3,604 research outputs found
Subset Warping: Rubber Sheeting with Cuts
Image warping, often referred to as "rubber sheeting" represents the deformation of a domain image space into a range image space. In this paper, a technique is described which extends the definition of a rubber-sheet transformation to allow a polygonal region to be warped into one or more subsets of itself, where the subsets may be multiply connected. To do this, it constructs a set of "slits" in the domain image, which correspond to discontinuities in the range image, using a technique based on generalized Voronoi diagrams. The concept of medial axis is extended to describe inner and outer medial contours of a polygon. Polygonal regions are decomposed into annular subregions, and path homotopies are introduced to describe the annular subregions. These constructions motivate the definition of a ladder, which guides the construction of grid point pairs necessary to effect the warp itself
The Morse theory of \v{C}ech and Delaunay complexes
Given a finite set of points in and a radius parameter, we
study the \v{C}ech, Delaunay-\v{C}ech, Delaunay (or Alpha), and Wrap complexes
in the light of generalized discrete Morse theory. Establishing the \v{C}ech
and Delaunay complexes as sublevel sets of generalized discrete Morse
functions, we prove that the four complexes are simple-homotopy equivalent by a
sequence of simplicial collapses, which are explicitly described by a single
discrete gradient field.Comment: 21 pages, 2 figures, improved expositio
A Distributed Model Predictive Control Framework for Road-Following Formation Control of Car-like Vehicles (Extended Version)
This work presents a novel framework for the formation control of multiple
autonomous ground vehicles in an on-road environment. Unique challenges of this
problem lie in 1) the design of collision avoidance strategies with obstacles
and with other vehicles in a highly structured environment, 2) dynamic
reconfiguration of the formation to handle different task specifications. In
this paper, we design a local MPC-based tracking controller for each individual
vehicle to follow a reference trajectory while satisfying various constraints
(kinematics and dynamics, collision avoidance, \textit{etc.}). The reference
trajectory of a vehicle is computed from its leader's trajectory, based on a
pre-defined formation tree. We use logic rules to organize the collision
avoidance behaviors of member vehicles. Moreover, we propose a methodology to
safely reconfigure the formation on-the-fly. The proposed framework has been
validated using high-fidelity simulations.Comment: Extended version of the conference paper submission on ICARCV'1
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