Automated Reconstruction of Curvilinear Networks from 2D and 3D Imagery
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Suppose that the vertices of a graph G are colored with two colors in an unknown way. The color that occurs on more than half of the vertices is called the majority color (if it exists), and any vertex of this color is called a majority vertex. We study th ...
Curvilinear networks are prevalent in nature and span many different scales, ranging from micron-scale neural structures in the brain to petameter-scale dark-matter arbors binding massive galaxy clusters. Reliably reconstructing them in an automated fashio ...
State-of-the-art data analysis tools have to deal with high-dimensional data. Fortunately, the inherent dimensionality of data is often much smaller, as it has an internal structure limiting its degrees of freedom. In most cases, this structure can be appr ...
Real-life acquisition systems are fundamentally limited in their ability to reproduce point sources. For example, a point source object, a star say, observed with an optical telescope is blurred by the imperfect lenses composing the system. Mathematically, ...
Biomedical image segmentation is an active field of research where deformable models have proved to be efficient. The geometric representation of such models determines their ability to approximate the shape of interest as well as the speed of convergence ...
We consider the variation of Ramsey numbers introduced by Erdos and Pach [J. Graph Theory, 7 (1983), pp. 137-147], where instead of seeking complete or independent sets we only seek a t-homogeneous set, a vertex subset that induces a subgraph of minimum de ...
This master thesis provides in-depth explanations of how deep learning and graph theory can be used together to perform pointwise classification in 3D point clouds obtained by combinations of geospatial images. That scene understanding problem arises in a ...
We consider the problem of reliably connecting an arbitrarily large set of computers (nodes) with communication channels. Reliability means here the ability, for any two nodes, to remain connected (i.e., their ability to communicate) with probability at le ...
Airborne Laser Scanning is a well-known remote sensing technology, which provides a dense and highly accurate, yet unorganized point cloud of earth surface. During the last decade, extracting information from the data generated by airborne LiDAR systems ha ...
Graph signals offer a very generic and natural representation for data that lives on networks or irregular structures. The actual data structure is however often unknown a priori but can sometimes be estimated from the knowledge of the application domain. ...