In this paper, we introduce a surface reconstruction method that can perform gracefully with non-uniformly-distributed, noisy, and
even sparse data. We reconstruct the surface by estimating an implicit function and then obtain a triangle mesh by extracting an iso-surface from it. Our implicit function takes advantage of both the indicator function and
the signed distance function. It is dominated by the indicator function
at the regions away from the surface and approximates (up to scaling)
the signed distance function near the surface. On one hand,
it is well defined over the entire space so that the extracted iso-surface
must lie near the underlying true surface and is free of spurious sheets.
On the other hand, thanks to the nice properties of the signed distance
function, a smooth iso-surface can be extracted using the approach of
marching cubes with simple linear interpolations.
More importantly, our implicit function can be estimated directly from
an explicit integral formula without solving any linear system.
This direct approach leads to a simple, accurate and robust reconstruction method,
which can be paralleled with little overhead.
We call our reconstruction method Gauss surface reconstruction.
We apply our method to both synthetic and real-world scanned
data and demonstrate the accuracy, robustness and efficiency of
our method. The performance of Gauss surface reconstruction is also compared with that of
several state-of-the-art methods.