PhD Thesis Proposal Defence


"Curve and Surface Reconstruction from Noisy Samples"

By Mr. Sheung Hung Poon


Abstract:

Practical sample point sets, like two-dimensional images obtained by
scanning, three-dimensional medical data, and three-dimensional scanned
data points obtained by three-dimensional scanners, could be noisy. In
computer graphics, a lot of reconstruction algorithms has already been
developed. However, one common drawback is that they do not have
theoretical guarantees even when the input samples are very dense.  This
motivates computational geometers to propose algorithms that guarantee
faithful reconstruction.

There are known algorithms that produce faithful reconstructions of curves
and surfaces from noiseless sample points.  However, there is no
theoretical result for reconstruction from noisy sample points.  We obtain
the first curve reconstruction algorithm from noisy samples guaranteeing
that the output is correct with probability approaching 1 as the sampling
density increases.  The noise model we assumed is that the samples are
obtained by first drawing points on the curves according to a locally
uniform distribution followed by a uniform perturbation in the normal
directions.

We propose to generalize this approach to do faithful surface
reconstruction from noisy samples.


Date:     		Thursday, 18 September 2003

Time:                   1:00p.m.-3:00p.m.

Venue:                  Room 2404
			lifts 17-18

Committee Members:      Dr. Siu Wing Cheng (Supervisor)
                        Dr. Mordecai Golin (Chairman)
			Dr. Sunil Arya
			Dr. Chi Keung Tang


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