Journées Traitement de l'image
24-25 novembre 2011

Abstract:
Noisy image segmentation is a fundamental task in image processing applications. In this talk, we propose a review of several techniques based on the Minimum Description Length (MDL) principle, allowing one not only to take into account the grey level fluctuations, but also to obtain a segmentation technique without undetermined parameter in the optimized criterion. The optimization of this MDL criterion is performed with polygonal active contours or with polygonal active grids when the image contains an arbitrary number of regions, the goal being to estimate both the number of nodes of the polygons and their location, and the number of regions in the image. Furthermore, this approach can lead to fast algorithms (typically, less than one second on 256x256 pixel images with a standard computer). In this talk, we will mainly emphasis on recent advances, concerning notably generalizations of the MDL criterion to non-parametric probability noise models, to non-homogeneous regions and to the segmentation of smooth objects still using a polygonal description of the contour.

Abstract:
This work takes place in an ongoing effort to define meaningful distances between sattelite images used in meteorology and oceanography through L^2 optimal transport. We will report experimental results on the computation of L^2 optimal transport plans, using a dual formulation as a non-smooth convex programming problem. This formulation leads to an efficient and robust algorithm to compute L^2 optimal transport plans between the measure define by a grayscale image and a finite sum of Dirac masses, using tools from computational geometry. In a second part, we apply this approach to the standard L^2 assignment problem and compare it to Bertsekas' auction algorithm. (The second part is in collaboration with Édouard Oudet.)

Abstract:
During the last few years, diffeomorphic methods for the registration of curves and surfaces have been developed using the mathematical notion of currents. At a discrete level, curves and surfaces are approximated in this framework by sums of vector-valued Dirac functionals which encode both position and tangential information. This leads to practical algorithms which avoid the necessity of parametrization of the submanifolds. Here I will present a similar framework based on second-order currents called normal cycles which encode also curvature information. The key point is the ability to define and build reproducing kernels and their corresponding Hilbert norms in this setting, which is used as a matching criterion for curves or surfaces. This new model appears to give more accurate results and does not require to specify an orientation on the sub-manifolds to be compared. This is a very useful property in practice, when curves are composed of several disconnected components and branches. Due to their high curvature, spiky shapes are highly weighted in this normal cycle model, whereas they are disregarded in the usual currents model. This implies a very different behavior, which can be noticed on simple synthetic experiments. I will also present some applications of such registration algorithms for the analysis of brain image datasets.

Abstract:
Cosmic Microwave Background (CMB) temperature anisotropies and polarisation measurements have been one of the key cosmological probes to establish the current cosmological model. The ESA’s PLANCK mission is designed to deliver full-sky coverage, low-noise level, high resolution temperature and polarisations maps. We will briefly review some of the key problem of the PLANCK data analysis, and we will present how sparsity can be used to analyze such data set.

Abstract:
Pushbroom imagery system consists in capturing the scrolling landscape with the CCD line scan camera of a satellite. The reconstructed image is often damaged by the microvibrations of the satellite, but it can be restored if these microvibrations are known. We are dealing with 3D reconstruction where the relief is estimated from a stereoscopic image pair. We apply a variational method on the disparity map in order to keep the relief and microvibrations separate.

Abstract:
Dynamic positron emission tomography (PET) allows for noninvasive examination of physiological processes. Radioactive water (H215O) is the preferred candidate for examining myocardial blood flow because of its high diffusibility. However, the short half-time leads to noisy, low-resolution reconstructions which are then used for quantification. Instead of estimating physiological parameters from bad quality reconstructions we are incorporating a-priori information in the form of a physiological model into the reconstruction process and are identifying the physiological parameters directly form the dynamic dataset.

Abstract:
Crystalline regularization methods, like for instance the l^1 or total variation norm, became very popular due to their superior behavior in reconstructing sparse signals or sharp edges in images, however, come with the drawback of reducing the contrast of the original signals in the reconstruction procedure. We will demonstrate how inverse scale space methods can be used to restore this loss of contrast and show how the Proximal methods in CBCT and TEP tomography continuous inverse scale space flow can be computed exactly for crystalline functions

Abstract:
In the first part of this talk, I will review proximal splitting methods for the resolution of large scale non-smooth convex problems (see for instance [1,2]). I will show how each algorithm is able to take advantage of the structure of typical imaging problems. In the second part of this talk I will present the Generalized Forward Backward (GFB) splitting method [3] that is tailored for the minimization of the sum of a smooth function and an arbitrary number of "simple" functions (for which the proximal operator can be computed in closed form). I will show on several imaging applications the advantage of our approach over state of the art proximal splitting schemes. Demos and codes for these proximal splitting schemes can be obtained by visiting Numerical tours. This is a joint work with Hugo Raguet (Ceremade) and Jalal Fadili (Caen).
Bibliography:
[1] P. L. Combettes and J.-C. Pesquet, "Proximal splitting methods in signal processing," in: Fixed-Point Algorithms for Inverse Problems in Science and Engineering, pp. 185-212. Springer, New York, 2011
[2] A. Beck and M. Teboulle, "Gradient-Based Algorithms with Applications in Signal Recovery Problems",
In Convex Optimization in Signal Processing and Communications, pp. 33--88. Cambridge University Press, 2010.
[3] H. Raguet, J. Fadili and G. Peyré, "Generalized Forward-Backward Splitting", preprint HAL-00613637

Abstract:
The reconstruction of the images obtained via the Cone Beam Computerized Tomography (CBCT) and Positron Emission Tomography (PET) Scanners are ill-posed inverse problems. One needs to adress carefully the problem of inversion of the mathematical operators involved. Recent advances in optimization have yielded efficient algorithms to solve very general classes of inverse problems via the minimization of non-differentiable convex functions. We show that such models are well suited to solve the CBCT and PET reconstruction problems. On the one hand, they can incorporate directly the physics of new acquisition devices, free of dark noise; on the other hand, they can take into account the specificity of the pure Poisson noise. We propose various fast numerical schemes to recover the original data and compare them to state-of-the-art algorithms on simulated data. We study more specifically how different contrasts and resolutions may be resolved as the level of noise and/or the number of projections of the acquired sinograms decrease. We also show some numerical results with real data. This is a joint work with Sandrine Anthoine and Clothilde Mélot (LATP, Marseille), and Yannick Boursier (LATP, Marseille).

Abstract:
Regarding the topic of stochastic modeling devoted to practical issues such as analysis and synthesis of textured images, the main objective of the talk is to focus on the development of some approaches based on information theory tools. In the framework of the parametric modeling, we consider in the one hand the design of univariate and multivariate probabilistic models and in the other hand the mathematical foundations to provide adapted similarity measures leading to practical applications for which texture contents must be discriminated. Considering embedding manifolds, generative and discriminative models are proposed to address standard problems in image processing such as segmentation, supervised or unsupervised classification and indexing.

Abstract:
In this work, we present a novel hyperspectral image segmentation method base on a Gaussian Mixture Model with mixing weights varying spatialy. We show how to estimate efficiently all the parameters of the model, including the number of classes, by a penalized maximum likelihood principle. We present experiments on real datasets.