30 research outputs found
Information Recovery from Pairwise Measurements
A variety of information processing tasks in practice involve recovering
objects from single-shot graph-based measurements, particularly those taken
over the edges of some measurement graph . This paper concerns the
situation where each object takes value over a group of different values,
and where one is interested to recover all these values based on observations
of certain pairwise relations over . The imperfection of
measurements presents two major challenges for information recovery: 1)
: a (dominant) portion of measurements are
corrupted; 2) : a significant fraction of pairs are
unobservable, i.e. can be highly sparse.
Under a natural random outlier model, we characterize the , that is, the critical threshold of non-corruption rate
below which exact information recovery is infeasible. This accommodates a very
general class of pairwise relations. For various homogeneous random graph
models (e.g. Erdos Renyi random graphs, random geometric graphs, small world
graphs), the minimax recovery rate depends almost exclusively on the edge
sparsity of the measurement graph irrespective of other graphical
metrics. This fundamental limit decays with the group size at a square root
rate before entering a connectivity-limited regime. Under the Erdos Renyi
random graph, a tractable combinatorial algorithm is proposed to approach the
limit for large (), while order-optimal recovery is
enabled by semidefinite programs in the small regime.
The extended (and most updated) version of this work can be found at
(http://arxiv.org/abs/1504.01369).Comment: This version is no longer updated -- please find the latest version
at (arXiv:1504.01369
A Solution for Multi-Alignment by Transformation Synchronisation
The alignment of a set of objects by means of transformations plays an
important role in computer vision. Whilst the case for only two objects can be
solved globally, when multiple objects are considered usually iterative methods
are used. In practice the iterative methods perform well if the relative
transformations between any pair of objects are free of noise. However, if only
noisy relative transformations are available (e.g. due to missing data or wrong
correspondences) the iterative methods may fail.
Based on the observation that the underlying noise-free transformations can
be retrieved from the null space of a matrix that can directly be obtained from
pairwise alignments, this paper presents a novel method for the synchronisation
of pairwise transformations such that they are transitively consistent.
Simulations demonstrate that for noisy transformations, a large proportion of
missing data and even for wrong correspondence assignments the method delivers
encouraging results.Comment: Accepted for CVPR 2015 (please cite CVPR version
Multi-Image Semantic Matching by Mining Consistent Features
This work proposes a multi-image matching method to estimate semantic
correspondences across multiple images. In contrast to the previous methods
that optimize all pairwise correspondences, the proposed method identifies and
matches only a sparse set of reliable features in the image collection. In this
way, the proposed method is able to prune nonrepeatable features and also
highly scalable to handle thousands of images. We additionally propose a
low-rank constraint to ensure the geometric consistency of feature
correspondences over the whole image collection. Besides the competitive
performance on multi-graph matching and semantic flow benchmarks, we also
demonstrate the applicability of the proposed method for reconstructing
object-class models and discovering object-class landmarks from images without
using any annotation.Comment: CVPR 201
Fast multi-image matching via density-based clustering
We consider the problem of finding consistent matches
across multiple images. Previous state-of-the-art solutions
use constraints on cycles of matches together with convex
optimization, leading to computationally intensive iterative
algorithms. In this paper, we propose a clustering-based
formulation. We first rigorously show its equivalence with
the previous one, and then propose QuickMatch, a novel
algorithm that identifies multi-image matches from a density
function in feature space. We use the density to order the
points in a tree, and then extract the matches by breaking this
tree using feature distances and measures of distinctiveness.
Our algorithm outperforms previous state-of-the-art methods
(such as MatchALS) in accuracy, and it is significantly faster
(up to 62 times faster on some bechmarks), and can scale to
large datasets (with more than twenty thousands features).Accepted manuscriptSupporting documentatio
Higher-order Projected Power Iterations for Scalable Multi-Matching
The matching of multiple objects (e.g. shapes or images) is a fundamental
problem in vision and graphics. In order to robustly handle ambiguities, noise
and repetitive patterns in challenging real-world settings, it is essential to
take geometric consistency between points into account. Computationally, the
multi-matching problem is difficult. It can be phrased as simultaneously
solving multiple (NP-hard) quadratic assignment problems (QAPs) that are
coupled via cycle-consistency constraints. The main limitations of existing
multi-matching methods are that they either ignore geometric consistency and
thus have limited robustness, or they are restricted to small-scale problems
due to their (relatively) high computational cost. We address these
shortcomings by introducing a Higher-order Projected Power Iteration method,
which is (i) efficient and scales to tens of thousands of points, (ii)
straightforward to implement, (iii) able to incorporate geometric consistency,
(iv) guarantees cycle-consistent multi-matchings, and (iv) comes with
theoretical convergence guarantees. Experimentally we show that our approach is
superior to existing methods
Joint Cuts and Matching of Partitions in One Graph
As two fundamental problems, graph cuts and graph matching have been
investigated over decades, resulting in vast literature in these two topics
respectively. However the way of jointly applying and solving graph cuts and
matching receives few attention. In this paper, we first formalize the problem
of simultaneously cutting a graph into two partitions i.e. graph cuts and
establishing their correspondence i.e. graph matching. Then we develop an
optimization algorithm by updating matching and cutting alternatively, provided
with theoretical analysis. The efficacy of our algorithm is verified on both
synthetic dataset and real-world images containing similar regions or
structures
Robust Motion Segmentation from Pairwise Matches
In this paper we address a classification problem that has not been
considered before, namely motion segmentation given pairwise matches only. Our
contribution to this unexplored task is a novel formulation of motion
segmentation as a two-step process. First, motion segmentation is performed on
image pairs independently. Secondly, we combine independent pairwise
segmentation results in a robust way into the final globally consistent
segmentation. Our approach is inspired by the success of averaging methods. We
demonstrate in simulated as well as in real experiments that our method is very
effective in reducing the errors in the pairwise motion segmentation and can
cope with large number of mismatches