718 research outputs found
Partial-Matching and Hausdorff RMS Distance Under Translation: Combinatorics and Algorithms
We consider the RMS distance (sum of squared distances between pairs of
points) under translation between two point sets in the plane, in two different
setups. In the partial-matching setup, each point in the smaller set is matched
to a distinct point in the bigger set. Although the problem is not known to be
polynomial, we establish several structural properties of the underlying
subdivision of the plane and derive improved bounds on its complexity. These
results lead to the best known algorithm for finding a translation for which
the partial-matching RMS distance between the point sets is minimized. In
addition, we show how to compute a local minimum of the partial-matching RMS
distance under translation, in polynomial time. In the Hausdorff setup, each
point is paired to its nearest neighbor in the other set. We develop algorithms
for finding a local minimum of the Hausdorff RMS distance in nearly linear time
on the line, and in nearly quadratic time in the plane. These improve
substantially the worst-case behavior of the popular ICP heuristics for solving
this problem.Comment: 31 pages, 6 figure
Computing Similarity between a Pair of Trajectories
With recent advances in sensing and tracking technology, trajectory data is
becoming increasingly pervasive and analysis of trajectory data is becoming
exceedingly important. A fundamental problem in analyzing trajectory data is
that of identifying common patterns between pairs or among groups of
trajectories. In this paper, we consider the problem of identifying similar
portions between a pair of trajectories, each observed as a sequence of points
sampled from it.
We present new measures of trajectory similarity --- both local and global
--- between a pair of trajectories to distinguish between similar and
dissimilar portions. Our model is robust under noise and outliers, it does not
make any assumptions on the sampling rates on either trajectory, and it works
even if they are partially observed. Additionally, the model also yields a
scalar similarity score which can be used to rank multiple pairs of
trajectories according to similarity, e.g. in clustering applications. We also
present efficient algorithms for computing the similarity under our measures;
the worst-case running time is quadratic in the number of sample points.
Finally, we present an extensive experimental study evaluating the
effectiveness of our approach on real datasets, comparing with it with earlier
approaches, and illustrating many issues that arise in trajectory data. Our
experiments show that our approach is highly accurate in distinguishing similar
and dissimilar portions as compared to earlier methods even with sparse
sampling
Video Registration in Egocentric Vision under Day and Night Illumination Changes
With the spread of wearable devices and head mounted cameras, a wide range of
application requiring precise user localization is now possible. In this paper
we propose to treat the problem of obtaining the user position with respect to
a known environment as a video registration problem. Video registration, i.e.
the task of aligning an input video sequence to a pre-built 3D model, relies on
a matching process of local keypoints extracted on the query sequence to a 3D
point cloud. The overall registration performance is strictly tied to the
actual quality of this 2D-3D matching, and can degrade if environmental
conditions such as steep changes in lighting like the ones between day and
night occur. To effectively register an egocentric video sequence under these
conditions, we propose to tackle the source of the problem: the matching
process. To overcome the shortcomings of standard matching techniques, we
introduce a novel embedding space that allows us to obtain robust matches by
jointly taking into account local descriptors, their spatial arrangement and
their temporal robustness. The proposal is evaluated using unconstrained
egocentric video sequences both in terms of matching quality and resulting
registration performance using different 3D models of historical landmarks. The
results show that the proposed method can outperform state of the art
registration algorithms, in particular when dealing with the challenges of
night and day sequences
Partial-Matching RMS Distance Under Translation: Combinatorics and Algorithms
We consider the problem of minimizing the RMS distance (sum of squared distances between pairs of points) under translation between two point sets A and B, in the plane, with (Formula presented.), in the partial-matching setup, in which each point in B is matched to a distinct point in A. Although the problem is not known to be polynomial, we establish several structural properties of the underlying subdivision (Formula presented.) of the plane and derive improved bounds on its complexity. Specifically, we show that this complexity is (Formula presented.), so it is only quadratic in |A|. These results lead to the best known algorithm for finding a translation for which the partial-matching RMS distance between the point sets is minimized. In addition, we show how to compute a local minimum of the partial-matching RMS distance under translation, in polynomial time. © 2017 Springer Science+Business Media New Yor
Revealing divergent evolution, identifying circular permutations and detecting active-sites by protein structure comparison
BACKGROUND: Protein structure comparison is one of the most important problems in computational biology and plays a key role in protein structure prediction, fold family classification, motif finding, phylogenetic tree reconstruction and protein docking. RESULTS: We propose a novel method to compare the protein structures in an accurate and efficient manner. Such a method can be used to not only reveal divergent evolution, but also identify circular permutations and further detect active-sites. Specifically, we define the structure alignment as a multi-objective optimization problem, i.e., maximizing the number of aligned atoms and minimizing their root mean square distance. By controlling a single distance-related parameter, theoretically we can obtain a variety of optimal alignments corresponding to different optimal matching patterns, i.e., from a large matching portion to a small matching portion. The number of variables in our algorithm increases with the number of atoms of protein pairs in almost a linear manner. In addition to solid theoretical background, numerical experiments demonstrated significant improvement of our approach over the existing methods in terms of quality and efficiency. In particular, we show that divergent evolution, circular permutations and active-sites (or structural motifs) can be identified by our method. The software SAMO is available upon request from the authors, or from and . CONCLUSION: A novel formulation is proposed to accurately align protein structures in the framework of multi-objective optimization, based on a sequence order-independent strategy. A fast and accurate algorithm based on the bipartite matching algorithm is developed by exploiting the special features. Convergence of computation is shown in experiments and is also theoretically proven
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