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.

In this talk, I will present two deblurring methods, one exploits the spatial interactions in images, i.e. the self-similarity; and the other explicitly takes into account the sparse characteristics of natural images and does not entail solving a numerically ill-conditioned backward-diffusion.

In particular, the self-similarity is defined by a weight function, which induces two types of regularization in a nonlocal fashion. Furthermore, we get superior results using preprocessed data as input for the weighted functionals.

The second part of the talk is based on the observation that the sparse coefficients that encode a given image with respect to an over-complete basis are the same that encode a blurred version of the image with respect to a modified basis. An explicit generative model is used to compute a sparse representation of the blurred image, and the coefficients of which are used to combine elements of the original basis to yield a restored image.

In this talk we will discuss various aniosotropic PDEs. We will then discuss integro-differential
equations inspired from (BV, L2) and (BV, L1) decompositions. Although the original motivation came from a variational approach, the resulting IDEs can be extended using standard techniques from PDE-based image processing. We use filtering, edge preserving and tangential smoothing to yield a family of modified IDE models with
applications to image denoising and image deblurring problems.