Xavier Bresson

Swiss Federal Institute of Technology in Lausanne | EPFL

MR Image segmentation and reconstruction have traditionally been regarded as separate processes. Recently, a novel joint reconstruction-segmentation framework[1] showed that incorporating a segmentation prior in the compressed-sensing reconstruction process of MR images provides a segmentation that degrades less with increasing undersampling compar...

Graph-structured data such as functional brain networks, social networks, gene regulatory networks, communications networks have brought the interest in generalizing neural networks to graph domains. In this paper, we are interested to de- sign efficient neural network architectures for graphs with variable length. Several existing works such as Sc...

The rise of graph-structured data such as social networks, regulatory networks, citation graphs, and functional brain networks, in combination with resounding success of deep learning in various applications, has brought the interest in generalizing deep learning models to non-Euclidean domains. In this paper, we introduce a new spectral domain con...

Matrix completion models are among the most common formulations of recommender systems. Recent works have showed a boost of performance of these techniques when introducing the pairwise relationships between users/items in the form of graphs, and imposing smoothness priors on these graphs. However, such techniques do not fully exploit the local sta...

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,...

This paper introduces Graph Convolutional Recurrent Network (GCRN), a deep learning model able to predict structured sequences of data. Precisely, GCRN is a generalization of classical recurrent neural networks (RNN) to data structured by an arbitrary graph. Such structured sequences can represent series of frames in videos, spatio-temporal measure...

We present a new music dataset that can be used for several music analysis tasks. Our major goal is to go beyond the existing limitations of available music datasets, which are either the small size of datasets with raw audio tracks, the availability and legality of the music data, or the lack of meta-data for artists analysis or song ratings for r...

We cast the problem of source localization on graphs as the simultaneous problem of sparse recovery and diffusion kernel learning. An l1 regularization term enforces the sparsity constraint while we recover the sources of diffusion from a single snapshot of the diffusion process. The diffusion kernel is estimated by assuming the process to be as ge...

Convolutional neural networks (CNNs) have greatly improved state-of-the-art performances in a number of fields, notably computer vision and natural language processing. In this work, we are interested in generalizing the formulation of CNNs from low-dimensional regular Euclidean domains, where images (2D), videos (3D) and audios (1D) are represente...

We cast the problem of source localization on graphs as the simultaneous problem of sparse recovery and diffusion ker- nel learning. An l1 regularization term enforces the sparsity constraint while we recover the sources of diffusion from a single snapshot of the diffusion process. The diffusion ker- nel is estimated by assuming the process to be a...

This work formulates a novel song recommender system as a matrix completion problem that benefits from collaborative filtering through Non-negative Matrix Factorization (NMF) and content-based filtering via total variation (TV) on graphs. The graphs encode both playlist proximity information and song similarity, using a rich combination of audio, m...

This work aims at recovering signals that are sparse on graphs. Compressed sensing offers techniques for signal recovery from a few linear measurements and graph Fourier analysis provides a signal representation on graph. In this paper, we leverage these two frameworks to introduce a new Lasso recovery algorithm on graphs. More precisely, we presen...

This work aims at recovering signals that are sparse on graphs. Compressed sensing offers techniques for signal recovery from a few linear measurements and graph Fourier analysis provides a signal representation on graph. In this paper, we leverage these two frameworks to introduce a new Lasso recovery algorithm on graphs. More precisely, we presen...

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) im...

Principal Component Analysis (PCA) is the most widely used tool for linear dimensionality reduction and clustering. Still it is highly sensitive to outliers and does not scale well with respect to the number of data samples. Robust PCA solves the first issue with a sparse penalty term. The second issue can be handled with the matrix factorization m...

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...

In this paper, we consider the problem of finding dense intrinsic correspondence between manifolds using the recently introduced functional framework. We pose the functional correspondence problem as matrix completion with manifold geometric structure and inducing functional localization with the $L_1$ norm. We discuss efficient numerical procedure...

This paper establishes the consistency of a family of graph-cut-based algorithms for clustering of data clouds. We consider point clouds obtained as samples of a ground-truth measure. We investigate approaches to clustering based on minimizing objective functionals defined on proximity graphs of the given sample. Our focus is on functionals based o...

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...

The problem of finding the missing values of a matrix given a few of its entries, called matrix completion, has gathered a lot of attention in the recent years. Although the problem is NP-hard, Cand\`es and Recht showed that it can be exactly relaxed if the matrix is low-rank and the number of observed entries is sufficiently large. In this work, w...

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...

In this work we propose a simple and easily parallelizable algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, and then randomly reseeding the thresholded clusters. We demonstrate experimentally that the proper combination of the...

In fetal brain MRI, most of the high-resolution reconstruction algorithms rely on brain segmentation as a preprocessing step. Manual brain segmentation is highly time-consuming and therefore not a realistic solution for large-scale studies. Only few works have addressed this automatic extraction problem. In this study, we assess the validity of Mul...

Recent advances in ℓ 1 optimization for imaging problems provide promising tools to solve the fundamental high-dimensional data classification in machine learning. In this paper, we extend the main result of Szlam and Bresson (Proceedings of the 27th International Conference on Machine Learning, pp. 1039–1046, 2010), which introduced an exact ℓ 1 r...

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 aut...

We propose a segmentation method based on the geometric representation of images as two-dimensional 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 thi...

Image segmentation is an essential problem in imaging science. One of the most successful segmentation models is the piecewise constant Mumford-Shah minimization model. This minimization problem is however difficult to carry out, mainly due to the non-convexity of the energy. Recent advances based on convex relaxation methods are capable of estimat...

Ideas from the image processing literature have recently motivated a new set of clustering algorithms that rely on the concept of total variation. While these algorithms perform well for bi-partitioning tasks, their recursive extensions yield unimpressive results for multiclass clustering tasks. This paper presents a general framework for multiclas...

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, data-term and regularization term are combined trough multiplication in a single, parametrization inv...

We propose an adaptive version of the total variation algorithm proposed in [3] for computing the balanced cut of a graph. The algorithm from [3] used a sequence of inner total variation minimizations to guarantee descent of the balanced cut energy as well as convergence of the algorithm. In practice the total variation minimization step is never s...

Many problems in image processing can be posed as non-convex minimization problems. For certain classes of non-convex problems involving scalar-valued functions, it is possible to recast the problem in a convex form using a "functional lifting" technique. In this paper, we present a variational functional lifting technique that can be viewed as a g...

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...

We introduce semi-supervised data classification algorithms based on total variation (TV), Reproducing Kernel Hilbert Space (RKHS), support vector machine (SVM), Cheeger cut, labeled and unlabeled data points. We design binary and multi-class semi-supervised classification algorithms. We compare the TV-based classification algorithms with the relat...

Ultrasound image segmentation is very challenging due to the inherent speckle, artifacts, shadows, attenuation, and signal dropout, present in the images. Existing methods must include strong priors like shape priors or analytical intensity models to succeed in the segmen-tation. This paper presents an efficient semi-supervised segmentation method...

The level set method [1] 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. Firstly, the level set method does not implicitly preserve the level set function as a...

Ultrasound segmentation is very challenging due to the in-herent speckle and some artifacts like shadows, attenuation and signal dropout. Existing methods must include strong pri-ors like shape priors or analytical intensity models to succeed in the segmentation. We present an efficient semi-supervised segmentation method for ultrasound segmentatio...

The active contours without edges model of Chan and Vese (IEEE Transactions on Image Processing 10(2):266–277, 2001) is a popular method for computing the segmentation of an image into two phases, based on the piecewise constant Mumford-Shah model. The minimization problem is non-convex even when the optimal region constants are known a priori. In...

Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Tight continuous relaxations of balanced cut problems have recently been shown to provide excellent clustering results. In this paper, we present an explicit-implicit gradient flow scheme for the relaxed ratio cut problem, and prove t...

Unsupervised clustering of scattered, noisy and high-dimensional data points is an important and difficult problem. Continuous relaxations of balanced cut problems yield excellent clustering results. This paper provides rigorous convergence results for two algorithms that solve the relaxed Cheeger Cut minimization. The first algorithm is a new stee...

We propose a segmentation method based on the geometric representation of images as surfaces embedded in a higher dimensional space, handling naturally multichannel images. The segmentation is based on an active contour embedded in the image manifold, along with a set of image features. Hence, both data-fidelity and regularity terms of the active c...

Surface reconstruction from a set of noisy point measurements has been a well studied problem for several decades. Recently, variational and discrete optimization approaches have been applied to solve it, demonstrating good robustness to outliers thanks to a global energy minimization scheme. In this work, we use a recent approach embedding several...

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 n...

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 to embe...

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 p...

Segmenting ultrasound images is a challenging problem where standard unsupervised segmentation methods such as the well-known Chan-Vese method fail. We propose in this paper an efficient segmentation method for this class of images. Our proposed algorithm is based on a semi-supervised approach (user labels) and the use of image patches as data feat...

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, data-term and regularization term are combined trough multiplication in a single, parametrization inv...

In this paper, we extend the Chan-Vese model for image segmentation in [1] to hyperspectral image segmentation with shape and signal priors. The use of the Split Bregman algorithm makes our method very efficient compared to other existing segmentation methods incorporating priors. We demonstrate our results on aerial hyperspectral images.

Variational models for image segmentation have many applications, but can be slow to compute. Recently, globally convex segmentation models have been introduced which are very reliable, but contain TV- regularizers, making them dicult to compute. The previously intro- duced Split Bregman method is a technique for fast minimization of L1 regularized...

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 to embe...

Bregman methods introduced in [S. Osher, M. Burger, D. Goldfarb, J. Xu, and W. Yin, Multiscale Model. Simul., 4 (2005), pp. 460-489] to image processing are demonstrated to be an efficient optimization method for solving sparse reconstruction with convex functionals, such as the ℓ1 norm and total variation [W. Yin, S. Osher, D. Goldfarb, and J. Dar...

In this work, inspired by (Buhler & Hein, 2009), (Strang, 1983), and (Zhang et al., 2009), we give a continuous relaxation of the Cheeger cut problem on a weighted graph. We show that the relaxation is actually equiv- alent to the original problem. We then de- scribe an algorithm for finding good cuts sug- gested by the similarities of the energy o...

In this paper, we present an efficient approach for unsupervised segmentation of natural and textural images based on the extraction of image features and a fast active contour segmentation model. We address the problem of textures where neither the gray-level information nor the boundary information is adequate for object extraction. This is often...

Most variational models for multi-phase image segmentation are non-convex and possess multiple local minima, which makes solving for a global solution an extremely difficult task. In this work, we pro-vide a method for computing a global solution for the (non-convex) multi-phase piecewise constant Mumford-Shah (spatially continuous Potts) image seg...

We introduce several color image restoration algorithms based on the Mumford-Shah model and nonlocal image information. The standard Ambrosio-Tortorelli and Shah models are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, textures are not local in nature and require semi-l...

We propose and analyze a nonparametric region-based active contour model for segmenting cluttered scenes. The proposed model is unsupervised and assumes pixel intensity is independently identically distributed. Our proposed energy functional consists of a geometric regularization term that penalizes the length of the partition boundaries and a regi...

We propose a semi-supervised image segmentation method that relies on a non-local continuous version of the min-cut algorithm and labels or seeds provided by a user. The segmentation process is performed via energy minimization. The proposed energy is composed of three terms. The ¯rst term de¯nes labels or seed points assigned to objects that the u...

In this work, inspired by (3) and (13), we give a continuous relaxation of the Cheeger cut problem on a weighted graph. We show that the relaxation is actually equivalent to the original problem, and based on (8, 16), we give an algorithm which experimentally is very e-cient on some clustering benchmarks. We also give a heuristic variant of the alg...

We propose a regularization algorithm for color/vectorial images which is fast, easy to code and mathematically well-posed. More precisely, the regulariza- tion model is based on the dual formulation of the vectorial Total Variation (VTV) norm and it may be regarded as the vectorial extension of the dual approach de- fined by Chambolle in (13) for...

We present an approach for unsupervised segmentation of natural and textural images based on active contour, differential geometry and information theoretical concept. More precisely, we propose a new texture descriptor which intrinsically defines the geometry of textural regions using the shape operator borrowed from differential geometry. Then, w...

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 vi...

⋆ Abstract. New image denoising models based on non-local image information have been recently introduced in the literature. These so-called "non-local" denoising models provide excellent results because these models can denoise smooth regions or/and textured regions simultaneously, unlike standard denoising models. Stan- dard variational models s....

We present an approach for unsupervised segmentation of natural and textural images based on active contour, differential geometry and information theoretical concept. More precisely, we propose a new texture descriptor which intrinsically defines the geometry of textural regions using the shape operator borrowed from differential geometry. Then, w...

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 repre...

This paper proposes an algorithm to solve most of existing active contour problems based on the approach of mean curvature motion proposed by Chambolle (2004) and the image denoising model of Rudin, Osher and Fatemi (ROF) (1992). More precisely, the motion of active contours is discretized by the ROF model applied to the signed distance of the evol...

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...

The active contour/snake model is one of the most successful variational models in image segmentation. It consists of evolving a contour in images toward the boundaries of objects. Its success is based on strong mathematical properties and efficient numerical schemes based on the level set method. The only drawback of this model is the existence of...

We present a method for segmenting white matter as well as the gray matter structures from diffusion tensor magnetic resonance images (DT-MRI). The segmentation is done evolving a set of coupled level set functions. The zero level set of each level set function forms a surface in 3D that is driven by the region-based force including all tensors bel...