IPOL is a research journal of image processing and image analysis which emphasizes the role of mathematics as a source for algorithm design and the reproducibility of the research. Each article contains a text on an algorithm and its source code, with an online demonstration facility and an archive of experiments. Text and source code are peer-reviewed and the demonstration is controlled. IPOL is an Open Science and Reproducible Research journal.

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# Latest Articles

Fundamental Matrix of a Stereo Pair, with A Contrario Elimination of Outliers

2016-05-17 · Lionel Moisan, Pierre Moulon, Pascal Monasse

2016-05-17 · Lionel Moisan, Pierre Moulon, Pascal Monasse

Directional Filters for Cartoon + Texture Image Decomposition

2016-05-05 · Antoni Buades, Jose-Luis Lisani

2016-05-05 · Antoni Buades, Jose-Luis Lisani

On the Implementation of Collaborative TV Regularization: Application to Cartoon+Texture Decomposition

2016-04-20 · Joan Duran, Michael Moeller, Catalina Sbert, Daniel Cremers

2016-04-20 · Joan Duran, Michael Moeller, Catalina Sbert, Daniel Cremers

Small Neural Networks can Denoise Image Textures Well: a Useful Complement to BM3D

2016-01-19 · Yi-Qing Wang

2016-01-19 · Yi-Qing Wang

# Series and Special Issues

## Special Issue on Discrete Geometry (DGCI 2011)

A Streaming Distance Transform Algorithm for Neighborhood-Sequence Distances
We describe an algorithm that computes a “translated” 2D Neighborhood-Sequence Distance
Transform (DT) using a look up table approach. It requires a single raster scan of the input
image and produces one line of output for every line of input. The neighborhood sequence is
specified either by providing one period of some integer periodic sequence or by providing the rate of
appearance of neighborhoods. The full algorithm optionally derives the regular (centered) DT
from the “translated” DT, providing the result image on-the-ﬂy, with a minimal delay, before the
input image is fully processed. Its efficiency can benefit all applications that use neighborhood-
sequence distances, particularly when pipelined processing architectures are involved, or when
the size of objects in the source image is limited.

Digital Level Layers for Digital Curve Decomposition and Vectorization
The purpose of this paper is to present Digital Level Layers and show
the motivations for working with such analytical primitives in the
framework of Digital Geometry. We first compare their properties to
morphological and topological counterparts, and then we explain how to
recognize them and use them to decompose or vectorize digital curves
and contours.

A Near-Linear Time Guaranteed Algorithm for Digital Curve
Simplification Under the Fréchet Distance
In this paper, we propose an algorithm that, from a maximum error and a
digital curve (4- or 8-connected), computes a simplification of the
curve (a polygonal curve) such that the Fréchet distance between the
original and the simplified curve is less than the error. The Fréchet
distance is known to nicely measure the similarity between two
curves. The algorithm we propose uses an approximation of the Fréchet
distance, but a guarantee over the quality of the simplification is
proved. Moreover, even if the theoretical complexity of the algorithm
is in O(n log(n)), experiments show a linear behaviour in practice.

Meaningful Scales Detection: an Unsupervised Noise Detection Algorithm for Digital Contours
This work presents an algorithm which permits to detect locally on digital contour what is the amount of noise estimated from a given maximal scale. The method is based on the asymptotic properties of the length of the maximal segment primitive.

Interactive Segmentation Based on Component-trees
Component-trees associate to a discrete gray-level image a descriptive
data structure induced by the inclusion relation between the binary
components obtained at successive level-sets. This article presents an
interactive segmentation methodology based on component-trees. It
consists of the extraction of a subset of the image component-tree,
enabling the generation of a binary object which fits at best (with
respect to the gray-level structure of the image) a given binary
target selected beforehand in the image. Compared to other interactive
segmentation methods, the proposed methodology has the following
advantages: (i) the segmentation result is only composed of a union
of connected components of the level-sets, which ensures that no
'false contours' are included; (ii) only one image marker is needed:
in particular, there is no need to give a marker for the background
(contrary to some other methods); (iii) the method is fast and
efficient, leading to a result computed in real-time on common
image sizes.

Extraction of Connected Region Boundary in Multidimensional Images
This paper presents an algorithm to extract the boundary of a
connected region(s) using classical topology definitions. From a given
adjacency definition, the proposed method is able to extract the
boundary of an object in a generic way, independently of the dimension
of the digital space.

## SIIMS Companion Papers

Recovering the Subpixel PSF from Two Photographs at Different Distances
In most typical digital cameras, even high-end digital single lens
reflex ones (DSLR), the acquired images are sampled at rates below
the Nyquist critical rate, causing aliasing effects. In this work
we describe a new algorithm for the estimation of the point spread
function (PSF) of a digital camera from aliased photographs, that
achieves subpixel accuracy. The procedure is based on taking two
parallel photographs of the same scene, from different distances
leading to different geometric zooms, and then estimating the kernel
blur between them.

The Implementation of SURE Guided Piecewise Linear Image Denoising
SURE (Stein's Unbiased Risk Estimator) guided Piecewise Linear Estimation (S-PLE) is a recently introduced patch-based state-of-the-art denoising algorithm. In this article, we focus on its implementation and show its performance by comparing it with several other acclaimed algorithms.

Implementation of the "Non-Local Bayes" (NL-Bayes) Image Denoising Algorithm
This article presents a detailed implementation of the Non-Local Bayes
(NL-Bayes) image denoising algorithm. In a nutshell, NL-Bayes is an
improved variant of NL-means. In the NL-means algorithm, each patch is
replaced by a weighted mean of the most similar patches present in a
neighborhood. Images being mostly self-similar, such instances of
similar patches are generally found, and averaging them increases the
SNR. The NL-Bayes strategy improves on NL-means by evaluating for
each group of similar patches a Gaussian vector model. To each patch
is therefore associated a mean (which would be the result of
NL-means), but also a covariance matrix estimating the variability of
the patch group. This permits to compute an optimal (in the sense of
Bayesian minimal mean square error) estimate of each noisy patch in
the group, by a simple matrix inversion.
The implementation proceeds in two identical iterations, but the
second iteration uses the denoised image of the first iteration to
estimate better the mean and covariance of the patch Gaussian models.
A discussion of the algorithm shows that it is close in spirit to
several state of the art algorithms (TSID, BM3D, BM3D-SAPCA), and that
its structure is actually close to BM3D. Thorough experimental
comparison made in this paper also shows that the algorithm achieves
the best state of the art on color images in terms of PSNR and image
quality. On grey level images, it reaches a performance similar to the
more complex BM3D-SAPCA (no color version is available for this last
algorithm).

<TMPL_VAR raw_title>
<TMPL_VAR raw_abstract>

Image Interpolation with Geometric Contour Stencils
We consider the image interpolation problem where given an image
v<sub>m,n</sub>
with uniformly-sampled pixels vm,n and point spread function h, the
goal is to find function u(x,y) satisfying v<sub>m,n</sub> = (h*u)(m,n)
for all m,n in Z.
This article improves upon the IPOL article Image Interpolation
with Contour Stencils. In the previous work, contour stencils are used
to estimate the image contours locally as short line segments. This
article begins with a continuous formulation of total variation
integrated over a collection of curves and defines contour stencils as
a consistent discretization. This discretization is more reliable than
the previous approach and can effectively distinguish contours that
are locally shaped like lines, curves, corners, and circles. These
improved contour stencils sense more of the geometry in the image.
Interpolation is performed using an extension of the method described
in the previous article. Using the improved contour stencils, there is
an increase in image quality while maintaining similar computational
efficiency.

# Topics

## 3D

Farman Institute 3D Point Sets - High Precision 3D Data Sets

2011-09-27 · Julie Digne, Nicolas Audfray, Claire Lartigue, Charyar Mehdi-Souzani, Jean-Michel Morel

2011-09-27 · Julie Digne, Nicolas Audfray, Claire Lartigue, Charyar Mehdi-Souzani, Jean-Michel Morel

## Blur

## Calibration

Automatic Lens Distortion Correction Using One-Parameter Division Models

2014-11-20 · Miguel Alemán-Flores, Luis Alvarez, Luis Gomez, Daniel Santana-Cedrés

2014-11-20 · Miguel Alemán-Flores, Luis Alvarez, Luis Gomez, Daniel Santana-Cedrés

Recovering the Subpixel PSF from Two Photographs at Different Distances

2013-10-23 · Mauricio Delbracio, Andrés Almansa, Pablo Musé

2013-10-23 · Mauricio Delbracio, Andrés Almansa, Pablo Musé

Non-parametric Sub-pixel Local Point Spread Function Estimation

2012-03-23 · Mauricio Delbracio, Pablo Musé, Andrés Almansa

2012-03-23 · Mauricio Delbracio, Pablo Musé, Andrés Almansa

An Iterative Optimization Algorithm for Lens Distortion Correction Using Two-Parameter Models

PREPRINT · Daniel Santana-Cedrés, Luis Gómez, Miguel Alemán-Flores, Agustín Salgado, Julio Esclarín, Luis Mazorra, Luis Álvarez

PREPRINT · Daniel Santana-Cedrés, Luis Gómez, Miguel Alemán-Flores, Agustín Salgado, Julio Esclarín, Luis Mazorra, Luis Álvarez

## Color and Contrast

An Algorithmic Analysis of Variational Models for Perceptual Local Contrast Enhancement

2015-07-29 · Sira Ferradans, R. Palma-Amestoy, E. Provenzi

2015-07-29 · Sira Ferradans, R. Palma-Amestoy, E. Provenzi

Screened Poisson Equation for Image Contrast Enhancement

2014-03-11 · Jean-Michel Morel, Ana-Belen Petro, Catalina Sbert

2014-03-11 · Jean-Michel Morel, Ana-Belen Petro, Catalina Sbert

Color and Contrast Enhancement by Controlled Piecewise Affine Histogram Equalization

2012-10-17 · Jose-Luis Lisani, Ana-Belen Petro, Catalina Sbert

2012-10-17 · Jose-Luis Lisani, Ana-Belen Petro, Catalina Sbert

Simplest Color Balance

2011-10-24 · Nicolas Limare, Jose-Luis Lisani, Jean-Michel Morel, Ana Belén Petro, Catalina Sbert

2011-10-24 · Nicolas Limare, Jose-Luis Lisani, Jean-Michel Morel, Ana Belén Petro, Catalina Sbert

Image Color Cube Dimensional Filtering and Visualization

2011-06-22 · Jose-Luis Lisani, Antoni Buades, Jean-Michel Morel

2011-06-22 · Jose-Luis Lisani, Antoni Buades, Jean-Michel Morel

Retinex Poisson Equation: a Model for Color Perception

2011-04-05 · Nicolas Limare, Ana Belén Petro, Catalina Sbert, Jean-Michel Morel

2011-04-05 · Nicolas Limare, Ana Belén Petro, Catalina Sbert, Jean-Michel Morel

## Computational Photography

Obtaining High Quality Photographs of Paintings by Image Fusion

2015-06-27 · Antoni Buades, Gloria Haro, Enric Meinhardt-Llopis

2015-06-27 · Antoni Buades, Gloria Haro, Enric Meinhardt-Llopis

## Demosaicking

A Demosaicking Algorithm with Adaptive Inter-Channel Correlation

2015-12-21 · Joan Duran, Antoni Buades

2015-12-21 · Joan Duran, Antoni Buades

Implementation of Nonlocal Pansharpening Image Fusion

2014-02-28 · Antoni Buades, Bartomeu Coll, Joan Duran, Catalina Sbert

2014-02-28 · Antoni Buades, Bartomeu Coll, Joan Duran, Catalina Sbert

Gunturk-Altunbasak-Mersereau Alternating Projections Image Demosaicking

2011-09-01 · Pascal Getreuer

2011-09-01 · Pascal Getreuer

Self-similarity Driven Demosaicking

2011-06-01 · Antoni Buades, Bartomeu Coll, Jean-Michel Morel, Catalina Sbert

2011-06-01 · Antoni Buades, Bartomeu Coll, Jean-Michel Morel, Catalina Sbert

## Denoising

On the Implementation of Collaborative TV Regularization: Application to Cartoon+Texture Decomposition

2016-04-20 · Joan Duran, Michael Moeller, Catalina Sbert, Daniel Cremers

2016-04-20 · Joan Duran, Michael Moeller, Catalina Sbert, Daniel Cremers

Small Neural Networks can Denoise Image Textures Well: a Useful Complement to BM3D

2016-01-19 · Yi-Qing Wang

2016-01-19 · Yi-Qing Wang

The Noise Clinic: a Blind Image Denoising Algorithm

2015-01-28 · Marc Lebrun, Miguel Colom, Jean-Michel Morel

2015-01-28 · Marc Lebrun, Miguel Colom, Jean-Michel Morel

Analysis and Extension of the Percentile Method, Estimating a Noise Curve from a Single Image

2013-12-20 · Miguel Colom, Antoni Buades

2013-12-20 · Miguel Colom, Antoni Buades

Chambolle's Projection Algorithm for Total Variation Denoising

2013-12-17 · Joan Duran, Bartomeu Coll, Catalina Sbert

2013-12-17 · Joan Duran, Bartomeu Coll, Catalina Sbert

Analysis and Extension of the Ponomarenko et al. Method, Estimating a Noise Curve from a Single Image

2013-07-23 · Miguel Colom, Antoni Buades

2013-07-23 · Miguel Colom, Antoni Buades

Implementation of the "Non-Local Bayes" (NL-Bayes) Image Denoising Algorithm

2013-06-17 · Marc Lebrun, Antoni Buades, Jean-Michel Morel

2013-06-17 · Marc Lebrun, Antoni Buades, Jean-Michel Morel

An Implementation and Detailed Analysis of the K-SVD Image Denoising Algorithm

2012-05-19 · Marc Lebrun, Arthur Leclaire

2012-05-19 · Marc Lebrun, Arthur Leclaire

DCT Image Denoising: a Simple and Effective Image Denoising Algorithm

2011-10-24 · Guoshen Yu, Guillermo Sapiro

2011-10-24 · Guoshen Yu, Guillermo Sapiro

PARIGI: a Patch-based Approach to Remove Impulse-Gaussian Noise from Images

PREPRINT · Julie Delon, Agnès Desolneux, Thierry Guillemot

PREPRINT · Julie Delon, Agnès Desolneux, Thierry Guillemot

Analysis and Extension of the PCA Method, Estimating a Noise Curve from a Single Image

PREPRINT · Miguel Colom, Antoni Buades

PREPRINT · Miguel Colom, Antoni Buades

## Geometry

A Streaming Distance Transform Algorithm for Neighborhood-Sequence Distances

2014-09-01 · Nicolas Normand, Robin Strand, Pierre Evenou, Aurore Arlicot

2014-09-01 · Nicolas Normand, Robin Strand, Pierre Evenou, Aurore Arlicot

Digital Level Layers for Digital Curve Decomposition and Vectorization

2014-07-30 · Laurent Provot, Yan Gerard, Fabien Feschet

2014-07-30 · Laurent Provot, Yan Gerard, Fabien Feschet

A Near-Linear Time Guaranteed Algorithm for Digital Curve
Simplification Under the Fréchet Distance

2014-05-22 · Isabelle Sivignon

2014-05-22 · Isabelle Sivignon

Meaningful Scales Detection: an Unsupervised Noise Detection Algorithm for Digital Contours

2014-05-07 · Bertrand Kerautret, Jacques-Olivier Lachaud

2014-05-07 · Bertrand Kerautret, Jacques-Olivier Lachaud

Extraction of Connected Region Boundary in Multidimensional Images

2014-03-26 · David Coeurjolly, Bertrand Kerautret, Jacques-Olivier Lachaud

2014-03-26 · David Coeurjolly, Bertrand Kerautret, Jacques-Olivier Lachaud

## Infrared

Non-uniformity Correction of Infrared Images by Midway Equalization

2012-07-12 · Yohann Tendero, Stéphane Landeau, Jérôme Gilles

2012-07-12 · Yohann Tendero, Stéphane Landeau, Jérôme Gilles

## Learning and Detection

A Fast C++ Implementation of Neural Network Backpropagation Training Algorithm: Application to Bayesian Optimal Image Demosaicing

2015-09-16 · Yi-Qing Wang, Nicolas Limare

2015-09-16 · Yi-Qing Wang, Nicolas Limare

## Inpainting

Variational Framework for Non-Local Inpainting

2015-12-26 · Vadim Fedorov, Gabriele Facciolo, Pablo Arias

2015-12-26 · Vadim Fedorov, Gabriele Facciolo, Pablo Arias

Combined First and Second Order Total Variation Inpainting using Split Bregman

2013-07-12 · Konstantinos Papafitsoros, Carola Bibiane Schoenlieb, Bati Sengul

2013-07-12 · Konstantinos Papafitsoros, Carola Bibiane Schoenlieb, Bati Sengul

## Interpolation

Linear Filtering : from the Continuous Spectral Definition to the Numerical Computations

PREPRINT · Thibaud Briand

PREPRINT · Thibaud Briand

## Image Comparison

Automatic Homographic Registration of a Pair of Images, with A Contrario Elimination of Outliers

2012-05-19 · Lionel Moisan, Pierre Moulon, Pascal Monasse

2012-05-19 · Lionel Moisan, Pierre Moulon, Pascal Monasse

ASIFT: An Algorithm for Fully Affine Invariant Comparison

2011-02-24 · Guoshen Yu, Jean-Michel Morel

2011-02-24 · Guoshen Yu, Jean-Michel Morel

Geometric Expansion for Local Feature Analysis and Matching

PREPRINT · Erez Farhan, Elad Meir, Rami Hagege

PREPRINT · Erez Farhan, Elad Meir, Rami Hagege

## Optical Flow

An Implementation of Combined Local-Global Optical Flow

2015-06-25 · Jorge Jara-Wilde, Mauricio Cerda, José Delpiano, Steffen Härtel

2015-06-25 · Jorge Jara-Wilde, Mauricio Cerda, José Delpiano, Steffen Härtel

A Line Search Multilevel Truncated Newton Algorithm for Computing the Optical Flow

2015-06-19 · Lluís Garrido, El Mostafa Kalmoun

2015-06-19 · Lluís Garrido, El Mostafa Kalmoun

Robust Optical Flow Estimation

2013-10-28 · Javier Sánchez Pérez, Nelson Monzón López, Agustín Salgado de la Nuez

2013-10-28 · Javier Sánchez Pérez, Nelson Monzón López, Agustín Salgado de la Nuez

Horn-Schunck Optical Flow with a Multi-Scale Strategy

2013-07-19 · Enric Meinhardt-Llopis, Javier Sánchez Pérez, Daniel Kondermann

2013-07-19 · Enric Meinhardt-Llopis, Javier Sánchez Pérez, Daniel Kondermann

TV-L1 Optical Flow Estimation

2013-07-19 · Javier Sánchez Pérez, Enric Meinhardt-Llopis, Gabriele Facciolo

2013-07-19 · Javier Sánchez Pérez, Enric Meinhardt-Llopis, Gabriele Facciolo

Robust Discontinuity Preserving Optical Flow Methods

PREPRINT · Nelson Monzón, Agustín Salgado, Javier Sánchez

PREPRINT · Nelson Monzón, Agustín Salgado, Javier Sánchez

Joint TV-L1 Optical Flow and Occlusion Estimation

PREPRINT · Juan Francisco Garamendi Bragado, Coloma Ballester, Lluís Garrido, Vanel Lazcano, Vicent Caselles

PREPRINT · Juan Francisco Garamendi Bragado, Coloma Ballester, Lluís Garrido, Vanel Lazcano, Vicent Caselles

## PDE

Image Curvature Microscope

PREPRINT · Adina Ciomaga, Lionel Moisan, Pascal Monasse, Jean-Michel Morel

PREPRINT · Adina Ciomaga, Lionel Moisan, Pascal Monasse, Jean-Michel Morel

## Segmentation and Edges

An Unsupervised Point Alignment Detection Algorithm

2015-12-15 · José Lezama, Gregory Randall, Jean-Michel Morel, Rafael Grompone von Gioi

2015-12-15 · José Lezama, Gregory Randall, Jean-Michel Morel, Rafael Grompone von Gioi

LSD: a Line Segment Detector

2012-03-24 · Rafael Grompone von Gioi, Jérémie Jakubowicz, Jean-Michel Morel, Gregory Randall

2012-03-24 · Rafael Grompone von Gioi, Jérémie Jakubowicz, Jean-Michel Morel, Gregory Randall

A Real Time Morphological Snakes Algorithm

2012-03-23 · Luis Alvarez, Luis Baumela, Pablo Márquez-Neila, Pedro Henríquez

2012-03-23 · Luis Alvarez, Luis Baumela, Pablo Márquez-Neila, Pedro Henríquez

A C++ Implementation of Otsu’s Image Segmentation Method

PREPRINT · Juan Pablo Balarini, Sergio Nesmachnow

PREPRINT · Juan Pablo Balarini, Sergio Nesmachnow

Vanishing Point Detection in Urban Scenes Using Point Alignments

PREPRINT · José Lezama, Gregory Randall, Rafael Grompone von Gioi

PREPRINT · José Lezama, Gregory Randall, Rafael Grompone von Gioi

## Stereovision

Fundamental Matrix of a Stereo Pair, with A Contrario Elimination of Outliers

2016-05-17 · Lionel Moisan, Pierre Moulon, Pascal Monasse

2016-05-17 · Lionel Moisan, Pierre Moulon, Pascal Monasse

Bilaterally Weighted Patches for Disparity Map Computation

2015-03-11 · Laura Fernández Julià, Pascal Monasse

2015-03-11 · Laura Fernández Julià, Pascal Monasse

Integral Images for Block Matching

2014-12-16 · Gabriele Facciolo, Nicolas Limare, Enric Meinhardt-Llopis

2014-12-16 · Gabriele Facciolo, Nicolas Limare, Enric Meinhardt-Llopis

Stereo Disparity through Cost Aggregation with Guided Filter

2014-10-23 · Pauline Tan, Pascal Monasse

2014-10-23 · Pauline Tan, Pascal Monasse

Kolmogorov and Zabih’s Graph Cuts Stereo Matching Algorithm

2014-10-15 · Vladimir Kolmogorov, Pascal Monasse, Pauline Tan

2014-10-15 · Vladimir Kolmogorov, Pascal Monasse, Pauline Tan

## Texture

Directional Filters for Cartoon + Texture Image Decomposition

2016-05-05 · Antoni Buades, Jose-Luis Lisani

2016-05-05 · Antoni Buades, Jose-Luis Lisani

The Heeger & Bergen Pyramid Based Texture Synthesis Algorithm

2014-11-17 · Thibaud Briand, Jonathan Vacher, Bruno Galerne, Julien Rabin

2014-11-17 · Thibaud Briand, Jonathan Vacher, Bruno Galerne, Julien Rabin

Exemplar-based Texture Synthesis: the Efros-Leung Algorithm

2013-10-23 · Cecilia Aguerrebere, Yann Gousseau, Guillaume Tartavel

2013-10-23 · Cecilia Aguerrebere, Yann Gousseau, Guillaume Tartavel

Micro-Texture Synthesis by Phase Randomization

2011-09-23 · Bruno Galerne, Yann Gousseau, Jean-Michel Morel

2011-09-23 · Bruno Galerne, Yann Gousseau, Jean-Michel Morel

Cartoon+Texture Image Decomposition

2011-09-13 · Antoni Buades, Triet Le, Jean-Michel Morel, Luminita Vese

2011-09-13 · Antoni Buades, Triet Le, Jean-Michel Morel, Luminita Vese

Efros and Freeman Image Quilting Algorithm for Texture Synthesis

PREPRINT · Lara Raad, Bruno Galerne

PREPRINT · Lara Raad, Bruno Galerne

## Vision Through Turbulence

Implementation of the Centroid Method for the Correction of Turbulence

2014-07-31 · Enric Meinhardt-Llopis, Mario Micheli

2014-07-31 · Enric Meinhardt-Llopis, Mario Micheli

Study of the Principal Component Analysis Method for the Correction of Images Degraded by Turbulence

PREPRINT · Tristan Dagobert, Yohann Tendero, Stéphane Landeau

PREPRINT · Tristan Dagobert, Yohann Tendero, Stéphane Landeau

## Computer Graphics

Accelerating Monte Carlo Renderers by Ray Histogram Fusion

2015-03-11 · Mauricio Delbracio, Pablo Musé, Antoni Buades, Jean-Michel Morel

2015-03-11 · Mauricio Delbracio, Pablo Musé, Antoni Buades, Jean-Michel Morel

## Satellite Imaging

Attitude Refinement for Orbiting Pushbroom Cameras: a Simple Polynomial Fitting Method

2015-12-26 · Carlo de Franchis, Enric Meinhardt-Llopis, Daniel Greslou, Gabriele Facciolo

2015-12-26 · Carlo de Franchis, Enric Meinhardt-Llopis, Daniel Greslou, Gabriele Facciolo