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Robust Meshes from Multiple Range Maps: Slide 5 of 14.

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We wanted to implement this idea to see whether it could handle our
difficult data set. Since we had to implement it from scratch, we
wanted to make it as simple as possible.

Curless and Levoy combine the steps 3 and 4 of our first slide in their
method, they use weighted averaging to get accurate surfaces right
away. Since we had our mesh optimization algorithm that seemed to be
more resistant to low quality data, we decided to concentrate on
getting the topology of the initial mesh right. In particular, we only
wanted to use robust methods such as interval analysis and leave things
like fitting and averaging to a later stage. In interval analysis one
takes a conservative approach for determining function values. Instead
of trying to find out the actual value, one tries to obtain as narrow
bounds for them as possible.

Also, Curless and Levoy reported that their method in its current form
had difficulties in reconstructing thin surfaces, we kept that in mind
when thinking how we could improve on their method.

We also wanted to create a hierarchical algorithm. The advantages
include gains in speed and storage, and automatically concentrating
most of the effort close to the surface. Also it is not clear that you
know beforehand at what level of resolution you should process your
data. It seems natural to start at low resolution, and increase the
resolution (and therefore processing time) only if really needed.

Finally, we use the following assumptions. We assume that the input
data comes in the form of range maps. That is, each view, or data set,
is organized as a 2D grid of range values or 3D points. We can think of
this 2D grid lying on a conceptual image plane of the scanner. We
further assume that we know the calibration parameters of the scanner
so that we know how a given 3D point projects to its image plane. Or at
least we know the projection principle of the scanner, for example
whether it uses central or cylindrical projection, so that we can
approximate the parameters from the data. We finally assume that the
data sets have been already registered.