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Non-rigid image registration (NIR) is an essential tool for morphologic comparisons in the presence of intra-and inter-individual anatomic variations. Many NIR methods have been developed, but are especially difficult to evaluate since point-wise inter-image correspondence is usually unknown, i.e., there is no " Gold Standard " to evaluate performance. The(More)
Given a metric <i>d</i> defined on a set <i>V</i> of points (a metric space), we define the ball B(<i>v, r</i>) centered at <i>u</i> &#8712; <i>V</i> and having radius <i>r</i> &#8805; 0 to be the set {<i>q</i> &#8712; <i>V/d(v, q)</i> &#8804;<i>r</i>}. In this work, we consider the problem of computing a minimum cost <i>k</i>-cover for a given set <i>P</i>(More)
The quality of an embedding Φ : V → R 2 of a graph G = (V, E) into the Euclidean plane is the ratio of max {u,v}∈E ||Φ(u) − Φ(v)||2 to min {u,v}} ∈E ||Φ(u) − Φ(v)||2. Given a graph G = (V, E), that is known to be a unit ball graph in fixed dimensional Euclidean space R d , we seek algorithms to compute an embedding Φ : V → R 2 of best (smallest) quality.(More)
Given an n-point metric (P , d) and an integer k > 0, we consider the problem of covering P by k balls so as to minimize the sum of the radii of the balls. We present a randomized algorithm that runs in n O(log n·log) time and returns with high probability the optimal solution. Here, is the ratio between the maximum and minimum interpoint distances in the(More)
We present a distributed topology control protocol that runs on a d-QUDG for d ≥ 1/ √ 2, and computes a sparse, constant-spanner, both in Euclidean distance and in hop distance. QUDGs (short for Quasi Unit Disk Graphs) generalize Unit Disk Graphs and permit more realistic modeling of wireless networks, allowing for imperfect and non-uniform transmission(More)
We consider the problem of partitioning the set of vertices of a given unit disk graph (UDG) into a minimum number of cliques. The problem is NP-hard and various constant factor approximations are known, with the current best ratio of 3. Our main result is a weakly robust polynomial time approximation scheme (PTAS) for UDGs expressed with edge-lengths that(More)
A data structure is stabilizing if, for any arbitrary (and possibly illegitimate) initial state, any sequence of sufficiently many operations brings the data structure to a legitimate state. A data structure is available if, for any arbitrary state, the effect of any operation on the structure is consistent with the operation's response. This paper presents(More)