filtering)
- tools for computing normals from scattered point sets
- and many other tools for comparing/measuring/cleaning/simplifying the resulting meshes.

Sources are protected by GPL, so you could not use them in a commercial closed source project, but it is very important to get the right feeling about the properties of the various surface reconstruction algorithms (how sensitive to noise they are, the speed, the robustness to outliers, how they preserve fine details etc etc) before starting to implement one of them.

You might start looking at some recent work in the field - currently something like Fast low-memory streaming MLS reconstruction of point-sampled surfaces by Gianmauro Cuccuru, Enrico Gobbetti, Fabio Marton, Renato Pajarola, and Ruggero Pintus. Its citations can get you going through the literature pretty quickly.

As I had this problem too, I did develop and implement my own point cloud crust algorithm. The sources as well as the documentation can be found on github.com: https://github.com/ricebean-net/PointCloudCrust. The algorithm is implemented in Java.

Maybe, this can help you. You can find also a short python script on the page which illustrates how to use the library. Have fun!