Re: how to extract an image from lissajous-scanned data
- From: "Dave Eberly" <dNOSPAMeberly@xxxxxxxxxxxxxxx>
- Date: Tue, 28 Jun 2005 03:53:23 GMT
"Eran Mukamel" <emukamel@xxxxxxxxxxxx> wrote in message
news:Pine.GSO.4.44.0506271712350.7811-100000@xxxxxxxxxxxxxxxxxxxxxxx
> I've recently tackled a seemingly simple problem of fitting some data to a
> surface, and am wondering if there are some industry standard algorithms
> or, better, some standard literature on the subject. My data are
> collected from a scanning microscope that traces out a 2D Lissajous
> pattern, returning (x,y) coordinates and image value (intensity) for each
> data point. I need to convert these data to an image, without needlessly
> sacrificing any resolution (e.g. by choosing a large bin size). My
> intuition is that I need to first fit a surface by interpolating the data
> (using some sort of Delaunay algorithm?) at the nodes of a square grid.
> Is this true?
Delaunay triangulation may be used to form a mesh on which you
resample, but the domain of interpolation is the convex hull of the
data points. If you need to resample to a rectangular grid for which
some of the grid points are outside the convex hull, you will need
to devise an extrapolation algorithm for those points. You also
need an interpolation scheme on the triangles. Linear is simplest,
but you might want smoother results. The Cendes-Wong algorithm
is one that produces a globally C1 interpolation for a triangle mesh
domain.
An alternative is to use thin plate splines. This circumvents the
problem with the hull domain, but resampling at grid points that
are far away from the data points might still produce results
that are not useful. From the point of view of simplicity, this
is the easiest approach to get a resampling on a grid.
> And how can I best take into account the method of scanning
> when processing the data? My current approach is to first fit a surface
> using a fine grid, then smooth the data by convolving with a 2D Gaussian.
> The smoothing seems to be necessary to reduce the noise in the data, but I
> suspect there must be a better approach that takes into account the
> trajectory of the scanning tip.
If your data has noise, convolving with a 2D Gaussian gives you
correlated noise. To take advantage of the scanning process, consider
your scanned data as a 1-dimensional signal in time. Median filtering
or generalized order statistic filters might help eliminate some of the
noisy data *before* you resample (and convolve).
--
Dave Eberly
http://www.geometrictools.com
.
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