Showing papers by "Nicholas Ayache published in 2007"

Geometric means in a novel vector space structure on symmetric positive-definite matrices

Abstract: In this work we present a new generalization of the geometric mean of positive numbers on symmetric positive‐definite matrices, called Log‐Euclidean. The approach is based on two novel algebraic structures on symmetric positive‐definite matrices: first, a lie group structure which is compatible with the usual algebraic properties of this matrix space; second, a new scalar multiplication that smoothly extends the Lie group structure into a vector space structure. From bi‐invariant metrics on the Lie group structure, we define the Log‐Euclidean mean from a Riemannian point of view. This notion coincides with the usual Euclidean mean associated with the novel vector space structure. Furthermore, this means corresponds to an arithmetic mean in the domain of matrix logarithms. We detail the invariance properties of this novel geometric mean and compare it to the recently introduced affine‐invariant mean. The two means have the same determinant and are equal in a number of cases, yet they are not identical in g...

Non-parametric diffeomorphic image registration with the demons algorithm

Abstract: We propose a non-parametric diffeomorphic image registration algorithm based on Thirion's demons algorithm. The demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. The main idea of our algorithm is to adapt this procedure to a space of diffeomorphic transformations. In contrast to many diffeomorphic registration algorithms, our solution is computationally efficient since in practice it only replaces an addition of free form deformations by a few compositions. Our experiments show that in addition to being diffeomorphic, our algorithm provides results that are similar to the ones from the demons algorithm but with transformations that are much smoother and closer to the true ones in terms of Jacobians.

Automatic segmentation of bladder and prostate using coupled 3D deformable models

Abstract: In this paper, we propose a fully automatic method for the coupled 3D localization and segmentation of lower abdomen structures. We apply it to the joint segmentation of the prostate and bladder in a database of CT scans of the lower abdomen of male patients. A flexible approach on the bladder allows the process to easily adapt to high shape variation and to intensity inhomogeneities that would be hard to characterize (due, for example, to the level of contrast agent that is present). On the other hand, a statistical shape prior is enforced on the prostate. We also propose an adaptive non-overlapping constraint that arbitrates the evolution of both structures based on the availability of strong image data at their common boundary. The method has been tested on a database of 16 volumetric images, and the validation process includes an assessment of inter-expert variability in prostate delineation, with promising results.

An anisotropic multi-front fast marching method for real-time simulation of cardiac electrophysiology

Abstract: Cardiac arrhythmias can develop complex electrophysiological patterns which complexify the planning and control of therapies, especially in the context of radio-frequency ablation. The development of electrophysiology models aims at testing different therapy strategies. However, current models are computationally expensive and often too complex to be adjusted with limited clinical data. In this paper, we propose a real-time method to simulate cardiac electrophysiology on triangular meshes. This model is based on a multi-front integration of the Fast Marching Method. This efficient approach opens new possibilities, including the ability to directly integrate modelling in the interventional room.

An Automatic Segmentation of T2-FLAIR Multiple Sclerosis Lesions

Abstract: Multiple sclerosis diagnosis and patient follow-up can be helped by an evaluation of the lesion load in MRI sequences. A lot of automatic methods to segment these lesions are available in the literature. The MICCAI workshop Multiple Sclerosis (MS) lesion segmentation Challenge 08 allows to test and compare these algorithms. This paper presents a method designed to detect hyperintense signal area on T2-FLAIR sequence and its results on the Challenge test data. The proposed algorithm uses only three conventional MRI sequences: T1, T2 and T2-FLAIR. First, images are cropped, spatially unbiased and skull-stripped. A segmentation of the brain into its different compartments is performed on the T1 and the T2 sequences. From these segmentations, a threshold for the T2-FLAIR sequence is automatically computed. Then postprocessing operations select the most plausible lesions in the obtained hyperintense signals. Average global result on the test data (80/100) is close to the inter-expert variability (90/100).

A recursive anisotropic fast marching approach to reaction diffusion equation: application to tumor growth modeling

Abstract: Bridging the gap between clinical applications and mathematical models is one of the new challenges of medical image analysis. In this paper, we propose an efficient and accurate algorithm to solve anisotropic Eikonal equations, in order to link biological models using reaction-diffusion equations to clinical observations, such as medical images. The example application we use to demonstrate our methodology is tumor growth modeling. We simulate the motion of the tumor front visible in images and give preliminary results by solving the derived anisotropic Eikonal equation with the recursive fast marching algorithm.

Insight into efficient image registration techniques and the demons algorithm

Abstract: As image registration becomes more and more central to many biomedical imaging applications, the efficiency of the algorithms becomes a key issue. Image registration is classically performed by optimizing a similarity criterion over a given spatial transformation space. Even if this problem is considered as almost solved for linear registration, we show in this paper that some tools that have recently been developed in the field of vision-based robot control can outperform classical solutions. The adequacy of these tools for linear image registration leads us to revisit non-linear registration and allows us to provide interesting theoretical roots to the different variants of Thirion's demons algorithm. This analysis predicts a theoretical advantage to the symmetric forces variant of the demons algorithm. We show that, on controlled experiments, this advantage is confirmed, and yields a faster convergence.

Diffeomorphic Demons Using ITK's Finite Difference Solver Hierarchy

Abstract: This article provides an implementation of our non-parametric diffeomorphic image registration algorithm generalizing Thirion’s demons algorithm. Within the Insight Toolkit (ITK), the demons algorithm is implemented as part of the finite difference solver framework. We show that this framework can be extended to handle diffeomorphic transformations. The source code is composed of a set of reusable ITK filters and classes. In addition to an overview of our implementation, we provide a small example program that allows the user to compare the different variants of the demons algorithm.

Measuring brain variability via sulcal lines registration: a diffeomorphic approach

Abstract: In this paper we present a new way of measuring brain variability based on the registration of sulcal lines sets in the large deformation framework. Lines are modelled geometrically as currents, avoiding then matchings based on point correspondences. At the end we retrieve a globally consistent deformation of the underlying brain space that best matches the lines. Thanks to this framework the measured variability is defined everywhere whereas a previous method introduced by P. Fillard requires tensors extrapolation. Evaluating both methods on the same database, we show that our new approach enables to describe different details of the variability and to highlight the major trends of deformation in the database thanks to a Tangent-PCA analysis.

Robust mosaicing method, notably with correction of motion distortions and tissue deformations for a vivo fibered microscopy

Abstract: A mosaicing method taking into account motion distortions, irregularly sampled frames and non-rigid deformations of the imaged tissue. The method for mosaicing frames from a video sequence acquired from a scanning device such as a scanning microscope, includes the steps of: a) compensating for motion and motion distortion due to the scanning microscope, b) applying a global optimization of inter-frame registration to align consistently the frames c) applying a construction algorithm on the registered frames to construct a mosaic, and d) applying a fine frame-to-mosaic non rigid registration. The method is based on a hierarchical framework that is able to recover a globally consistent alignment of the input frames, to compensate for the motion distortions and to capture the non-rigid deformations.

Deformable Atlases for the Segmentation of Internal Brain Nuclei in Magnetic Resonance Imaging

Abstract: Magnetic resonance imaging (MRI) is commonly employed for the depiction of soft tissues, most notably the human brain. Computer-aided image analysis techniques lead to image enhancement and automatic detection of anatomical structures. However, the information contained in images does not often offer enough contrast to robustly obtain a good detection of all internal brain structures, not least the deep grey matter nuclei. We propose a method that incorporates prior anatomical knowledge in the shape of digital atlases that deform to fit the image data to be analysed. Our technique is based on a combination of rigid, affine and non-rigid registration, segmentation of key anatomical landmarks and propagation of the information of the atlas to detect deep grey matter nuclei. The Montreal Neurological Institute (MNI) and Zubal atlases are employed. Results show that detecting important structures such as the ventricles and brain outlines greatly improves the results. Our method is fully automatic.

Shape analysis using a point-based statistical shape model built on correspondence probabilities

Abstract: A fundamental problem when computing statistical shape models is the determination of correspondences between the instances of the associated data set. Often, homologies between points that represent the surfaces are assumed which might lead to imprecise mean shape and variability results. We propose an approach where exact correspondences are replaced by evolving correspondence probabilities. These are the basis for a novel algorithm that computes a generative statistical shape model. We developed an unified MAP framework to compute the model parameters ('mean shape' and 'modes of variation') and the nuisance parameters which leads to an optimal adaption of the model to the set of observations. The registration of the model on the instances is solved using the Expectation Maximization - Iterative Closest Point algorithm which is based on probabilistic correspondences and proved to be robust and fast. The alternated optimization of the MAP explanation with respect to the observation and the generative model parameters leads to very efficient and closed-form solutions for (almost) all parameters. Experimental results on brain structure data sets demonstrate the efficiency and well-posedness of the approach. The algorithm is then extended to an automatic classification method using the k-means clustering and applied to synthetic data as well as brain structure classification problems.

Towards an identification of tumor growth parameters from time series of images

Abstract: In cancer treatment, understanding the aggressiveness of the tumor is essential in therapy planning and patient follow-up. In this article, we present a novel method for quantifying the speed of invasion of gliomas in white and grey matter from time series of magnetic resonance (MR) images. The proposed approach is based on mathematical tumor growth models using the reaction-diffusion formalism. The quantification process is formulated by an inverse problem and solved using anisotropic fast marching method yielding an efficient algorithm. It is tested on a few images to get a first proof of concept with promising new results.

Evaluating Brain Anatomical Correlations via Canonical Correlation Analysis of Sulcal Lines

Abstract: Modeling and understanding the degree of correlations between brain structures is a challenging problem in neuroscience. Correlated anatomic measures may arise from common genetic and trophic influences across brain regions, and may be overlooked if structures are modeled independently. Here, we propose a new method to analyze structural brain correlations based on a large set of cortical sulcal landmarks (72 per brain) delineated in 98 healthy subjects (age: 51.8 +/-6.2 years). First, we evaluate the correlation between any pair of sulcal positions via the total covariance matrix, a 6x6 symmetric positive-definite matrix. We use Log-Euclidean metrics to extrapolate this sparse field of total covariance matrices to obtain a dense representation. Second, we perform canonical correlation analysis to measure the degree of correlations between any two positions, and derive from it a p-value map for significance testing. We present maps of both local and long-range correlations, including maps of covariation between corresponding structures in opposite hemispheres, which show different degrees of hemispheric specialization. Results show that the central and inferior temporal sulci are highly correlated with their symmetric counterparts in the opposite brain hemisphere. Moreover, several functionally unrelated cortical landmarks show a high correlation as well. This structural dependence is likely attributable to common genetic programs, experience-driven plasticity, and coordinated brain growth or presence of anatomical links (neural fibers).

Statistical shape analysis via principal factor analysis

Abstract: Statistical shape analysis techniques commonly employed in the medical imaging community, such as active shape models or active appearance models, rely on principal component analysis (PCA) to decompose shape variability into a reduced set of interpretable components. In this paper we propose principal factor analysis (PFA) as an alternative and complementary tool to PCA providing a decomposition into modes of variation that can be more easily interpretable, while still being a linear efficient technique that performs dimensionality reduction (as opposed to independent component analysis, ICA). The key difference between PFA and PCA is that PFA models covariance between variables, rather than the total variance in the data. The added value of PFA is illustrated on 2D landmark data of corpora callosa outlines. Then, a study of the 3D shape variability of the human left femur is performed. Finally, we report results on vector-valued 3D deformation fields resulting from non-rigid registration of ventricles in MRI of the brain.

Statistical comparison of cardiac fibre architectures

Abstract: In this paper, a statistical atlas of DT-MRIs based on a population of nine ex vivo normal canine hearts is compared with a human cardiac DT-MRI and with a synthetic model of the fibre orientation. The aim of this paper is to perform a statistical inter-species comparison of the cardiac fibre architecture and to assess the quality of a synthetic description of the fibre orientation. We present the framework to build a statistical atlas of cardiac DT-MRIs providing a mean and a covariance matrix of diffusion tensors at each voxel of an average geometry. The comparison of human and synthetic data with this atlas involves the non-rigid registration into the average atlas geometry where voxel to voxel comparison can be performed. For each eigenvector of the diffusion tensors, we compute the angular difference with the average atlas and its Mahalanobis distance to the canine population. The results show a better consistence of the fibre orientation than the laminar sheet orientation between the human and the canine heart, while the homogeneous synthetic model appears to be too simple compared to the complexity of real cardiac geometry and fibre architecture.

Point-Based Statistical Shape Models with Probabilistic Correspondences and Affine EM-ICP

Abstract: A fundamental problem when computing statistical shape models (SSMs) is the determination of correspondences between the instances. Often, homologies between points that represent the surfaces are assumed which might lead to imprecise mean shape and variation results. We present a novel algorithm based on the affine Expectation Maximization - Iterative Closest Point (EM-ICP) registration method. Exact correspondences are replaced by iteratively evolving correspondence probabilities which provide the basis for the computation of mean shape and variability model. We validated our approach by computing SSMs using inexact correspondences for kidney and putamen data. In ongoing work, we want to use our methods for automatic classification applications.

Segmentation propagation from deformable atlases for brain mapping and analysis

Abstract: Magnetic resonance imaging (MRI) is commonly employed for the depiction of soft tissues, most notably the human brain. Computer-aided image analysis techniques lead to image enhancement and automatic detection of anatomical structures. However, the intensity information contained in images does not often offer enough contrast to robustly obtain a good detection of all internal brain structures, not least the deep gray matter nuclei. We propose digital atlases that deform to fit the image data to be analyzed. In this application, deformable atlases are employed for the detection and segmentation of brain nuclei, to allow analysis of brain structures. Our fully automatic technique is based on a combination of rigid, affine and non-linear registration, a priori information on key anatomical landmarks and propagation of the information of the atlas. The Internet Brain Segmentation Repository (IBSR) data provide manually segmented brain data. Using prior anatomical knowledge in local brain areas from a randomly chosen brain scan (atlas), a first estimation of the deformation fields is calculated by affine registration. The image alignment is refined through a non-linear transformation to correct the segmentation of nuclei. The local segmentation results are greatly improved. They are robust over the patient data and in accordance with the clinical ground truth. Validation of results is assessed by comparing the automatic segmentation of deep gray nuclei by the proposed method with manual segmentation. The technique offers the accurate segmentation of difficultly identifiable brain structures in conjuncture with deformable atlases. Such automated processes allow the study of large image databases and provide consistent measurements over the data. The method has a wide range of clinical

In Vivo Microscopy for Real-Time Structural and Functional Cellular Imaging.

Abstract: Current medical practice is moving towards more quantitative and personalized methods of diagnosis and decisionmaking. This has led to a need for more complex and detailed patient-specific digital models. The resolution at which the model is described is important and may vary from macroscopic to microscopic and even molecular scales, ideally through multiscale descriptions. As these individualized models start to integrate knowledge of cellular dynamics, it becomes crucial to acquire patientspecific information at the cellular level.