465 research outputs found
TVL<sub>1</sub> Planarity Regularization for 3D Shape Approximation
The modern emergence of automation in many industries has given impetus to extensive research into mobile robotics. Novel perception technologies now enable cars to drive autonomously, tractors to till a field automatically and underwater robots to construct pipelines. An essential requirement to facilitate both perception and autonomous navigation is the analysis of the 3D environment using sensors like laser scanners or stereo cameras. 3D sensors generate a very large number of 3D data points when sampling object shapes within an environment, but crucially do not provide any intrinsic information about the environment which the robots operate within.
This work focuses on the fundamental task of 3D shape reconstruction and modelling from 3D point clouds. The novelty lies in the representation of surfaces by algebraic functions having limited support, which enables the extraction of smooth consistent implicit shapes from noisy samples with a heterogeneous density. The minimization of total variation of second differential degree makes it possible to enforce planar surfaces which often occur in man-made environments. Applying the new technique means that less accurate, low-cost 3D sensors can be employed without sacrificing the 3D shape reconstruction accuracy
Planar Ultrametric Rounding for Image Segmentation
We study the problem of hierarchical clustering on planar graphs. We
formulate this in terms of an LP relaxation of ultrametric rounding. To solve
this LP efficiently we introduce a dual cutting plane scheme that uses minimum
cost perfect matching as a subroutine in order to efficiently explore the space
of planar partitions. We apply our algorithm to the problem of hierarchical
image segmentation
New Approaches to Classic Graph-Embedding Problems - Orthogonal Drawings & Constrained Planarity
Drawings of graphs are often used to represent a given data set in a human-readable way. In this thesis, we consider different classic algorithmic problems that arise when automatically generating graph drawings. More specifically, we solve some open problems in the context of orthogonal drawings and advance the current state of research on the problems clustered planarity and simultaneous planarity
Short Plane Supports for Spatial Hypergraphs
A graph is a support of a hypergraph if every hyperedge
induces a connected subgraph in . Supports are used for certain types of
hypergraph visualizations. In this paper we consider visualizing spatial
hypergraphs, where each vertex has a fixed location in the plane. This is the
case, e.g., when modeling set systems of geospatial locations as hypergraphs.
By applying established aesthetic quality criteria we are interested in finding
supports that yield plane straight-line drawings with minimum total edge length
on the input point set . We first show, from a theoretical point of view,
that the problem is NP-hard already under rather mild conditions as well as a
negative approximability results. Therefore, the main focus of the paper lies
on practical heuristic algorithms as well as an exact, ILP-based approach for
computing short plane supports. We report results from computational
experiments that investigate the effect of requiring planarity and acyclicity
on the resulting support length. Further, we evaluate the performance and
trade-offs between solution quality and speed of several heuristics relative to
each other and compared to optimal solutions.Comment: Appears in the Proceedings of the 26th International Symposium on
Graph Drawing and Network Visualization (GD 2018
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