Statistical Models for Images

Research workshop in Luminy, 17-21 May 2010



Titles and abstracts


 Practical informations 

 workshop 2008 

Titles and abstracts

  • Hermine Biermé and Agnès Desolneux, Université Paris Descartes

    Title: ``Shot noise models: applications and properties''

    Abstract: Shot noise models, also sometimes called "filtered Poisson processes", are defined as real-valued random fields, where the value at each point is the sum of the contributions of a (deterministic) kernel function centered at the points of a (random) Poisson point process. Our talk will be divided in two parts. In the first part, we will review applications of shot noise random fields in Physics and in Image Processing, mainly for texture synthesis. In the second part, we will study the properties of shot noise random fields and in the 1D case, we will describe the crossings of such a process. In particular we will be interested in the three following questions: 1) describing the behavior of the shot noise random field as the intensity of the underlying Poisson point process goes to infinity; 2) giving an explicit formula for the crossings in the 1D case; and 3) studying the particular case where the kernel function is a 1D Gaussian.

  • Toni Buades, Université Paris Descartes and CNRS

    Title: ``A note on multi-image denoising''

    Abstract: Taking photographs under low light conditions with a hand-held camera is problematic. A long exposure time can cause motion blur due to the camera shaking and a short exposure time gives a noisy image. We consider the new technical possibility offered by cameras that take image bursts. Each image of the burst is sharp but noisy. In this preliminary investigation, we explore a strategy to efficiently denoise multi-images or video. The proposed algorithm is a complex image processing chain involving accurate registration, video equalization, noise estimation and the use of state-of-the-art denoising methods. Yet, we show that this complex chain may become risk free thanks to a key feature: the noise model can be estimated accurately from the image burst. Preliminary tests will be presented. On the technical side, the method can already be used to estimate a non parametric camera noise model from any image burst.

  • Serge Cohen, Synchrotron Soleil

    Title: ``Unsupervised segmentation of images from spectro-microscopy based on gaussian mixture model and model selection''

    Abstract: Spectro-microscopy produce images composed of hundreds to thousands pixels, each pixel being characterised by a hi-resolution spectra, that is a curve of around one thousand values. The aim of this work is to perform a segmentation of the image based not only on similarities of spectra measured on each pixel, but also the spatial proximity of pixels. Here we propose to use a model selection approach where the models represent simultaneously the population of observed spectra and the segmentation of the image. The criteria is a penalised likelihood, where the penalty depends both on the number and parametrisation of cluster of spectra and on the complexity of the segmentation. Practically, to perform the segmentation, an initial non-parametric dimension reduction step with a "best approximation" target is taken. Then we carry out a Gaussian mixture modelling of the spectra, using a modified EM algorithm that performs segmentation as part of the M step, where the segmentation optimises a penalised likelihood target favouring simple segmentation. Finally a model selection step is conduced, to find the optimal number of clusters in the image (and possibly selecting the discriminating variables).
    joint work with E. Le Pennec

  • Bartomeu Coll, Universitat de les Illes Balears, Spain

    Title: ``Impact of the compression in the stereo problem''

    Abstract: Recent Earth observation satellite projects, in particular the Pleiades project (to be launched in 2010) contemplate the acquisition of quasi-simultaneous stereo pairs. This paper evaluates the impact of the (necessary) compression of the stereo pairs. It compares two compression strategies. The first compression strategy uses classic JPEG 1992 or JPEG 2000, which retain the best perceptual performance. The second compression strategy maintains a shift invariance by simply sub-sampling both views after applying an anti-aliasing Gaussian filter. The quantitative comparison of these two basic strategies shows that JPEG algorithms must compress twice less than sub-sampling to reach the same disparity precision. This dramatic result is explained by the lack of translation invariance of classic compression algorithms. Nonetheless, the sweeping conclusion is that shift invariant algorithms are better compression tools for future stereo Earth observation satellites.
    authors: G. Blanchet, A. Buades, B. Coll, J.-M. Morel and B. Rougé

  • Baptiste Coulange, Université Paris Descartes

    Title: ``An aliasing detection algorithm based on suspicious colocalizations of Fourier coefficients''

    Abstract: We propose a new algorithm to detect the presence and the localization of aliasing in a single image. Considering images in Fourier domain, the fact that two frequencies in aliasing relation contribute to similar parts of the image domain is a suspicious coincidence we detect with an a-contrario model. This leads to a localization of the aliasing phenomenon in both spatial and spectral domains, with a detection algorithm that keeps control of the number of false alarms. Experiments on several images show that this new method favorably compares to the state of the art, and opens interesting perspectives in terms of image enhancement.

  • Arnak Dalalyan, École des Ponts ParisTech

    Title: ``Robust Estimation for an Inverse Problems Arising in Multiview Geometry''

    Abstract: We propose a new approach to the problem of robust estimation for a class of inverse problems arising in multiview geometry. Inspired by recent advances in the statistical theory of recovering sparse vectors, we define our estimator as a Bayesian maximum a posteriori with multivariate Laplace prior on the vector describing the outliers. This leads to an estimator in which the fidelity to the data is measured by the L∞- norm while the regularization is done by the L1-norm. The proposed procedure is fairly fast since the outlier removal is done by solving one linear program (LP). An important difference compared to existing algorithms is that for our estimator it is not necessary to specify neither the number nor the proportion of the outliers; only an upper bound on the maximal measurement error for the inliers should be specified. We present theoretical results assessing the accuracy of our procedure, as well as numerical examples illustrating its efficiency on synthetic and real data.

  • Xavier Descombes, INRIA Sophia Antipolis

    Title: ``Marked point processes for image analysis''

    Abstract: Image sensors provide now high or very high resolution images. At this scale, the information embedded by radiometric or texture property is not sufficient to fully exploit the image content. Indeed, the geometric information becomes a key feature to describe these images. On the other, stochastic models, and especially Markov Random Fields, have proved to be a powerful framework for analyzing images. These models are mostly defined at a pixel level and are adapted to represent the contextual information. Modeling geometry by considering local potential function is hardly feasible. Markov Random Fields on graph may be a solution but they require the definition of graoh, which how mayn objects there are in the scene and what is there distribution in the space. This data means to almost solve the problem of image analysis. To overcome this limit, we propose to consider marked point process for which an object is associated to each point in the configuration, the number of objects being random. In this talk, we will consider the different aspects of the approach, that is modeling, optimizing and parameter estimating. Some examples on object detection will be given (tree, roads, flamingos,...)

  • Bruno Galerne, École Normale Supérieure de Cachan

    Title: ``Transparent dead leaves process''

    Abstract: Several classic random field models are defined in combining random objects according to a superimposition principle (e.g. linear superimposition for shot noise models, occlusion for the colored dead leaves model).
    In this talk we define and study the transparent dead leaves process (TDL process), a random field obtained in sequentially superimposing random transparent objects. Basic statistics of this new model are derived as well as a simulation algorithm. The influence of the transparency coefficient of the objects is then detailed. When the random objects are opaque, the TDL process is the randomly colored dead leaves model. On the other extreme, one shows that when the objects tends to be fully transparent, the (normalized) TDL process tends towards a Gaussian random field. In all the other cases, the TDL process is a random field with bounded variation having discontinuities almost everywhere.

  • Donald Geman, Johns Hopkins University, USA

    Title: ``A Synthetic Visual Reasoning Test''

    Abstract: I will discuss a new challenge for machine learning and computer vision that Francois Fleuret and I have designed. The SVRT consists of a series of 23 hand-designed, image-based, binary classification problems. For each task there is a generator in C++ which allows one to produce as many i.i.d samples as desired. Our intention is to expose some limitations of current methods for pattern recognition, and to argue for making a larger investment in other paradigms and strategies, emphasizing the pivotal role of relationships among parts, complex hidden states and a rich dependency structure. Another motivation is to compare the performance of humans and machines (and possibly monkeys). The human experiments are already complete, and were conducted in the laboratory of Prof. Steven Yantis, a cognitive psychologist at Johns Hopkins University. Baseline experiments with machine learning methods are underway and there is also an official "competition" (in fact a "Pascal Challenge") intended accurately asses the state-of-the-art of machine learning methods.

  • Joan Glaunès, Université Paris Descartes

    Title: ``Distributions for modelling sub-manifolds and applications to template estimation''

    Abstract: Currents are generalizations of mathematical distributions which can represent sub-manifolds of arbitrary dimension in euclidean space. They allow to represent mathematically curves and surfaces and their discretizations without any underlying specific parametrization. They can also model more specific geometrical objects such as bundles of curves, vector or tensor fields, functions defined on surfaces, etc. Next, by defining Hilbert dual norms on spaces of currents, we get a practicable notion of closeness between geometrical objects, and it becomes possible to apply some statistical methods in this framework. We will see the example of template estimation, which is of great interest for the analysis of medical images: how to estimate a geometrical template out of a collection of observed objects which are modelled as noisy deformations of the template. I will present different methods to answer this problem in the framework of currents; and I will show several applications, mainly in the field of brain imaging.

  • Yann Gousseau, Telecom ParisTech

    Title: ``Germ-grain models and image synthesis''

    Abstract: Germ-grain models enable the modeling of images by means of random shapes. In this talk, I will present several models in which shapes interact in various ways : addition (shot noise), union (boolean models), occlusion (dead leaves) or transparency. Several applications of these models will be presented, with an emphasis on texture synthesis. Then, I will show how variants of germ-grain models enable the synthesis of complex abstract images, the reproduction of stroke-based vector textures as well as the creation of image abstractions.

  • Rafael Grompone, École Normale Supérieure de Cachan

    Title: ``Towards Partial Gestalt Fusion''

    Abstract: In this talk I will present preliminary results of ongoing work toward a mathematical and computational formalization of Gestalt grouping laws. We did not try to formalize the Gestalt laws in exactly the same terms as they were expressed. Instead, we formalized some simple geometric structures that we hope include the same concepts. The structures currently analyzed are line segment chains, alignments of points and line segments, and a restricted form of parallelism that we called strokes. To evaluate the relevance of the results, we developed a perceptual test that we called the Nachtanz, that allows to compare the analysis done with these tools to human perception.

  • Laurent Itti, University of Southern California, USA

    Title: ``Statistical modeling of surprise with applications to images and videos''

    Abstract: The amount of information contained in a piece of data can be measured by the effect this data has on its observer. Fundamentally, this effect is to transform the observer's prior beliefs into posterior beliefs, according to Bayes theorem. Thus the amount of information can be measured in a natural way by the distance (relative entropy) between the prior and posterior distributions of the observer over the available space of hypotheses. This facet of information, termed ``surprise'', is important in dynamic situations where beliefs change, in particular during learning and adaptation. Surprise can often be computed analytically, for instance in the case of distributions from the exponential family, or it can be numerically approximated. During sequential Bayesian learning, surprise decreases like the inverse of the number of training examples. Theoretical properties of surprise are discussed, in particular how it differs and complements Shannon's definition of information. A computer vision neural network architecture is then presented capable of computing surprise over images and video stimuli. Hypothesizing that surprising data ought to attract natural or artificial attention systems, the output of this architecture is used in a psychophysical experiment to analyze human eye movements in the presence of natural video stimuli. Surprise is found to yield robust performance at predicting human gaze (ROC-like ordinal dominance score ~0.7 compared to ~0.8 for human inter-observer repeatability, ~0.6 for simpler intensity contrast-based predictor, and 0.5 for chance). The resulting theory of surprise is applicable across different spatio-temporal scales, modalities, and levels of abstraction.
    Joint work with Prof. Pierre Baldi, University of California Irvine.

  • Jérémie Jakubowicz, Telecom ParisTech

    Title: ``Low-resolution aircraft detection using level set statistics''

    Abstract: In this talk we will show that level sets are well suited to detect aircraft on low resolution infrared images. Aircraft correspond to hot temperatures at the sensor level. Hence it is natural to rely on a test that considers the hottest pixels in the sensed image. If these pixels are close, they are likely to come from a target; otherwise they should belong to the clutter. Instead of proposing an ad hoc procedure to test the neighborhood of each hot pixel, we rely on level sets. However, calibrating the test raise some questions about the level sets statistical properties under a random fields models. We will recall some known facts from the statistical level lines geometry theory mainly from the work of Adler & Taylor and Azais & Wschebor. After what we will conclude with some open questions.

    Adler, R. J. and Taylor, J. E., "Random Fields And Their Geometry", Springer, 2007.
    Azais, J.-M. and Wschebor, M., "Level Sets and Extrema of Random Processes and Fields", Wiley-Blackwell, 2009.

  • Ann Lee, Carnegie Mellon University, USA

    Title: ``Spectral Connectivity Analysis with an Application to Image Retrieval and Texture Discrimination''

    Abstract: For natural images, the dimension of the given input space is often very large while the data themselves have a low intrinsic dimensionality. Spectral kernel methods are non-linear techniques for transforming data into a coordinate system that efficiently reveals the geometry of the underlying distribution. In this talk, we describe ``diffusion maps''; the construction is based on a Markov random walk on the data and offers a general scheme of simultaneously reorganizing and quantizing arbitrarily shaped data sets in high dimensions using intrinsic geometry. We present a novel extension of the diffusion framework to comparing distributions in high-dimensional feature spaces with an application to image retrieval and texture discrimination.

  • Erwan Le Pennec, Université Paris 7

    Title: ``An aggregated point of view on NL-Means''

    Abstract: Patch based estimators, examplified by the Non Local Means, give results close to the state of the art despite their conceptual simplicity. Tackling their mathematical properties is still a challenge.
    In this work with J. Salmon, we propose an approach based on PAC-Bayesian aggregation techniques. The estimators obtained are, as in the NL Mean case, local weighted average of patches. The weights are different and allow to obtain some control on the peformance of these estimators.
    I would like to present the corresponding theoretical framework and explain how to deduce some estimators efficient theoretically and numerically.

  • Nicolas Lermé, Université Paris 13

    Title: ``Reducing graphs for graph cut segmentation''

    Abstract: In few years, graph cuts have become a leading method for solving a wide range of problems in computer vision and graphics. However, graph cuts involve the construction of huge graphs which sometimes do not fit in memory. Currently, most of the max-flow algorithms are totally impracticable to solve such large scale problems. In the image segmentation context, some authors have proposed banded of hierarchical approximation methods to get round this problem. We propose a new strategy for reducing graphs during the creation of the graph where the nodes of the reduced graph are typically located in a narrow band surrounding the object edges. Empirically, solutions obtained on the reduced graphs are identical to the solutions on the complete graphs. Moreover, the time required by the reduction if often compensated by the time that would be needed to create the remove nodes and the additional time required by the max-flow on the larger graph. Finally, we show experiments for segmenting large volume data in 2D and 3D.
    Keywords: segmentation, graph cut, reduction.

  • Cécile Louchet, Université d'Orléans

    Title: ``Total Variation as a local filter''

    Abstract: In the Rudin-Osher-Fatemi (ROF) image denoising model, Total Variation (TV) is used as a global regularization term. However, as we observe, the local interactions induced by Total Variation do not propagate much at long distances in practice, so that the ROF model is not far from being a local filter. In this talk, we propose to build a purely local filter by considering the ROF model in a given neighborhood of each pixel. We study theoretical properties of the obtained local filter, and show that it brings an interesting optimization of the bias-variance trade-off, and a strong reduction a ROF drawback called "staircasing effect". We finally present a new denoising algorithm, TV-means, that efficiently combines the idea of local TV-filtering with the non-local means patch-based method.

  • Julien Mairal, INRIA

    Title: ``Non-local sparse models for image restoration''

    Abstract: We propose to unify two different approaches to image restoration: On the one hand, learning a basis set (dictionary) adapted to sparse signal descriptions has proven to be very effective in image reconstruction and classification tasks. On the other hand, explicitly exploiting the self-similarities of natural images has led to the successful non-local means approach to image restoration. We propose simultaneous sparse coding as a framework for combining these two approaches in a natural manner. This is achieved by jointly decomposing groups of similar signals on subsets of the learned dictionary. Experimental results in image denoising and demosaicking tasks with synthetic and real noise show that the proposed method outperforms the state of the art, making it possible to effectively restore raw images from digital cameras at a reasonable speed and memory cost.

  • Éric Moulines, Telecom ParisTech

    Title: ``Adaptive and interacting MCMC algorithms''

    Abstract: We review adaptive Markov chain Monte Carlo algorithms (MCMC) as a mean to optimise their mixing property. Using simple examples, we introduce a general theoretical framework, covering a large number of adaptation algorithms, including both "internal" and "external" adaptations and the case where the parameter to adapt is infinite dimensional (the so-called self-interacting MCMC).
    This theory leads to guidelines concerning the design of proper algorithms. We then review criteria and propose methods which allows one to systematically optimize generally used criteria, but also analyze the properties of the resulting adaptive MCMC algorithms. We then propose a series of novel adaptive algorithms which prove to be robust and reliable in practice. The behavior of these algorithms is illustrated on some challenging simulation problems.

  • Gabriel Peyré, Université Paris-Dauphine and CNRS

    Title: ``A review of statistical texture synthesis methods, with a new one''

    Abstract: In this talk, I will survey statistical approaches to the problem of natural texture synthesis. I will focuss in particular on simple statistical constraints over transformed domains, such as oriented filter banks or wavelets. These constraints can be enforced using histogram equalization. This allows to model complicated joint densities using optimal transport algorithms, which offers a conventien unifying framework for color texture modeling. In a joint work with Julien Rabin, we are using this formalism to perform texture mixing, which allows to perform arbitrary convex combination of textures using barycentric coordinates using the Wasserstein optimal transport distance.
    Many of the proposed models can be "tested" though a series of Matlab/Scilab experiments, the "Numerical Tours of Signal Processing", section "Computer Graphics".

  • Brian Potetz, University of Kansas, USA

    Title: ``Causes & Consequences of the Nearness/Brightness Correlation in Natural Images''

    Abstract: Since Leonardo da Vinci, artists and psychologists have known that, all other things being equal, brighter stimuli are perceived to be closer than darker stimuli. Using a laser range scanner, we have shown that this perceptual bias is adaptive: in natural scenes, brighter stimuli are in fact more likely to be closer. I present evidence that this statistical tendency is caused by shadows in complex natural scenes, and discuss the implications of this with respect to previous explanations offered for the psychophysical phenomenon. Next, we show the potential that this cue has in computer vision, and demonstrate that in natural scenes, the strength of this cue can rival that of shading. Finally, we present single-cell recording data from awake behaving macaques that shows that this statistical trend is exploited in the visual system as early as V1. Specifically, cells that prefer near disparities tend to prefer brighter stimuli.

  • Maël Primet, Université Paris Descartes

    Title: ``Trajectory detection in the a-contrario framework''

    Abstract: Given a sequence of point sets, can we detect smooth trajectories that may be partially occluded and mixed to noise points? Using the a-contrario framework and dynamic programming, we obtain a parameterless algorithm that performs an exhaustive search of meaningful trajectories while controlling the number of (false) detections in pure noise sequences. The a-contrario framework also provides a simple perceptual criterion for trajectory appearances, which enables us to gain a theoretical insight on perceptual limits for the trajectory detection problem. We show the benefits and drawbacks of this approach, and compare it to state-of-the-art point tracking algorithms.

  • Frédéric Richard, Université Paris Descartes

    Title: ``Statistical analysis of anisotropic Brownian image textures''

    Abstract: In this talk, I focus on the analysis of anisotropy in image textures. To deal mathematically with this issue, I present a statistical framework gathering some anisotropic extensions of the fractional Brownian field. In this framework, I give several asymptotic results about the estimation of model parameters and the testing of anisotropy. I also present some applications to bone X-ray images and mammograms.

  • François Roueff, Telecom ParisTech

    Title: ``Weak convergence of a regularization path''

    Abstract: Consider an estimator defined as the minimizer of a goodness-of-fit measure including a penalty. The regularization path, sometimes also called the solution path, is defined as the curve described by the estimator as the penalty weight varies from zero to infinity. The higher the penalty weight, the more regular the estimator in a sense depending on the penalty choice. A quadratic penalty is often used for ill-posed inverse problems and amounts to look for solutions within an Euclidean ball. On the other hand, an absolute deviation penalty is used to impose sparse solutions. Since the choice of the penalty weight is a difficult issue, the practitionner is often interested in the whole or a part of the regularization path. It is thus important to understand how this path behaves, at least asymptotically for a large number of observations. The goal of this talk is to explain how, under fairly general conditions, this behavior is depicted by a non-central limit theorem of the regularization path, conveniently centered and normalized.

  • Neus Sabater, École Normale Supérieure de Cachan

    Title: ``Optimal Stereo Matching Reaches Theoretical Accuracy Bounds''

    Abstract: 3D reconstruction from two images requires the perfect control of a long chain of algorithms: internal and external calibration, stereo-rectification, block-matching, and 3D reconstruction. This work focuses on the crucial block-matching step. This work provides an exact mathematical formula to estimate the disparity error caused by noise. Then, this exact estimate is confirmed by a new implementation of block matching eliminating most false alarms, where the residual errors are therefore mainly due to the noise. Based on several examples we have shown that in a completely realistic setting 40% to 90% of pixels of an image could be matched with an accuracy of about 5/100 pixels. Moreover, the predicted theoretical error due to noise is nearly equal to the error achieved by our algorithm on simulated and real images pairs.

  • Hichem Sahbi, Telecom ParisTech

    Title: ``Context-Dependent Image Matching, Recognition and Retrieval''

    Abstract: Initially motivated by the success of closely related areas, "context-dependent" scene recognition and retrieval techniques are currently emerging; their general principle consists of modeling the visual appearance of objects into scenes as well as their dependencies.
    In this talk, I will focus on kernel machines for object/scene recognition and retrieval using a new class of kernels, referred to as "context-dependent" (CDKs). This class is defined as the fixed point of an energy function mixing (1) a fidelity term which measures the intrinsic visual similarity between images (2) a neighborhood criterion that captures image geometry/context and (3) a regularization term. I will also discuss some theoretical issues about the convergence of CDKs and their positive definiteness so they can be used in many kernel methods including support vector machines. Finally, I will illustrate some results mainly in object recognition, network-dependent image search, pattern matching and detection.

  • Joseph Salmon, Université Paris Diderot

    Title: ``Reprojections for Non-Local Means''

    Abstract: Since their introduction in denoising, the family of non-local methods, whose Non-Local Means (NL-Means) is the most famous member, has proved its ability to challenge other powerful methods like wavelets or variational techniques. Though simple to implement and efficient in practice, the classical NL-Means algorithm suffers from several limitations: ringing artifacts are created around edges and regions with few repetitions in the image are not treated at all. We present an easy to implement and time efficient modification of the NL-means based on a better reprojection from the patches space to the original pixels space, specially designed to reduce those artifacts.
    Authors: J. Salmon , Y.Strozecki.

  • Alain Trouvé, École Normale Supérieure de Cachan

    Title: ``The more you look, the more you see: Efficient resource allocation for optimal speed curve detection and identification in noise images''

    Abstract: Despite both problems of statistical detectability on one hand and deterministic algorithm complexity on the other hand are quite well studied, the problem of understanding the fundamental statistical and computational limits of object detection and recognition algorithms are much less explored. We propose in this talk to have a closer look at this problem in the toy but still theoretically and practically challenging situation of curve detection and identification in noise images.
    On going work with Yali Amit.

  • Tieyong Zeng, Hong Kong Baptist University, China

    Title: ``Poisson noise removal''

    Abstract: In this talk, we address a new variational approach for Poisson noise removal problem. The new proposed model contains three terms: one is from the sparse representation of the transformed image via VST; one is a data-fidelity term caused by the statistical properties of Poisson noise, and a Total Variation regularization (TV) in the transformed image domain. Comparative experiments for gray images are carried out to show the leading performance of our new model.