Approximation & smoothing surface data with RBFs
It is not always desirable to exactly interpolate surface data when the
data are contaminated with noise. A smooth approximation is often more appropriate.
FastRBFTM offers two complimentary approaches. The first is to smooth an RBF which has been fitted exactly to the data by applying a low pass filter during surface evaluation. The alternative approach avoids an exact fit (interpolating the data) alltogether. Instead the data are approximated during fitting. Two methods, spline smoothing and error-bar fitting, are offered in this latter case.
Smoothing or approximating the data is also desirable when the data contain excessive detail or the RBF is being sub-sampled, in which case filtering reduces aliasing artefacts.
The methods
FastRBFTM offers are not equivalent, though in some cases they appear to produce similar results, as in the following example.
Low pass filtering is applied during evaluation and so can be continuously varied or even `undone'. It is most suitable when sub-sampling an RBF. The approximating methods apply during fitting and therefore require good estimates of the noise or maximum desired level of detail since higher detail in the data will be lost in the resulting RBF. The RBF will, however, generally be more compact since less high frequency information is repesented.
A more detailed discussion can be found in the
RBF smoothing and approximation FAQ.
The following images are cropped from a
LIDAR scan of a statute. The full scan can be seen in the
spline smoothing LIDAR example. The images illustrate the different smoothing and approximation techniques described above.
 |
|
Exact fit |
