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IPOL Preprints — Latest public preprints from IPOL.Hamiltonian Fast Marching: A Numerical Solver for Anisotropic and Non-Holonomic Eikonal PDEsJean-Marie Mirebeau,
Jorg Portegieshttp://www.ipol.im/pub/pre/227/
http://www.ipol.im/pub/pre/227/
Wed, 13 Feb 2019 12:57:28 +01002019-02-13T12:52:39ZWe introduce a generalized Fast-Marching algorithm, able to compute paths globally minimizing
a measure of length, defined w.r.t. a variety of metrics in dimension two to five. Our
method applies in particular to arbitrary Riemannian metrics, and implements features such as
second order accuracy, sensitivity analysis, and various stopping criteria. We also address the
singular metrics associated with several non-holonomic control models, related with curvature
penalization, such as the Reeds-Shepp's car with or without reverse gear, the Euler-Mumford
elastica curves, and the Dubins car. Applications to image processing and to motion planning
are demonstrated.Blind Image Deblurring using the l0 Gradient PriorJérémy Anger,
Gabriele Facciolo,
Mauricio Delbraciohttp://www.ipol.im/pub/pre/243/
http://www.ipol.im/pub/pre/243/
Sun, 23 Dec 2018 21:45:11 +01002018-12-24T00:21:27ZMany blind image deblurring methods rely on unnatural image priors that are explicitly designed to restore salient image structures, necessary to estimate the blur kernel. In this article, we describe the blur kernel estimation method introduced by Pan, Hu, Su and Yang in 2014 that uses an l0 prior on the gradient image. We analyze the method after removing unnecessary steps, leading to a fast and elegant blur kernel estimator. We present deconvolution results using the estimated blur kernels. Our experiments show the effectiveness of the method as well as some of its shortcomings.An Analysis and Speedup of the FALDOI Method for Optical Flow EstimationFerran P. Gamonal,
Coloma Ballester,
Gloria Haro,
Enric Meinhardt-Llopis,
Roberto P. Palomareshttp://www.ipol.im/pub/pre/238/
http://www.ipol.im/pub/pre/238/
Tue, 27 Nov 2018 14:06:53 +01002018-12-04T12:44:52ZWe present a detailed analysis of FALDOI, a large displacement optical flow
method proposed by P.Palomares et al. This method requires a set of discrete
matches, which can be extremely sparse, and an energy functional which
locally guides the interpolation from the matches. It follows a two-step
minimization method at the finest scale which is very robust to the outliers of the
sparse matcher and can capture large displacements of small objects. The results
shown in the original paper consistently outperformed the coarse-to-fine
approaches and achieved good qualitative and quantitative performance on
the standard optical flow benchmarks. In this paper we revise the proposed
method and the changes done to significantly reduce its execution time while
reporting nearly the same accuracy. Finally, we also compare it against the
current state-of-the-art to assess its performance.Implementation of a Denoising Algorithm based on High-Order Singular Value Decomposition of TensorsFabien Feschethttp://www.ipol.im/pub/pre/226/
http://www.ipol.im/pub/pre/226/
Wed, 30 May 2018 11:57:10 +02002018-09-13T23:34:24ZThis article presents an implementation of a denoising algorithm based on High-Order Singular
Value Decomposition (HOSVD) of tensors. It belongs to the class of patch-based methods such
as BM3D and NL-Bayes. It exploits the grouping of similar patches in a local neighbourhood
into a 3D matrix also called a third order tensor. Instead of performing different processing
in different dimension, as in BM3D for instance, it is based on the decomposition of a tensor
simultaneously in all dimensions reducing it to a core tensor in a similar way as SVD does for
matrices in computing the diagonal matrix of singular values. The core tensor is filtered and
a tensor is reconstructed by inverting the HOSVD. As common in patch-based algorithms, all
tensors containing a pixel are then merged to produce an output image.Comparison of Optical Flow Methods under Stereomatching with Short BaselinesTristan Dagobert,
Nelson Monzón,
Javier Sánchezhttp://www.ipol.im/pub/pre/217/
http://www.ipol.im/pub/pre/217/
Mon, 16 Oct 2017 14:24:59 +02002019-01-21T12:49:29ZThis article studies the effectiveness of optical flow methods applied to short
baseline image pairs under different noise levels. New metrics have been
developed to analyze the results because the usual metrics are inadequate in a
subpixel context. We have used the implementation of some standard optical flow
methods adapted to the stereo problem. Our experiments show that the Brox
et al. method produces the least errors, with a 60% success rate and a
relative precision at 1/100th of a pixel. On the other hand, our comparison
shows that a discontinuity preserving method, derived from Brox et al.,
also provides competitive results at the same time that it yields disparities
with more details and correct contours.Joint Large-Scale Motion Estimation and Image ReconstructionHendrik Dirkshttp://www.ipol.im/pub/pre/193/
http://www.ipol.im/pub/pre/193/
Thu, 24 Nov 2016 14:13:55 +01002018-07-22T11:40:36ZThis article describes the implementation of the joint motion estimation and image reconstruction framework presented by Burger, Dirks and Schönlieb and extends this framework to large-scale motion between consecutive image frames. The variational framework uses displacements between consecutive frames based on the optical
flow approach to improve the image reconstruction quality on the one hand and the motion estimation quality on the other. The energy functional consists of a
data-fidelity term with a general operator that connects the input sequence to the solution, it has a total variation term for the image sequence and is connected to the underlying flow using an optical flow term. Additional spatial regularity for the flow is modeled by a total variation regularizer for both components of the flow. The numerical minimization is performed in an alternating manner using
primal-dual techniques. The resulting schemes are presented as pseudo-code together with a short numerical evaluation.Joint TV-L1 Optical Flow and Occlusion EstimationJuan Francisco Garamendi Bragado,
Coloma Ballester,
Lluís Garrido,
Vanel Lazcano,
Vicent Caselleshttp://www.ipol.im/pub/pre/118/
http://www.ipol.im/pub/pre/118/
Thu, 05 Feb 2015 13:37:40 +01002018-07-22T11:40:36ZThis document describes an implementation of the energy functional minimization proposed by Ballester, Garrido, Lazcano and Caselles for joint optical flow and occlusion estimation. The method is based on the TV-L1 approach introduced Zach, Pock and Bischof in 2007 but with the particularity of detecting occlusions. The energy functional is composed by a regularization term (over the optical flow and the occlusion fields) using the total variation, a data term using the L1 norm, and a term, which is based on the divergence of the flow, for dealing with the occlusions.