Abstract:
In this talk we will present our recent work on 3D LIDAR point clouds
compression. The new algorithm is based on the idea of compression by
classification. It utilizes the unique height function simplicity as well
as the local spatial coherence and linearity of the aerial LIDAR data and
can automatically compress the data to the desired level-of-details
defined by the user. The random sample consensus (RANSAC) and principal
component analysis (PCA) algorithms are employed for robust and efficient
local fitting and approximation. Moreover, supervised machine learning
techniques such as support vector machine (SVM) is used to automatically
detect regions that are not locally linear such as vegetations or trees.
In those regions, the local statistics descriptions such as mean,
variance, expectation, etc are stored to efficiently represent the region
and restore the geometry in the decompression phase. The new algorithm has
been tested in several aerial LIDAR datasets with very good results. If
time permits I will also discuss our recent work in virtual navigation of
the interior spaces of urban structures, rock geo-mechanics analysis for
highway safety, etc.

Let $C$ be a curve over a local field whose reduction is totally
degenerate. We discuss the related problems of 1) determining the
group structure of the torsion subgroup of the Jacobian of $C$, and 2)
determining if a given line bundle on $C$ is divisible by a given
integer $r$. Under certain hypotheses on the reduction of $C$, we
exhibit explicit algorithms for answering these two questions.