## 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.