16,300 research outputs found
From tree matching to sparse graph alignment
In this paper we consider alignment of sparse graphs, for which we introduce
the Neighborhood Tree Matching Algorithm (NTMA). For correlated
Erd\H{o}s-R\'{e}nyi random graphs, we prove that the algorithm returns -- in
polynomial time -- a positive fraction of correctly matched vertices, and a
vanishing fraction of mismatches. This result holds with average degree of the
graphs in and correlation parameter that can be bounded away from 1,
conditions under which random graph alignment is particularly challenging. As a
byproduct of the analysis we introduce a matching metric between trees and
characterize it for several models of correlated random trees. These results
may be of independent interest, yielding for instance efficient tests for
determining whether two random trees are correlated or independent.Comment: 33 pages, 10 figures, accepted at COLT 2020. Typos corrected, some
new figures, some remarks and explanations detailed, minor changes in proof
of Th. 1.
From tree matching to sparse graph alignment
33 pages. Typos corrected, some new figures, some remarks and explanations detailed, minor changes in proof of Th. 1.2International audienceIn this paper we consider alignment of sparse graphs, for which we introduce the Neighborhood Tree Matching Algorithm (NTMA). For correlated Erd\H{o}s-R\'{e}nyi random graphs, we prove that the algorithm returns -- in polynomial time -- a positive fraction of correctly matched vertices, and a vanishing fraction of mismatches. This result holds with average degree of the graphs in and correlation parameter that can be bounded away from 1, conditions under which random graph alignment is particularly challenging. As a byproduct of the analysis we introduce a matching metric between trees and characterize it for several models of correlated random trees. These results may be of independent interest, yielding for instance efficient tests for determining whether two random trees are correlated or independent
Keyframe-based monocular SLAM: design, survey, and future directions
Extensive research in the field of monocular SLAM for the past fifteen years
has yielded workable systems that found their way into various applications in
robotics and augmented reality. Although filter-based monocular SLAM systems
were common at some time, the more efficient keyframe-based solutions are
becoming the de facto methodology for building a monocular SLAM system. The
objective of this paper is threefold: first, the paper serves as a guideline
for people seeking to design their own monocular SLAM according to specific
environmental constraints. Second, it presents a survey that covers the various
keyframe-based monocular SLAM systems in the literature, detailing the
components of their implementation, and critically assessing the specific
strategies made in each proposed solution. Third, the paper provides insight
into the direction of future research in this field, to address the major
limitations still facing monocular SLAM; namely, in the issues of illumination
changes, initialization, highly dynamic motion, poorly textured scenes,
repetitive textures, map maintenance, and failure recovery
Data-Driven Shape Analysis and Processing
Data-driven methods play an increasingly important role in discovering
geometric, structural, and semantic relationships between 3D shapes in
collections, and applying this analysis to support intelligent modeling,
editing, and visualization of geometric data. In contrast to traditional
approaches, a key feature of data-driven approaches is that they aggregate
information from a collection of shapes to improve the analysis and processing
of individual shapes. In addition, they are able to learn models that reason
about properties and relationships of shapes without relying on hard-coded
rules or explicitly programmed instructions. We provide an overview of the main
concepts and components of these techniques, and discuss their application to
shape classification, segmentation, matching, reconstruction, modeling and
exploration, as well as scene analysis and synthesis, through reviewing the
literature and relating the existing works with both qualitative and numerical
comparisons. We conclude our report with ideas that can inspire future research
in data-driven shape analysis and processing.Comment: 10 pages, 19 figure
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