Publications by authors named "Xavier Bresson"

19 Publications

  • Page 1 of 1

Multigraph Transformer for Free-Hand Sketch Recognition.

IEEE Trans Neural Netw Learn Syst 2021 Apr 7;PP. Epub 2021 Apr 7.

Learning meaningful representations of free-hand sketches remains a challenging task given the signal sparsity and the high-level abstraction of sketches. Existing techniques have focused on exploiting either the static nature of sketches with convolutional neural networks (CNNs) or the temporal sequential property with recurrent neural networks (RNNs). In this work, we propose a new representation of sketches as multiple sparsely connected graphs. We design a novel graph neural network (GNN), the multigraph transformer (MGT), for learning representations of sketches from multiple graphs, which simultaneously capture global and local geometric stroke structures as well as temporal information. We report extensive numerical experiments on a sketch recognition task to demonstrate the performance of the proposed approach. Particularly, MGT applied on 414k sketches from Google QuickDraw: 1) achieves a small recognition gap to the CNN-based performance upper bound (72.80% versus 74.22%) and infers faster than the CNN competitors and 2) outperforms all RNN-based models by a significant margin. To the best of our knowledge, this is the first work proposing to represent sketches as graphs and apply GNNs for sketch recognition. Code and trained models are available at https://github.com/PengBoXiangShang/multigraph_transformer.
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http://dx.doi.org/10.1109/TNNLS.2021.3069230DOI Listing
April 2021

Transient networks of spatio-temporal connectivity map communication pathways in brain functional systems.

Neuroimage 2017 07 12;155:490-502. Epub 2017 Apr 12.

Department of Radiology, Centre Hospitalier Universitaire Vaudois (CHUV) and University of Lausanne (UNIL), Lausanne 1011, Switzerland; Signal Processing Laboratory 5 (LTS5), École Polytechnique Fédérale de Lausanne (EPFL), Lausanne 1015, Switzerland.

The study of brain dynamics enables us to characterize the time-varying functional connectivity among distinct neural groups. However, current methods suffer from the absence of structural connectivity information. We propose to integrate infra-slow neural oscillations and anatomical-connectivity maps, as derived from functional and diffusion MRI, in a multilayer-graph framework that captures transient networks of spatio-temporal connectivity. These networks group anatomically wired and temporary synchronized brain regions and encode the propagation of functional activity on the structural connectome. In a group of 71 healthy subjects, we find that these transient networks demonstrate power-law spatial and temporal size, globally organize into well-known functional systems and describe wave-like trajectories of activation across anatomically connected regions. Within the transient networks, activity propagates through polysynaptic paths that include selective ensembles of structural connections and differ from the structural shortest paths. In the light of the communication-through-coherence principle, the identified spatio-temporal networks could encode communication channels' selection and neural assemblies, which deserves further attention. This work contributes to the understanding of brain structure-function relationships by considering the time-varying nature of resting-state interactions on the axonal scaffold, and it offers a convenient framework to study large-scale communication mechanisms and functional dynamics.
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http://dx.doi.org/10.1016/j.neuroimage.2017.04.015DOI Listing
July 2017

An efficient total variation algorithm for super-resolution in fetal brain MRI with adaptive regularization.

Neuroimage 2015 Sep 10;118:584-97. Epub 2015 Jun 10.

Centre d'Imagerie BioMédicale (CIBM), Switzerland; Radiology department, Lausanne University Hospital Center (CHUV), University of Lausanne (UNIL), Switzerland; Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland.

Although fetal anatomy can be adequately viewed in new multi-slice MR images, many critical limitations remain for quantitative data analysis. To this end, several research groups have recently developed advanced image processing methods, often denoted by super-resolution (SR) techniques, to reconstruct from a set of clinical low-resolution (LR) images, a high-resolution (HR) motion-free volume. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has been quite attracted by Total Variation energies because of their ability in edge preserving but only standard explicit steepest gradient techniques have been applied for optimization. In a preliminary work, it has been shown that novel fast convex optimization techniques could be successfully applied to design an efficient Total Variation optimization algorithm for the super-resolution problem. In this work, two major contributions are presented. Firstly, we will briefly review the Bayesian and Variational dual formulations of current state-of-the-art methods dedicated to fetal MRI reconstruction. Secondly, we present an extensive quantitative evaluation of our SR algorithm previously introduced on both simulated fetal and real clinical data (with both normal and pathological subjects). Specifically, we study the robustness of regularization terms in front of residual registration errors and we also present a novel strategy for automatically select the weight of the regularization as regards the data fidelity term. Our results show that our TV implementation is highly robust in front of motion artifacts and that it offers the best trade-off between speed and accuracy for fetal MRI recovery as in comparison with state-of-the art methods.
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http://dx.doi.org/10.1016/j.neuroimage.2015.06.018DOI Listing
September 2015

Adaptive regularization with the structure tensor.

IEEE Trans Image Process 2015 Jun 6;24(6):1777-90. Epub 2015 Mar 6.

Natural images exhibit geometric structures that are informative of the properties of the underlying scene. Modern image processing algorithms respect such characteristics by employing regularizers that capture the statistics of natural images. For instance, total variation (TV) respects the highly kurtotic distribution of the pointwise gradient by allowing for large magnitude outlayers. However, the gradient magnitude alone does not capture the directionality and scale of local structures in natural images. The structure tensor provides a more meaningful description of gradient information as it describes both the size and orientation of the image gradients in a neighborhood of each point. Based on this observation, we propose a variational model for image reconstruction that employs a regularization functional adapted to the local geometry of image by means of its structure tensor. Our method alternates two minimization steps: 1) robust estimation of the structure tensor as a semidefinite program and 2) reconstruction of the image with an adaptive regularizer defined from this tensor. This two-step procedure allows us to extend anisotropic diffusion into the convex setting and develop robust, efficient, and easy-to-code algorithms for image denoising, deblurring, and compressed sensing. Our method extends naturally to nonlocal regularization, where it exploits the local self-similarity of natural images to improve nonlocal TV and diffusion operators. Our experiments show a consistent accuracy improvement over classic regularization.
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http://dx.doi.org/10.1109/TIP.2015.2409562DOI Listing
June 2015

Efficient total variation algorithm for fetal brain MRI reconstruction.

Med Image Comput Comput Assist Interv 2014 ;17(Pt 2):252-9

Fetal MRI reconstruction aims at finding a high-resolution image given a small set of low-resolution images. It is usually modeled as an inverse problem where the regularization term plays a central role in the reconstruction quality. Literature has considered several regularization terms s.a. Dirichlet/Laplacian energy, Total Variation (TV)- based energies and more recently non-local means. Although TV energies are quite attractive because of their ability in edge preservation, standard explicit steepest gradient techniques have been applied to optimize fetal-based TV energies. The main contribution of this work lies in the introduction of a well-posed TV algorithm from the point of view of convex optimization. Specifically, our proposed TV optimization algorithm or fetal reconstruction is optimal w.r.t. the asymptotic and iterative convergence speeds O(1/n2) and O(1/√ε), while existing techniques are in O(1/n2) and O(1/√ε). We apply our algorithm to (1) clinical newborn data, considered as ground truth, and (2) clinical fetal acquisitions. Our algorithm compares favorably with the literature in terms of speed and accuracy.
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http://dx.doi.org/10.1007/978-3-319-10470-6_32DOI Listing
January 2015

Semi-supervised segmentation of ultrasound images based on patch representation and continuous min cut.

PLoS One 2014 10;9(7):e100972. Epub 2014 Jul 10.

Signal Processing Laboratory (LTS5), École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland; Department of Radiology, University Hospital Center and University of Lausanne, Lausanne, Switzerland; Center for Biomedical Imaging, Signal Processing Core, Lausanne, Switzerland.

Ultrasound segmentation is a challenging problem due to the inherent speckle and some artifacts like shadows, attenuation and signal dropout. Existing methods need to include strong priors like shape priors or analytical intensity models to succeed in the segmentation. However, such priors tend to limit these methods to a specific target or imaging settings, and they are not always applicable to pathological cases. This work introduces a semi-supervised segmentation framework for ultrasound imaging that alleviates the limitation of fully automatic segmentation, that is, it is applicable to any kind of target and imaging settings. Our methodology uses a graph of image patches to represent the ultrasound image and user-assisted initialization with labels, which acts as soft priors. The segmentation problem is formulated as a continuous minimum cut problem and solved with an efficient optimization algorithm. We validate our segmentation framework on clinical ultrasound imaging (prostate, fetus, and tumors of the liver and eye). We obtain high similarity agreement with the ground truth provided by medical expert delineations in all applications (94% DICE values in average) and the proposed algorithm performs favorably with the literature.
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http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0100972PLOS
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC4091944PMC
March 2015

Harmonic active contours.

IEEE Trans Image Process 2014 Jan 18;23(1):69-82. Epub 2013 Oct 18.

We propose a segmentation method based on the geometric representation of images as 2-D manifolds embedded in a higher dimensional space. The segmentation is formulated as a minimization problem, where the contours are described by a level set function and the objective functional corresponds to the surface of the image manifold. In this geometric framework, both data-fidelity and regularity terms of the segmentation are represented by a single functional that intrinsically aligns the gradients of the level set function with the gradients of the image and results in a segmentation criterion that exploits the directional information of image gradients to overcome image inhomogeneities and fragmented contours. The proposed formulation combines this robust alignment of gradients with attractive properties of previous methods developed in the same geometric framework: 1) the natural coupling of image channels proposed for anisotropic diffusion and 2) the ability of subjective surfaces to detect weak edges and close fragmented boundaries. The potential of such a geometric approach lies in the general definition of Riemannian manifolds, which naturally generalizes existing segmentation methods (the geodesic active contours, the active contours without edges, and the robust edge integrator) to higher dimensional spaces, non-flat images, and feature spaces. Our experiments show that the proposed technique improves the segmentation of multi-channel images, images subject to inhomogeneities, and images characterized by geometric structures like ridges or valleys.
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http://dx.doi.org/10.1109/TIP.2013.2286326DOI Listing
January 2014

Evaluation and comparison of current fetal ultrasound image segmentation methods for biometric measurements: a grand challenge.

IEEE Trans Med Imaging 2014 Apr 6;33(4):797-813. Epub 2013 Aug 6.

This paper presents the evaluation results of the methods submitted to Challenge US: Biometric Measurements from Fetal Ultrasound Images, a segmentation challenge held at the IEEE International Symposium on Biomedical Imaging 2012. The challenge was set to compare and evaluate current fetal ultrasound image segmentation methods. It consisted of automatically segmenting fetal anatomical structures to measure standard obstetric biometric parameters, from 2D fetal ultrasound images taken on fetuses at different gestational ages (21 weeks, 28 weeks, and 33 weeks) and with varying image quality to reflect data encountered in real clinical environments. Four independent sub-challenges were proposed, according to the objects of interest measured in clinical practice: abdomen, head, femur, and whole fetus. Five teams participated in the head sub-challenge and two teams in the femur sub-challenge, including one team who tackled both. Nobody attempted the abdomen and whole fetus sub-challenges. The challenge goals were two-fold and the participants were asked to submit the segmentation results as well as the measurements derived from the segmented objects. Extensive quantitative (region-based, distance-based, and Bland-Altman measurements) and qualitative evaluation was performed to compare the results from a representative selection of current methods submitted to the challenge. Several experts (three for the head sub-challenge and two for the femur sub-challenge), with different degrees of expertise, manually delineated the objects of interest to define the ground truth used within the evaluation framework. For the head sub-challenge, several groups produced results that could be potentially used in clinical settings, with comparable performance to manual delineations. The femur sub-challenge had inferior performance to the head sub-challenge due to the fact that it is a harder segmentation problem and that the techniques presented relied more on the femur's appearance.
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http://dx.doi.org/10.1109/TMI.2013.2276943DOI Listing
April 2014

Enhanced compressed sensing recovery with level set normals.

IEEE Trans Image Process 2013 Jul 20;22(7):2611-26. Epub 2013 Mar 20.

Signal Processing Laboratory, Ecole Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland.

We propose a compressive sensing algorithm that exploits geometric properties of images to recover images of high quality from few measurements. The image reconstruction is done by iterating the two following steps: 1) estimation of normal vectors of the image level curves, and 2) reconstruction of an image fitting the normal vectors, the compressed sensing measurements, and the sparsity constraint. The proposed technique can naturally extend to nonlocal operators and graphs to exploit the repetitive nature of textured images to recover fine detail structures. In both cases, the problem is reduced to a series of convex minimization problems that can be efficiently solved with a combination of variable splitting and augmented Lagrangian methods, leading to fast and easy-to-code algorithms. Extended experiments show a clear improvement over related state-of-the-art algorithms in the quality of the reconstructed images and the robustness of the proposed method to noise, different kind of images, and reduced measurements.
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http://dx.doi.org/10.1109/TIP.2013.2253484DOI Listing
July 2013

Fast Geodesic Active Fields for Image Registration Based on Splitting and Augmented Lagrangian Approaches.

IEEE Trans Image Process 2014 Feb 20;23(2):673-83. Epub 2013 Mar 20.

In this paper, we present an efficient numerical scheme for the recently introduced geodesic active fields (GAF) framework for geometric image registration. This framework considers the registration task as a weighted minimal surface problem. Hence, the data-term and the regularization-term are combined through multiplication in a single, parametrization invariant and geometric cost functional. The multiplicative coupling provides an intrinsic, spatially varying and data-dependent tuning of the regularization strength, and the parametrization invariance allows working with images of nonflat geometry, generally defined on any smoothly parametrizable manifold. The resulting energy-minimizing flow, however, has poor numerical properties. Here, we provide an efficient numerical scheme that uses a splitting approach; data and regularity terms are optimized over two distinct deformation fields that are constrained to be equal via an augmented Lagrangian approach. Our approach is more flexible than standard Gaussian regularization, since one can interpolate freely between isotropic Gaussian and anisotropic TV-like smoothing. In this paper, we compare the geodesic active fields method with the popular Demons method and three more recent state-of-the-art algorithms: NL-optical flow, MRF image registration, and landmark-enhanced large displacement optical flow. Thus, we can show the advantages of the proposed FastGAF method. It compares favorably against Demons, both in terms of registration speed and quality. Over the range of example applications, it also consistently produces results not far from more dedicated state-of-the-art methods, illustrating the flexibility of the proposed framework.
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http://dx.doi.org/10.1109/TIP.2013.2253473DOI Listing
February 2014

Efficient algorithm for level set method preserving distance function.

IEEE Trans Image Process 2012 Dec 5;21(12):4722-34. Epub 2012 Jun 5.

Signal Processing Laboratory, École Polytechnique Fédérale de Lausanne, Lausanne 1015, Switzerland.

The level set method is a popular technique for tracking moving interfaces in several disciplines, including computer vision and fluid dynamics. However, despite its high flexibility, the original level set method is limited by two important numerical issues. First, the level set method does not implicitly preserve the level set function as a distance function, which is necessary to estimate accurately geometric features, s.a. the curvature or the contour normal. Second, the level set algorithm is slow because the time step is limited by the standard Courant-Friedrichs-Lewy (CFL) condition, which is also essential to the numerical stability of the iterative scheme. Recent advances with graph cut methods and continuous convex relaxation methods provide powerful alternatives to the level set method for image processing problems because they are fast, accurate, and guaranteed to find the global minimizer independently to the initialization. These recent techniques use binary functions to represent the contour rather than distance functions, which are usually considered for the level set method. However, the binary function cannot provide the distance information, which can be essential for some applications, s.a. the surface reconstruction problem from scattered points and the cortex segmentation problem in medical imaging. In this paper, we propose a fast algorithm to preserve distance functions in level set methods. Our algorithm is inspired by recent efficient l(1) optimization techniques, which will provide an efficient and easy to implement algorithm. It is interesting to note that our algorithm is not limited by the CFL condition and it naturally preserves the level set function as a distance function during the evolution, which avoids the classical re-distancing problem in level set methods. We apply the proposed algorithm to carry out image segmentation, where our methods prove to be 5-6 times faster than standard distance preserving level set techniques. We also present two applications where preserving a distance function is essential. Nonetheless, our method stays generic and can be applied to any level set methods that require the distance information.
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http://dx.doi.org/10.1109/TIP.2012.2202674DOI Listing
December 2012

Active deformation fields: dense deformation field estimation for atlas-based segmentation using the active contour framework.

Med Image Anal 2011 Dec 23;15(6):787-800. Epub 2011 May 23.

Signal Processing Laboratory (LTS5), Ecole Polytechnique Fédérale de Lausanne (EPFL), Switzerland.

This paper presents a new and original variational framework for atlas-based segmentation. The proposed framework integrates both the active contour framework, and the dense deformation fields of optical flow framework. This framework is quite general and encompasses many of the state-of-the-art atlas-based segmentation methods. It also allows to perform the registration of atlas and target images based on only selected structures of interest. The versatility and potentiality of the proposed framework are demonstrated by presenting three diverse applications: In the first application, we show how the proposed framework can be used to simulate the growth of inconsistent structures like a tumor in an atlas. In the second application, we estimate the position of nonvisible brain structures based on the surrounding structures and validate the results by comparing with other methods. In the final application, we present the segmentation of lymph nodes in the Head and Neck CT images, and demonstrate how multiple registration forces can be used in this framework in an hierarchical manner.
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http://dx.doi.org/10.1016/j.media.2011.05.008DOI Listing
December 2011

Geodesic active fields--a geometric framework for image registration.

IEEE Trans Image Process 2011 May 18;20(5):1300-12. Epub 2010 Nov 18.

Signal Processing Laboratory, Ecole Polytechnique Fédérale de Lausanne, CH-1015 Lausanne, Switzerland.

In this paper we present a novel geometric framework called geodesic active fields for general image registration. In image registration, one looks for the underlying deformation field that best maps one image onto another. This is a classic ill-posed inverse problem, which is usually solved by adding a regularization term. Here, we propose a multiplicative coupling between the registration term and the regularization term, which turns out to be equivalent to embed the deformation field in a weighted minimal surface problem. Then, the deformation field is driven by a minimization flow toward a harmonic map corresponding to the solution of the registration problem. This proposed approach for registration shares close similarities with the well-known geodesic active contours model in image segmentation, where the segmentation term (the edge detector function) is coupled with the regularization term (the length functional) via multiplication as well. As a matter of fact, our proposed geometric model is actually the exact mathematical generalization to vector fields of the weighted length problem for curves and surfaces introduced by Caselles-Kimmel-Sapiro. The energy of the deformation field is measured with the Polyakov energy weighted by a suitable image distance, borrowed from standard registration models. We investigate three different weighting functions, the squared error and the approximated absolute error for monomodal images, and the local joint entropy for multimodal images. As compared to specialized state-of-the-art methods tailored for specific applications, our geometric framework involves important contributions. Firstly, our general formulation for registration works on any parametrizable, smooth and differentiable surface, including nonflat and multiscale images. In the latter case, multiscale images are registered at all scales simultaneously, and the relations between space and scale are intrinsically being accounted for. Second, this method is, to the best of our knowledge, the first reparametrization invariant registration method introduced in the literature. Thirdly, the multiplicative coupling between the registration term, i.e. local image discrepancy, and the regularization term naturally results in a data-dependent tuning of the regularization strength. Finally, by choosing the metric on the deformation field one can freely interpolate between classic Gaussian and more interesting anisotropic, TV-like regularization.
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http://dx.doi.org/10.1109/TIP.2010.2093904DOI Listing
May 2011

Nonlocal Mumford-Shah regularizers for color image restoration.

IEEE Trans Image Process 2011 Jun 15;20(6):1583-98. Epub 2010 Nov 15.

Department of Mathematics, University of California, Los Angeles, CA 90095, USA.

We propose here a class of restoration algorithms for color images, based upon the Mumford-Shah (MS) model and nonlocal image information. The Ambrosio-Tortorelli and Shah elliptic approximations are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, texture is nonlocal in nature and requires semilocal/non-local information for efficient image denoising and restoration. Inspired from recent works (nonlocal means of Buades, Coll, Morel, and nonlocal total variation of Gilboa, Osher), we extend the local Ambrosio-Tortorelli and Shah approximations to MS functional (MS) to novel nonlocal formulations, for better restoration of fine structures and texture. We present several applications of the proposed nonlocal MS regularizers in image processing such as color image denoising, color image deblurring in the presence of Gaussian or impulse noise, color image inpainting, color image super-resolution, and color filter array demosaicing. In all the applications, the proposed nonlocal regularizers produce superior results over the local ones, especially in image inpainting with large missing regions. We also prove several characterizations of minimizers based upon dual norm formulations.
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http://dx.doi.org/10.1109/TIP.2010.2092433DOI Listing
June 2011

An active contour-based atlas registration model applied to automatic subthalamic nucleus targeting on MRI: method and validation.

Med Image Comput Comput Assist Interv 2008 ;11(Pt 2):980-8

Signal Processing Laboratory (LTS5), EPFL, CH-1015 Lausanne.

This paper presents a new non parametric atlas registration framework, derived from the optical flow model and the active contour theory, applied to automatic subthalamic nucleus (STN) targeting in deep brain stimulation (DBS) surgery. In a previous work, we demonstrated that the STN position can be predicted based on the position of surrounding visible structures, namely the lateral and third ventricles. A STN targeting process can thus be obtained by registering these structures of interest between a brain atlas and the patient image. Here we aim to improve the results of the state of the art targeting methods and at the same time to reduce the computational time. Our simultaneous segmentation and registration model shows mean STN localization errors statistically similar to the most performing registration algorithms tested so far and to the targeting expert's variability. Moreover, the computational time of our registration method is much lower, which is a worthwhile improvement from a clinical point of view.
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http://dx.doi.org/10.1007/978-3-540-85990-1_118DOI Listing
December 2008

Representing diffusion MRI in 5-D simplifies regularization and segmentation of white matter tracts.

IEEE Trans Med Imaging 2007 Nov;26(11):1547-54

Signal Processing Institute (ITS), Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland.

We present a new five-dimensional (5-D) space representation of diffusion magnetic resonance imaging (dMRI) of high angular resolution. This 5-D space is basically a non-Euclidean space of position and orientation in which crossing fiber tracts can be clearly disentangled, that cannot be separated in three-dimensional position space. This new representation provides many possibilities for processing and analysis since classical methods for scalar images can be extended to higher dimensions even if the spaces are not Euclidean. In this paper, we show examples of how regularization and segmentation of dMRI is simplified with this new representation. The regularization is used with the purpose of denoising and but also to facilitate the segmentation task by using several scales, each scale representing a different level of resolution. We implement in five dimensions the Chan-Vese method combined with active contours without edges for the segmentation and the total variation functional for the regularization. The purpose of this paper is to explore the possibility of segmenting white matter structures directly as entirely separated bundles in this 5-D space. We will present results from a synthetic model and results on real data of a human brain acquired with diffusion spectrum magnetic resonance imaging (MRI), one of the dMRI of high angular resolution available. These results will lead us to the conclusion that this new high-dimensional representation indeed simplifies the problem of segmentation and regularization.
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http://dx.doi.org/10.1109/TMI.2007.899168DOI Listing
November 2007

Scale space analysis and active contours for omnidirectional images.

IEEE Trans Image Process 2007 Jul;16(7):1888-901

Insitute of Microtechnology, Université de Neuchâtel, 2000 Neuchâtel, Switzerland.

A new generation of optical devices that generate images covering a larger part of the field of view than conventional cameras, namely catadioptric cameras, is slowly emerging. These omnidirectional images will most probably deeply impact computer vision in the forthcoming years, provided that the necessary algorithmic background stands strong. In this paper, we propose a general framework that helps define various computer vision primitives. We show that geometry, which plays a central role in the formation of omnidirectional images, must be carefully taken into account while performing such simple tasks as smoothing or edge detection. Partial differential equations (PDEs) offer a very versatile tool that is well suited to cope with geometrical constraints. We derive new energy functionals and PDEs for segmenting images obtained from catadioptric cameras and show that they can be implemented robustly using classical finite difference schemes. Various experimental results illustrate the potential of these new methods on both synthetic and natural images.
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http://dx.doi.org/10.1109/tip.2007.899008DOI Listing
July 2007

Representing diffusion MRI in 5D for segmentation of white matter tracts with a level set method.

Inf Process Med Imaging 2005 ;19:311-20

Signal Processing Institute (ITS), Swiss Federal Institute of Technology (EPFL), CH-1015 Lausanne, Switzerland.

We present a method for segmenting white matter tracts from high angular resolution diffusion MR. images by representing the data in a 5 dimensional space of position and orientation. Whereas crossing fiber tracts cannot be separated in 3D position space, they clearly disentangle in 5D position-orientation space. The segmentation is done using a 5D level set method applied to hyper-surfaces evolving in 5D position-orientation space. In this paper we present a methodology for constructing the position-orientation space. We then show how to implement the standard level set method in such a non-Euclidean high dimensional space. The level set theory is basically defined for N-dimensions but there are several practical implementation details to consider, such as mean curvature. Finally, we will show results from a synthetic model and a few preliminary results on real data of a human brain acquired by high angular resolution diffusion MRI.
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http://dx.doi.org/10.1007/11505730_26DOI Listing
April 2007

White matter fiber tract segmentation in DT-MRI using geometric flows.

Med Image Anal 2005 Jun;9(3):223-36

Signal Processing Institute (ITS), Swiss Federal Institute of Technology, (EPFL), CH-1015 Lausanne, Switzerland.

In this paper, we present a 3D geometric flow designed to segment the main core of fiber tracts in diffusion tensor magnetic resonance images. The fundamental assumption of our fiber segmentation technique is that adjacent voxels in a tract have similar properties of diffusion. The fiber segmentation is carried out with a front propagation algorithm constructed to fill the whole fiber tract. The front is a 3D surface that evolves with a propagation speed proportional to a measure indicating the similarity of diffusion between the tensors lying on the surface and their neighbors in the direction of propagation. We use a level set implementation to assure a stable and accurate evolution of the surface and to handle changes of topology of the surface during the evolution process. The fiber tract segmentation method does not need a regularized tensor field since the surface is automatically smoothed as it propagates. The smoothing is done by an intrinsic surface force, based on the minimal principal curvature. This segmentation can be used for obtaining quantitative measures of the diffusion in the fiber tracts and it can also be used for white matter registration and for surgical planning.
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http://dx.doi.org/10.1016/j.media.2004.07.004DOI Listing
June 2005