Francois Lauze - Academia.edu (original) (raw)

Papers by Francois Lauze

Lecture Notes in Computer Science, 2017

We propose a variational approach for simultaneous reconstruction and multiclass segmentation of ... more We propose a variational approach for simultaneous reconstruction and multiclass segmentation of X-ray CT images, with limited field of view and missing data. We propose a simple energy minimisation approach, loosely based on a Bayesian rationale. The resulting non convex problem is solved by alternating reconstruction steps using an iterated relaxed proximal gradient, and a proximal approach for the segmentation. Preliminary results on synthetic data demonstrate the potential of the approach for synchrotron imaging applications.

Journal of medical imaging, Nov 17, 2022

arXiv (Cornell University), Nov 2, 2014

We consider kernel methods on general geodesic metric spaces and provide both negative and positi... more We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically.

Lecture Notes in Computer Science, 2017

The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Proceedings of SPIE, Mar 21, 2016

We present a simple approach to the voxelwise classification of brain tissue acquired with diffus... more We present a simple approach to the voxelwise classification of brain tissue acquired with diffusion weighted MRI (DWI). The approach leverages the power of spherical harmonics to summarise the diffusion information, sampled at many points over a sphere, using only a handful of coefficients. We use simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic coefficients therefore may permit classification of DWI voxels according to their inferred underlying fibre properties, whilst ignoring the specifics of orientation. After smoothing apparent diffusion coefficients volumes, we apply a spherical harmonic transform, which models the multi-directional diffusion data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing alternatives for tissue classification e.g. fractional anisotropy (FA) or the standard model used by Camino.1 The approach was implemented on both two publicly-available datasets: an ex-vivo pig brain and in-vivo human brain from the Human Connectome Project (HCP). We have demonstrated how a robust classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre-processing stages, such as model fitting, where it could inform about individual voxel complexities and improve model parameter choice.

HAL (Le Centre pour la Communication Scientifique Directe), May 20, 2023

In this article we show how to extend the multi-view stereo technique when the object to be recon... more In this article we show how to extend the multi-view stereo technique when the object to be reconstructed is inside a transparent-but refractive-medium, which causes distortions in the images. We provide a theoretical formulation of the problem accounting for a general, non-planar shape of the refractive interface, and then a discrete solving method. We also present a pipeline to recover precisely the geometry of the refractive interface, considered as a convex polyhedral object. It is based on the extraction of visible polyhedron vertices from silhouette images and matching across a sequence of images acquired under circular camera motion. These contributions are validated by tests on synthetic and real data.

HAL (Le Centre pour la Communication Scientifique Directe), Sep 23, 2020

Dans cet article, nous nous attachons à reconstruire en 3D un objet opaque plongé dans un milieu ... more Dans cet article, nous nous attachons à reconstruire en 3D un objet opaque plongé dans un milieu réfringent. Plus précisément, le cas qui nous intéresse est celui d'un insecte piégé dans l'ambre. Cette matière, certes transparente, est colorée et réfringente, ce qui provoque des distorsions dans les images. Dans un tel cas de figure, l'estimation de la pose par structure-from-motion a été étudiée en détail, mais il n'en va pas de même de la reconstruction 3D par stéréoscopie multi-vues. Cette étude de faisabilité est validée par des tests sur images de synthèse, puis sur les images réelles d'un insecte coulé dans la résine. La qualité de ces premiers résultats est très encourageante.

We present a pipeline to recover precisely the geometry of a convex polyhedral object from multip... more We present a pipeline to recover precisely the geometry of a convex polyhedral object from multiple views under circular motion. It is based on the extraction of visible polyhedron vertices from silhouette images and matching across a sequence of images. Compared to standard structure-from-motion pipelines, the method is well suited to the 3D-reconstruction of low-textured and non-Lambertian materials. Experiments on synthetic and real datasets show the efficacy of the proposed framework. * After normalizing all the points so that they are located within [−1, 1] 2 .

Springer eBooks, 2023

We conduct a discussion on the problem of 3D-reconstruction by calibrated photometric stereo, whe... more We conduct a discussion on the problem of 3D-reconstruction by calibrated photometric stereo, when the surface of interest is embedded in a refractive medium. We explore the changes refraction induces on the problem geometry (surface and normal parameterization), and we put forward a complete image formation model accounting for refracted lighting directions, change of light density and Fresnel coefficients. We further show that as long as the camera is orthographic, lighting is directional and the interface is planar, it is easy to adapt classic methods to take into account the geometric and photometric changes induced by refraction. Moreover, we show on both simulated and real-world experiments that incorporating these modifications of PS methods drastically improves the accuracy of the 3D-reconstruction.

Lecture Notes in Computer Science, 2019

This paper presents a 2D and 3D variational segmentation approach based on a similarity invariant... more This paper presents a 2D and 3D variational segmentation approach based on a similarity invariant, i.e., translation, scaling, and rotation invariant shape regulariser. Indeed, shape moments of order up to 2 for shapes with limited symmetries can be combined to provide a shape normalisation for the group of similarities. In order to obtain a segmentation objective function, a two-means or two-local-means data term is added to it. Segmentation is then obtained by standard gradient descent on it. We demonstrate the capabilities of the approach on a series of experiments, of different complexity levels. We specifically target rat brain shapes in MR scans, where the setting is complex, because of bias field and complex anatomical structures. Our last experiments show that our approach is indeed capable of recovering brain shapes automatically.

This paper presents two variational multiphase segmentation methods for recovery of segments in w... more This paper presents two variational multiphase segmentation methods for recovery of segments in weakly structured images, presenting local and global intensity bias fields, as often is the case in micro-tomography. The proposed methods assume a fixed number of classes. They use local image averages as discriminative features and binary labelling for class membership and their relaxation to per pixel/voxel posterior probabilities, Hidden Markov Measure Field Models (HMMFM). The first model uses a Total Variation weighted semi-norm (wTV) for label field regularization, similar to Geodesic Active Contours, but with a different and possibly richer representation. The second model uses a weighted Dirichlet (squared gradient) regularization. Both problems are solved by alternating minimization on computation of local class averages and label fields. The quadratic problem is essentially smooth, except for HMMFM constraints. The wTV problem uses a Chambolle-Pock scheme for label field updates. We demonstrate on synthetic examples the capabilities of the approaches, and illustrate it on a real examples.

Journal of Mathematical Imaging and Vision, Oct 5, 2018

arXiv (Cornell University), Jun 6, 2021

We present a graph neural network model for solving graph-to-graph learning problems. Most deep l... more We present a graph neural network model for solving graph-to-graph learning problems. Most deep learning on graphs considers "simple" problems such as graph classification or regressing real-valued graph properties. For such tasks, the main requirement for intermediate representations of the data is to maintain the structure needed for output, i.e. keeping classes separated or maintaining the order indicated by the regressor. However, a number of learning tasks, such as regressing graph-valued output, generative models, or graph autoencoders, aim to predict a graph-structured output. In order to successfully do this, the learned representations need to preserve far more structure. We present a conditional auto-regressive model for graph-to-graph learning and illustrate its representational capabilities via experiments on challenging subgraph predictions from graph algorithmics; as a graph autoencoder for reconstruction and visualization; and on pretraining representations that allow graph classification with limited labeled data. Preprint. Under review.

HAL (Le Centre pour la Communication Scientifique Directe), May 27, 2019

Nous proposons un nouveau modèle d'inpainting vidéo pour la restauration de films, qui combine la... more Nous proposons un nouveau modèle d'inpainting vidéo pour la restauration de films, qui combine la reconstruction de la structure par une méthode de diffusion et la reconstruction de la texture par une méthode de recopie de patchs. Les énergies proposées pour chacune de ces deux méthodes sont minimisées alternativement, afin de préserver la structure globale de l'image tout en affinant sa texture. Alors que la reconstruction de la structure est effectuée conjointement à l'estimation du mouvement par flux optique via plusieurs approches proximales, la reconstruction de la texture est traitée par une approche variationnelle non locale (NL-means). Les résultats sur différentes séquences d'images de la base de données Middlebury et de la Cinémathèque de Toulouse montrent une amélioration dans la qualité des reconstructions.

arXiv (Cornell University), Jun 12, 1995

Let k an algebraically closed field, P n the n-dimensional projective space over k and T P n the ... more Let k an algebraically closed field, P n the n-dimensional projective space over k and T P n the tangent vector bundle of P n. In this paper I prove the following result : for every integer ℓ, for every non-negative integer s, if Z s is the union of s points in sufficiently general position in P n , then the restriction map H 0 (P n , T P n (ℓ)) → H 0 (Z s , T P n (ℓ) |Zs) has maximal rank. This result implies that the last non-trivial term of the minimal free resolution of the homogeneous ideal of Z s is the conjectured one by the Minimal Resolution Conjecture of Anna Lorenzini (cf [Lo]).

Lecture Notes in Computer Science, 2017

This paper presents two similar multiphase segmentation methods for recovery of segments in compl... more This paper presents two similar multiphase segmentation methods for recovery of segments in complex weakly structured images, with local and global bias fields, because they can occur in some X-ray CT imaging modalities. Derived from the Mumford-Shah functional, the proposed methods assume a fixed number of classes. They use local image average as discriminative features. Region labels are modelled by Hidden Markov Measure Field Models. The resulting problems are solved by straightforward alternate minimisation methods, particularly simple in the case of quadratic regularisation of the labels. We demonstrate the proposed methods’ capabilities on synthetic data using classical segmentation criteria as well as criteria specific to geoscience. We also present a few examples using real data.

Lecture Notes in Computer Science, 2015

Standard statistics and machine learning tools require input data residing in a Euclidean space. ... more Standard statistics and machine learning tools require input data residing in a Euclidean space. However, many types of data are more faithfully represented in general nonlinear metric spaces or Riemannian manifolds, e.g. shapes, symmetric positive definite matrices, human poses or graphs. The underlying metric space captures domain specific knowledge, e.g. non-linear constraints, which is available a priori. The intrinsic geodesic metric encodes this knowledge, often leading to improved statistical models.

Springer eBooks, 2019

We propose a new video inpainting model for movies restoration application. Our model combines st... more We propose a new video inpainting model for movies restoration application. Our model combines structural reconstruction with a diffusion-based method and textural reconstruction with a patch-based method. Both proposed energies (one for each method) are alternatively minimized in order to preserve the overall structure while adding textural refinement. While the structural reconstruction is obtained jointly with optical flow computation with several proximal approaches, the textural reconstruction is processed by a variational non-local approach. Preliminary results on different Middlebury frames show quality improvement in the reconstruction.

Lecture Notes in Computer Science, 2017

We propose a variational approach for simultaneous reconstruction and multiclass segmentation of ... more We propose a variational approach for simultaneous reconstruction and multiclass segmentation of X-ray CT images, with limited field of view and missing data. We propose a simple energy minimisation approach, loosely based on a Bayesian rationale. The resulting non convex problem is solved by alternating reconstruction steps using an iterated relaxed proximal gradient, and a proximal approach for the segmentation. Preliminary results on synthetic data demonstrate the potential of the approach for synchrotron imaging applications.

Journal of medical imaging, Nov 17, 2022

arXiv (Cornell University), Nov 2, 2014

We consider kernel methods on general geodesic metric spaces and provide both negative and positi... more We consider kernel methods on general geodesic metric spaces and provide both negative and positive results. First we show that the common Gaussian kernel can only be generalized to a positive definite kernel on a geodesic metric space if the space is flat. As a result, for data on a Riemannian manifold, the geodesic Gaussian kernel is only positive definite if the Riemannian manifold is Euclidean. This implies that any attempt to design geodesic Gaussian kernels on curved Riemannian manifolds is futile. However, we show that for spaces with conditionally negative definite distances the geodesic Laplacian kernel can be generalized while retaining positive definiteness. This implies that geodesic Laplacian kernels can be generalized to some curved spaces, including spheres and hyperbolic spaces. Our theoretical results are verified empirically.

Lecture Notes in Computer Science, 2017

The use of general descriptive names, registered names, trademarks, service marks, etc. in this p... more The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Proceedings of SPIE, Mar 21, 2016

We present a simple approach to the voxelwise classification of brain tissue acquired with diffus... more We present a simple approach to the voxelwise classification of brain tissue acquired with diffusion weighted MRI (DWI). The approach leverages the power of spherical harmonics to summarise the diffusion information, sampled at many points over a sphere, using only a handful of coefficients. We use simple features that are invariant to the rotation of the highly orientational diffusion data. This provides a way to directly classify voxels whose diffusion characteristics are similar yet whose primary diffusion orientations differ. Subsequent application of machine-learning to the spherical harmonic coefficients therefore may permit classification of DWI voxels according to their inferred underlying fibre properties, whilst ignoring the specifics of orientation. After smoothing apparent diffusion coefficients volumes, we apply a spherical harmonic transform, which models the multi-directional diffusion data as a collection of spherical basis functions. We use the derived coefficients as voxelwise feature vectors for classification. Using a simple Gaussian mixture model, we examined the classification performance for a range of sub-classes (3-20). The results were compared against existing alternatives for tissue classification e.g. fractional anisotropy (FA) or the standard model used by Camino.1 The approach was implemented on both two publicly-available datasets: an ex-vivo pig brain and in-vivo human brain from the Human Connectome Project (HCP). We have demonstrated how a robust classification of DWI data can be performed without the need for a model reconstruction step. This avoids the potential confounds and uncertainty that such models may impose, and has the benefit of being computable directly from the DWI volumes. As such, the method could prove useful in subsequent pre-processing stages, such as model fitting, where it could inform about individual voxel complexities and improve model parameter choice.

HAL (Le Centre pour la Communication Scientifique Directe), May 20, 2023

In this article we show how to extend the multi-view stereo technique when the object to be recon... more In this article we show how to extend the multi-view stereo technique when the object to be reconstructed is inside a transparent-but refractive-medium, which causes distortions in the images. We provide a theoretical formulation of the problem accounting for a general, non-planar shape of the refractive interface, and then a discrete solving method. We also present a pipeline to recover precisely the geometry of the refractive interface, considered as a convex polyhedral object. It is based on the extraction of visible polyhedron vertices from silhouette images and matching across a sequence of images acquired under circular camera motion. These contributions are validated by tests on synthetic and real data.

HAL (Le Centre pour la Communication Scientifique Directe), Sep 23, 2020

Dans cet article, nous nous attachons à reconstruire en 3D un objet opaque plongé dans un milieu ... more Dans cet article, nous nous attachons à reconstruire en 3D un objet opaque plongé dans un milieu réfringent. Plus précisément, le cas qui nous intéresse est celui d'un insecte piégé dans l'ambre. Cette matière, certes transparente, est colorée et réfringente, ce qui provoque des distorsions dans les images. Dans un tel cas de figure, l'estimation de la pose par structure-from-motion a été étudiée en détail, mais il n'en va pas de même de la reconstruction 3D par stéréoscopie multi-vues. Cette étude de faisabilité est validée par des tests sur images de synthèse, puis sur les images réelles d'un insecte coulé dans la résine. La qualité de ces premiers résultats est très encourageante.

We present a pipeline to recover precisely the geometry of a convex polyhedral object from multip... more We present a pipeline to recover precisely the geometry of a convex polyhedral object from multiple views under circular motion. It is based on the extraction of visible polyhedron vertices from silhouette images and matching across a sequence of images. Compared to standard structure-from-motion pipelines, the method is well suited to the 3D-reconstruction of low-textured and non-Lambertian materials. Experiments on synthetic and real datasets show the efficacy of the proposed framework. * After normalizing all the points so that they are located within [−1, 1] 2 .

Springer eBooks, 2023

We conduct a discussion on the problem of 3D-reconstruction by calibrated photometric stereo, whe... more We conduct a discussion on the problem of 3D-reconstruction by calibrated photometric stereo, when the surface of interest is embedded in a refractive medium. We explore the changes refraction induces on the problem geometry (surface and normal parameterization), and we put forward a complete image formation model accounting for refracted lighting directions, change of light density and Fresnel coefficients. We further show that as long as the camera is orthographic, lighting is directional and the interface is planar, it is easy to adapt classic methods to take into account the geometric and photometric changes induced by refraction. Moreover, we show on both simulated and real-world experiments that incorporating these modifications of PS methods drastically improves the accuracy of the 3D-reconstruction.

Lecture Notes in Computer Science, 2019

This paper presents a 2D and 3D variational segmentation approach based on a similarity invariant... more This paper presents a 2D and 3D variational segmentation approach based on a similarity invariant, i.e., translation, scaling, and rotation invariant shape regulariser. Indeed, shape moments of order up to 2 for shapes with limited symmetries can be combined to provide a shape normalisation for the group of similarities. In order to obtain a segmentation objective function, a two-means or two-local-means data term is added to it. Segmentation is then obtained by standard gradient descent on it. We demonstrate the capabilities of the approach on a series of experiments, of different complexity levels. We specifically target rat brain shapes in MR scans, where the setting is complex, because of bias field and complex anatomical structures. Our last experiments show that our approach is indeed capable of recovering brain shapes automatically.

This paper presents two variational multiphase segmentation methods for recovery of segments in w... more This paper presents two variational multiphase segmentation methods for recovery of segments in weakly structured images, presenting local and global intensity bias fields, as often is the case in micro-tomography. The proposed methods assume a fixed number of classes. They use local image averages as discriminative features and binary labelling for class membership and their relaxation to per pixel/voxel posterior probabilities, Hidden Markov Measure Field Models (HMMFM). The first model uses a Total Variation weighted semi-norm (wTV) for label field regularization, similar to Geodesic Active Contours, but with a different and possibly richer representation. The second model uses a weighted Dirichlet (squared gradient) regularization. Both problems are solved by alternating minimization on computation of local class averages and label fields. The quadratic problem is essentially smooth, except for HMMFM constraints. The wTV problem uses a Chambolle-Pock scheme for label field updates. We demonstrate on synthetic examples the capabilities of the approaches, and illustrate it on a real examples.

Journal of Mathematical Imaging and Vision, Oct 5, 2018

arXiv (Cornell University), Jun 6, 2021

We present a graph neural network model for solving graph-to-graph learning problems. Most deep l... more We present a graph neural network model for solving graph-to-graph learning problems. Most deep learning on graphs considers "simple" problems such as graph classification or regressing real-valued graph properties. For such tasks, the main requirement for intermediate representations of the data is to maintain the structure needed for output, i.e. keeping classes separated or maintaining the order indicated by the regressor. However, a number of learning tasks, such as regressing graph-valued output, generative models, or graph autoencoders, aim to predict a graph-structured output. In order to successfully do this, the learned representations need to preserve far more structure. We present a conditional auto-regressive model for graph-to-graph learning and illustrate its representational capabilities via experiments on challenging subgraph predictions from graph algorithmics; as a graph autoencoder for reconstruction and visualization; and on pretraining representations that allow graph classification with limited labeled data. Preprint. Under review.

HAL (Le Centre pour la Communication Scientifique Directe), May 27, 2019

Nous proposons un nouveau modèle d'inpainting vidéo pour la restauration de films, qui combine la... more Nous proposons un nouveau modèle d'inpainting vidéo pour la restauration de films, qui combine la reconstruction de la structure par une méthode de diffusion et la reconstruction de la texture par une méthode de recopie de patchs. Les énergies proposées pour chacune de ces deux méthodes sont minimisées alternativement, afin de préserver la structure globale de l'image tout en affinant sa texture. Alors que la reconstruction de la structure est effectuée conjointement à l'estimation du mouvement par flux optique via plusieurs approches proximales, la reconstruction de la texture est traitée par une approche variationnelle non locale (NL-means). Les résultats sur différentes séquences d'images de la base de données Middlebury et de la Cinémathèque de Toulouse montrent une amélioration dans la qualité des reconstructions.

arXiv (Cornell University), Jun 12, 1995

Let k an algebraically closed field, P n the n-dimensional projective space over k and T P n the ... more Let k an algebraically closed field, P n the n-dimensional projective space over k and T P n the tangent vector bundle of P n. In this paper I prove the following result : for every integer ℓ, for every non-negative integer s, if Z s is the union of s points in sufficiently general position in P n , then the restriction map H 0 (P n , T P n (ℓ)) → H 0 (Z s , T P n (ℓ) |Zs) has maximal rank. This result implies that the last non-trivial term of the minimal free resolution of the homogeneous ideal of Z s is the conjectured one by the Minimal Resolution Conjecture of Anna Lorenzini (cf [Lo]).

Lecture Notes in Computer Science, 2017

This paper presents two similar multiphase segmentation methods for recovery of segments in compl... more This paper presents two similar multiphase segmentation methods for recovery of segments in complex weakly structured images, with local and global bias fields, because they can occur in some X-ray CT imaging modalities. Derived from the Mumford-Shah functional, the proposed methods assume a fixed number of classes. They use local image average as discriminative features. Region labels are modelled by Hidden Markov Measure Field Models. The resulting problems are solved by straightforward alternate minimisation methods, particularly simple in the case of quadratic regularisation of the labels. We demonstrate the proposed methods’ capabilities on synthetic data using classical segmentation criteria as well as criteria specific to geoscience. We also present a few examples using real data.

Lecture Notes in Computer Science, 2015

Standard statistics and machine learning tools require input data residing in a Euclidean space. ... more Standard statistics and machine learning tools require input data residing in a Euclidean space. However, many types of data are more faithfully represented in general nonlinear metric spaces or Riemannian manifolds, e.g. shapes, symmetric positive definite matrices, human poses or graphs. The underlying metric space captures domain specific knowledge, e.g. non-linear constraints, which is available a priori. The intrinsic geodesic metric encodes this knowledge, often leading to improved statistical models.

Springer eBooks, 2019

We propose a new video inpainting model for movies restoration application. Our model combines st... more We propose a new video inpainting model for movies restoration application. Our model combines structural reconstruction with a diffusion-based method and textural reconstruction with a patch-based method. Both proposed energies (one for each method) are alternatively minimized in order to preserve the overall structure while adding textural refinement. While the structural reconstruction is obtained jointly with optical flow computation with several proximal approaches, the textural reconstruction is processed by a variational non-local approach. Preliminary results on different Middlebury frames show quality improvement in the reconstruction.