IPOLIPOLhttp://www.ipol.im/feed/IPOL Preprints — Latest public preprints from IPOL.ikiwiki2018-05-25T22:41:28ZMultigrid Poisson Solvershttp://www.ipol.im/pub/pre/228/Matías Di Martino,
Gabriele Facciolo2018-05-22T12:31:58Z2018-05-22T12:31:58Z
The Poisson equation is the most studied partial differential equation, and it allows to formulate many useful image processing methods in an elegant and efficient mathematical framework. Using different variations of data terms and boundary conditions, Poisson-like problems can be developed, e.g., for local contrast enhancement, inpainting or image seamless cloning between many other applications. Multigrid solvers are among the most efficient numerical solvers for discrete Poisson-like equations. However, their correct implementation relies on: (i) the proper definition of the discrete problem, (ii) the right choice of Prolongation and Restriction operators, and (iii) the adequate formulation of the problem across different scales and layers. In the present work we address these aspects, and we provide a mathematical and practical description of multigrid methods. In addition, we present an alternative to the Extended formulation of Poisson equation proposed in [M. Mainberger, A. Bruhn, J. Weickert, and S. Forchhammer, Edge-based compression of cartoon-like images with homogeneous diffusion, Pattern Recognition, 44 (2011), pp. 1859–1873].
The proposed formulation of the problem suits better multigrid methods, in particular, because it has important mathematical properties that can be exploited to define the problem at different scales in a intuitive and natural way. In addition, common iterative solvers and Poisson-like problems are empirically analyzed and compared. For example, the complexity of problems is compared when the topology of Dirichlet boundary conditions changes in the interior of the regular domain of the image. We also show that multigrid methods convergence can be achieved in linear time (e.g. the time for convergence depends linearly with the number of pixels).
Improvements of the Inverse Compositional Algorithm for Parametric Motion Estimationhttp://www.ipol.im/pub/pre/222/Thibaud Briand,
Gabriele Facciolo,
Javier Sánchez2018-04-19T08:34:16Z2018-04-19T08:34:16Z
In this work, we propose several improvements of the inverse compositional algorithm for parametric registration. We propose an improved handling of boundary pixels, a different color handling and gradient estimation, and the possibility to skip scales in the multiscale coarse-to-fine scheme. In an experimental part, we analyze the influence of the modifications. The estimation accuracy is at least improved by a factor 1.3 while the computation time is at least reduced by a factor 2.2 for color images.
Video Denoising with Optical Flow Estimationhttp://www.ipol.im/pub/pre/224/Antoni Buades,
Jose-Luis Lisani2018-03-27T13:21:39Z2018-03-27T13:21:39Z
In this paper we describe the implementation of state-of-the-art video denoising algorithm SPTWO [A. Buades, J.L. Lisani, M. Miladinovic, Patch Based Video Denoising with Optical Flow Estimation, IEEE Transactions on Image Processing 25 (6), 2573--2586]. This algorithm, inspired by image fusion techniques, uses motion compensation by regularized optical flow methods, which permits robust patch comparison in spatiotemporal volumes. Groups of similar patches are denoised using Principal Component Analysis, which ensures the correct preservation of fine texture and details.
Theory and Practice of Image B-Spline Interpolationhttp://www.ipol.im/pub/pre/221/Thibaud Briand,
Pascal Monasse2018-01-12T10:21:10Z2018-01-12T10:21:10Z
We explain how the B-spline interpolation of signals and images can be efficiently performed by linear filtering. Based on the seminal two-step method proposed by Unser et al. in 1991, we propose two slightly different prefiltering algorithms whose precisions are proven to be controlled thanks to a rigorous boundary handling. This paper contains all the information, theoretical and practical, required to perform efficiently B-spline interpolation for any order and any boundary extension. We describe precisely how to evaluate the kernel and to compute the B-spline interpolator parameters. As a fundamental application we also provide an implementation of homographic transformation of images using B-spline interpolation.
Numerical Simulation of Landscape Evolution Modelshttp://www.ipol.im/pub/pre/205/Marc Lebrun,
Jean-Michel Morel,
Miguel Colom,
Jérôme Darbon2018-05-25T22:41:28Z2017-12-21T23:52:15Z
This paper gives the complete numerical schemes implementing the main physical laws pro-
posed in landscape evolution (LEMs). These laws can be modeled by a system of three partial
differential equations governing water run-off, stream incision, hill slope evolution and sedimentation. The goal of the presented algorithm, code and online facility is to be able to test these
equations on digital elevation models (DEMs) of any resolution, and to illustrate its potential
to simulate the fine structure of the river network, and to understand the landscape
morphology and its causes. The equations simulate plausible evolutions. We illustrate experiments on
DEMs of several sites, including one site, La Réunion where the DEM is given at three different
resolutions: the SRTM resolution (90m), and then 12m and 4m on DEMs derived from several
Pléiades pairs. Other many DEM’s are proposed in the online demo, which allows to upload and tests other DEMs.
Efficient Large-scale Image Search With a Vocabulary Treehttp://www.ipol.im/pub/pre/199/Esteban Uriza,
Francisco Gómez Fernández,
Martín Rais2018-04-26T09:06:41Z2017-12-21T23:23:56Z
The task of searching and recognizing objects in images has become an important research
topic in the area of image processing and computer vision. Looking for similar images in large
data sets given an input query and responding as fast as possible is a very challenging task.
In this work the Bag of Features approach is studied, and an implementation of the visual
vocabulary tree method from Nistér and Stewénius is presented. Images are described using
local invariant descriptor techniques and then indexed in a database using an inverted index
for further queries. The descriptors are quantized according to a visual vocabulary, creating
sparse vectors, which allows to compute very efficiently, for each query, a ranking of similarity
for indexed images. The performance of the method is analyzed varying different
factors, such as the parameters for the vocabulary tree construction, different techniques
of local descriptors extraction and dimensionality reduction with PCA.
It can be observed that the retrieval performance increases
with a richer vocabulary and decays very slowly as the size of the dataset grows.
Comparison of Optical Flow Methods under Stereomatching with Short Baselineshttp://www.ipol.im/pub/pre/217/Tristan Dagobert,
Nelson Monzón,
Javier Sánchez2017-10-17T10:52:47Z2017-10-16T12:24:59Z
This article studies the effectiveness of optical flow methods employed in the case of short baselines and different noise levels. New metrics have been developed to analyze the evaluation results because the usual metrics are inadequate in a subpixel context. Experiments conducted on the adequate Middlebury and CMLA dataset pairs show that the Brox et al. method produces the best errors, with a 60% success rate in relative precision at 1/100 th of a pixel. On the other hand, our comparison shows that the Monzón et al. method also provides competitive results at the same time that it yields disparities with more details and correct contours.
A Study of Rotation Invariant Copy-Move Forgery Detectionhttp://www.ipol.im/pub/pre/213/Thibaud Ehret2017-09-25T19:08:53Z2017-09-25T10:26:19Z
This article presents an implementation and discussion of the recently proposed Efficient dense-field copy-move forgery detection by Cozzolino et al.. This method is a forgery detection based on a dense field of descriptors chosen to be invariant by rotation. Zernike moments were suggested in the original article. An efficient matching of the descriptors is then performed using PatchMatch, which is extremely efficient to find duplicate regions. Regions matched by PatchMatch are processed to find the final detections. This allows a precise and accurate detection of copy-move forgeries inside a single suspicious image. We also extend successfully the method to the use of dense SIFT descriptors and show that they are better at detecting forgeries using Poisson editing.
An Affine Invariant Patch Similarityhttp://www.ipol.im/pub/pre/202/Vadim Fedorov,
Coloma Ballester2017-07-14T10:41:24Z2017-07-14T10:09:29Z
Image and video comparison is often approached by comparing patches of visual information. In this work we present a detailed description and implementation of an affine invariant patch similarity measure that performs an appropriate patch comparison by automatically and intrinsically adapting the size and shape of the patches. We also describe the complete implementation of the proposed iterative algorithm for computation of those shape-adaptive patches around each point in the image domain.
Recovering the Blur Kernel from Natural Image Statistics: An Analysis of the Goldstein-Fattal Methodhttp://www.ipol.im/pub/pre/211/Jérémy Anger,
Gabriele Facciolo,
Mauricio Delbracio2017-06-13T16:23:36Z2017-06-13T16:23:36Z
Despite the significant improvement in image quality mainly caused by the improvement in
optical sensors and general electronics, blur due to camera shake significantly undermines the
quality of hand-held photographs being one of the most active research topics. In this work,
we present a detailed description and implementation of the blurring kernel estimation algorithm
introduced by Goldstein and Fattal in 2012. Unlike most methods that attempt to solve
an inverse problem through a variational formulation (e.g., through a maximum a posteriori
estimation), this method directly estimates the blurring kernel by modeling statistical irregu-
larities in the power spectrum of blurred natural images. The adopted mathematical model
extends the well-known power-law by contemplating the presence of dominant strong edges in
particular directions. The blurring kernel is retrieved from an estimation of the blurring
kernel power spectrum, by solving a phase retrieval problem using additional constraints due to
the particular nature of camera shake blurring kernels (e.g., non-negativity and small spatial
support). Although the algorithm is conceptually simple, being based on several clean
mathematical/physical assumptions, the numerical implementation presents several challenges. This
work contributes to a detailed anatomy of the Goldstein and Fattal method, and the algorithms
that constitute it and its parameters.
Structural Similarity Metrics for Quality Image Fusion
Assessment: Algorithmshttp://www.ipol.im/pub/pre/196/Silvina Pistonesi,
Jorge Martinez,
Silvia Maria Ojeda,
Ronny Vallejos2017-04-13T22:43:08Z2017-04-13T22:43:08Z
The wide use of image fusion techniques in different fields such as medical diagnostics, digital
camera vision, military and surveillance applications, among others, has motivated the
development of various image quality fusion metrics, in order to evaluate them. In this paper, we
study and implement the algorithms of non-reference image structural similarity based metrics
for fusion assessment: Piella’s metric, Cvejic’s metric, Yang’s metric, and Codispersion Fusion
Quality metric. We conduct the comparative experiment of the selected image fusion metrics
over four multiresolution image fusion algorithms, performed on different pairs of images used
in different applications.
Joint Large-Scale Motion Estimation and Image Reconstructionhttp://www.ipol.im/pub/pre/193/Hendrik Dirks2016-11-24T21:36:43Z2016-11-24T13:13:55Z
This 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 Estimationhttp://www.ipol.im/pub/pre/118/Juan Francisco Garamendi Bragado,
Coloma Ballester,
Lluís Garrido,
Vanel Lazcano,
Vicent Caselles2016-07-29T13:27:05Z2015-02-05T12:37:40Z
This 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.
Study of the Principal Component Analysis Method for the Correction of Images Degraded by Turbulencehttp://www.ipol.im/pub/pre/47/Tristan Dagobert,
Yohann Tendero,
Stéphane Landeau2016-07-29T13:27:05Z2013-06-29T03:13:25Z
This article details the use of principal component analysis
in order to restore images degraded by atmospheric turbulence. It
analyzes and discusses a well-known paper and proposes a
generalization of the algorithm described in such article.
Examples using sequences of real atmospheric turbulence are
presented.
Real atmospheric turbulent image acquisition is described and
sequences are made accessible for downloading.