13,506 research outputs found
An ILP Solver for Multi-label MRFs with Connectivity Constraints
Integer Linear Programming (ILP) formulations of Markov random fields (MRFs)
models with global connectivity priors were investigated previously in computer
vision, e.g., \cite{globalinter,globalconn}. In these works, only Linear
Programing (LP) relaxations \cite{globalinter,globalconn} or simplified
versions \cite{graphcutbase} of the problem were solved. This paper
investigates the ILP of multi-label MRF with exact connectivity priors via a
branch-and-cut method, which provably finds globally optimal solutions. The
method enforces connectivity priors iteratively by a cutting plane method, and
provides feasible solutions with a guarantee on sub-optimality even if we
terminate it earlier. The proposed ILP can be applied as a post-processing
method on top of any existing multi-label segmentation approach. As it provides
globally optimal solution, it can be used off-line to generate ground-truth
labeling, which serves as quality check for any fast on-line algorithm.
Furthermore, it can be used to generate ground-truth proposals for weakly
supervised segmentation. We demonstrate the power and usefulness of our model
by several experiments on the BSDS500 and PASCAL image dataset, as well as on
medical images with trained probability maps.Comment: 19 page
Dynamic and Multi-functional Labeling Schemes
We investigate labeling schemes supporting adjacency, ancestry, sibling, and
connectivity queries in forests. In the course of more than 20 years, the
existence of labeling schemes supporting each of these
functions was proven, with the most recent being ancestry [Fraigniaud and
Korman, STOC '10]. Several multi-functional labeling schemes also enjoy lower
or upper bounds of or
respectively. Notably an upper bound of for
adjacency+siblings and a lower bound of for each of the
functions siblings, ancestry, and connectivity [Alstrup et al., SODA '03]. We
improve the constants hidden in the -notation. In particular we show a lower bound for connectivity+ancestry and
connectivity+siblings, as well as an upper bound of for connectivity+adjacency+siblings by altering existing
methods.
In the context of dynamic labeling schemes it is known that ancestry requires
bits [Cohen, et al. PODS '02]. In contrast, we show upper and lower
bounds on the label size for adjacency, siblings, and connectivity of
bits, and to support all three functions. There exist efficient
adjacency labeling schemes for planar, bounded treewidth, bounded arboricity
and interval graphs. In a dynamic setting, we show a lower bound of
for each of those families.Comment: 17 pages, 5 figure
A simple and optimal ancestry labeling scheme for trees
We present a ancestry labeling scheme for trees. The
problem was first presented by Kannan et al. [STOC 88'] along with a simple solution. Motivated by applications to XML files, the label size was
improved incrementally over the course of more than 20 years by a series of
papers. The last, due to Fraigniaud and Korman [STOC 10'], presented an
asymptotically optimal labeling scheme using
non-trivial tree-decomposition techniques. By providing a framework
generalizing interval based labeling schemes, we obtain a simple, yet
asymptotically optimal solution to the problem. Furthermore, our labeling
scheme is attained by a small modification of the original solution.Comment: 12 pages, 1 figure. To appear at ICALP'1
Elastic Registration of Geodesic Vascular Graphs
Vascular graphs can embed a number of high-level features, from morphological
parameters, to functional biomarkers, and represent an invaluable tool for
longitudinal and cross-sectional clinical inference. This, however, is only
feasible when graphs are co-registered together, allowing coherent multiple
comparisons. The robust registration of vascular topologies stands therefore as
key enabling technology for group-wise analyses. In this work, we present an
end-to-end vascular graph registration approach, that aligns networks with
non-linear geometries and topological deformations, by introducing a novel
overconnected geodesic vascular graph formulation, and without enforcing any
anatomical prior constraint. The 3D elastic graph registration is then
performed with state-of-the-art graph matching methods used in computer vision.
Promising results of vascular matching are found using graphs from synthetic
and real angiographies. Observations and future designs are discussed towards
potential clinical applications
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