1,913 research outputs found
Approximate Nearest Neighbor Fields in Video
We introduce RIANN (Ring Intersection Approximate Nearest Neighbor search),
an algorithm for matching patches of a video to a set of reference patches in
real-time. For each query, RIANN finds potential matches by intersecting rings
around key points in appearance space. Its search complexity is reversely
correlated to the amount of temporal change, making it a good fit for videos,
where typically most patches change slowly with time. Experiments show that
RIANN is up to two orders of magnitude faster than previous ANN methods, and is
the only solution that operates in real-time. We further demonstrate how RIANN
can be used for real-time video processing and provide examples for a range of
real-time video applications, including colorization, denoising, and several
artistic effects.Comment: A CVPR 2015 oral pape
On computational tools for Bayesian data analysis
While Robert and Rousseau (2010) addressed the foundational aspects of
Bayesian analysis, the current chapter details its practical aspects through a
review of the computational methods available for approximating Bayesian
procedures. Recent innovations like Monte Carlo Markov chain, sequential Monte
Carlo methods and more recently Approximate Bayesian Computation techniques
have considerably increased the potential for Bayesian applications and they
have also opened new avenues for Bayesian inference, first and foremost
Bayesian model choice.Comment: This is a chapter for the book "Bayesian Methods and Expert
Elicitation" edited by Klaus Bocker, 23 pages, 9 figure
On the Covariance of ICP-based Scan-matching Techniques
This paper considers the problem of estimating the covariance of
roto-translations computed by the Iterative Closest Point (ICP) algorithm. The
problem is relevant for localization of mobile robots and vehicles equipped
with depth-sensing cameras (e.g., Kinect) or Lidar (e.g., Velodyne). The
closed-form formulas for covariance proposed in previous literature generally
build upon the fact that the solution to ICP is obtained by minimizing a linear
least-squares problem. In this paper, we show this approach needs caution
because the rematching step of the algorithm is not explicitly accounted for,
and applying it to the point-to-point version of ICP leads to completely
erroneous covariances. We then provide a formal mathematical proof why the
approach is valid in the point-to-plane version of ICP, which validates the
intuition and experimental results of practitioners.Comment: Accepted at 2016 American Control Conferenc
A Computer-Assisted Uniqueness Proof for a Semilinear Elliptic Boundary Value Problem
A wide variety of articles, starting with the famous paper (Gidas, Ni and
Nirenberg in Commun. Math. Phys. 68, 209-243 (1979)) is devoted to the
uniqueness question for the semilinear elliptic boundary value problem
-{\Delta}u={\lambda}u+u^p in {\Omega}, u>0 in {\Omega}, u=0 on the boundary of
{\Omega}, where {\lambda} ranges between 0 and the first Dirichlet Laplacian
eigenvalue. So far, this question was settled in the case of {\Omega} being a
ball and, for more general domains, in the case {\lambda}=0. In (McKenna et al.
in J. Differ. Equ. 247, 2140-2162 (2009)), we proposed a computer-assisted
approach to this uniqueness question, which indeed provided a proof in the case
{\Omega}=(0,1)x(0,1), and p=2. Due to the high numerical complexity, we were
not able in (McKenna et al. in J. Differ. Equ. 247, 2140-2162 (2009)) to treat
higher values of p. Here, by a significant reduction of the complexity, we will
prove uniqueness for the case p=3
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