Gerardo Hermosillo

Variational Methods for Multimodal Image Matching

Matching images of different modalities can be achieved by the maximization of suitable statistical similarity measures within a given class of geometric transformations. Handling complex, nonrigid deformations in this context turns out to be particularly difficult and has attracted much attention in the last few years. The thrust of this paper is that many of the existing methods for nonrigid monomodal registration that use simple criteria for comparing the intensities (e.g. SSD) can be extended to the multimodal case where more complex intensity similarity measures are necessary. To this end, we perform a formal computation of the variational gradient of a hierarchy of statistical similarity measures, and use the results to generalize a recently proposed and very effective optical flow algorithm (L. Alvarez, J. Weickert, and J. Sánchez, 2000, Technical Report, and IJCV 39(1):41–56) to the case of multimodal image registrationOur method readily extends to the case of locally computed similarity measures, thus providing the flexibility to cope with spatial non-stationarities in the way the intensities in the two images are related. The well posedness of the resulting equations is proved in a complementary work (O.D. Faugeras and G. Hermosillo, 2001, Technical Report 4235, INRIA) using well established techniques in functional analysis. We briefly describe our numerical implementation of these equations and show results on real and synthetic data.

Flows of diffeomorphisms for multimodal image registration

We present a theoretical and computational framework for nonrigid multimodal registration. We proceed by minimization of statistical similarity criteria (global and local) in a variational framework, and use the corresponding gradients to drive a flow of diffeomorphisms allowing large deformations. This flow is introduced through a new template propagation method, by composition of small displacements. Regularization is performed using fast filtering techniques. This approach yields robust matching algorithms offering a good computational efficiency. We apply this method to compensate distortions between EPI images (fMRI) and anatomical MRI volumes.

A variational approach to multi-modal image matching

We address the problem of nonparametric multi-modal image matching. We propose a generic framework which relies on a global variational formulation and show its versatility through three different multi-modal registration methods: supervised registration by joint intensity learning, maximization of the mutual information and maximization of the correlation ratio. Regularization is performed by using a functional borrowed from linear elasticity theory. We also consider a geometry-driven regularization method. Experiments on synthetic images and preliminary results on the realignment of MRI datasets are presented.

Whole-Body PET/MR Imaging: Quantitative Evaluation of a Novel Model-Based MR Attenuation Correction Method Including Bone

In routine whole-body PET/MR hybrid imaging, attenuation correction (AC) is usually performed by segmentation methods based on a Dixon MR sequence providing up to 4 different tissue classes. Because of the lack of bone information with the Dixon-based MR sequence, bone is currently considered as soft tissue. Thus, the aim of this study was to evaluate a novel model-based AC method that considers bone in whole-body PET/MR imaging. Methods: The new method (“Model”) is based on a regular 4-compartment segmentation from a Dixon sequence (“Dixon”). Bone information is added using a model-based bone segmentation algorithm, which includes a set of prealigned MR image and bone mask pairs for each major body bone individually. Model was quantitatively evaluated on 20 patients who underwent whole-body PET/MR imaging. As a standard of reference, CT-based μ-maps were generated for each patient individually by nonrigid registration to the MR images based on PET/CT data. This step allowed for a quantitative comparison of all μ-maps based on a single PET emission raw dataset of the PET/MR system. Volumes of interest were drawn on normal tissue, soft-tissue lesions, and bone lesions; standardized uptake values were quantitatively compared. Results: In soft-tissue regions with background uptake, the average bias of SUVs in background volumes of interest was 2.4% ± 2.5% and 2.7% ± 2.7% for Dixon and Model, respectively, compared with CT-based AC. For bony tissue, the −25.5% ± 7.9% underestimation observed with Dixon was reduced to −4.9% ± 6.7% with Model. In bone lesions, the average underestimation was −7.4% ± 5.3% and −2.9% ± 5.8% for Dixon and Model, respectively. For soft-tissue lesions, the biases were 5.1% ± 5.1% for Dixon and 5.2% ± 5.2% for Model. Conclusion: The novel MR-based AC method for whole-body PET/MR imaging, combining Dixon-based soft-tissue segmentation and model-based bone estimation, improves PET quantification in whole-body hybrid PET/MR imaging, especially in bony tissue and nearby soft tissue.

Variational, Geometric and Statistical Methods for Modeling Brain Anatomy and Function

We survey the recent activities of the Odyssée Laboratory in the area of the application of mathematics to the design of models for studying brain anatomy and function. We start with the problem of reconstructing sources in MEG and EEG, and discuss the variational approach we have developed for solving these inverse problems. This motivates the need for geometric models of the head. We present a method for automatically and accurately extracting surface meshes of several tissues of the head from anatomical magnetic resonance (MR) images. Anatomical connectivity can be extracted from diffusion tensor magnetic resonance images but, in the current state of the technology, it must be preceded by a robust estimation and regularization stage. We discuss our work based on variational principles and show how the results can be used to track fibers in the white matter (WM) as geodesics in some Riemannian space. We then go to the statistical modeling of functional magnetic resonance imaging (fMRI) signals from the viewpoint of their decomposition in a pseudo-deterministic and stochastic part that we then use to perform clustering of voxels in a way that is inspired by the theory of support vector machines and in a way that is grounded in information theory. Multimodal image matching is discussed next in the framework of image statistics and partial differential equations (PDEs) with an eye on registering fMRI to the anatomy. The paper ends with a discussion of a new theory of random shapes that may prove useful in building anatomical and functional atlases.

Dense image matching with global and local statistical criteria: a variational approach

We present two novel algorithms for multimodal, dense matching of two images using a variational approach. These algorithms complete and generalise our previous work by treating the case of semi-local energy functionals (G. Hermosillo et al., 2001). In brief, they are derived from the maximization of two statistical criteria (mutual information and correlation ratio) estimated from corresponding regions around each pixel (or voxel in the 3D case). As a second contribution, we present a result of existence and uniqueness of the solution of the abstract evolution problems associated to these algorithms, as well as those of the corresponding global algorithms. This is important since it shows the well-posedness of the problems to solve. We finish by showing some applications of our methods to one synthetic and four real examples.

Maintaining the point correspondence in the level set framework

In this paper, we propose a completely Eulerian approach to maintain a point correspondence during a level set evolution. Our work is in the spirit of some recent methods (D. Adalsteinsson, J. Sethian, Transport and diffusion of material quantities on propagating interfaces via level set methods, Journal of Computational Physics 185(1) (2003) 271-288; J.-J. Xu, H.-K. Zhao, An Eulerian formulation for solving partial differential equations along a moving interface, Journal of Scientific Computing 19 (2003) 573-594) for handling interfacial data on moving level set interfaces. Our approach maintains an explicit backward correspondence from the evolving interface to the initial one, by advecting the initial point coordinates with the same velocity as the level set function. It leads to a system of coupled Eulerian partial differential equations. We describe in detail a robust numerical implementation of our approach, in accordance with the narrow band methodology. We show in a variety of numerical experiments that it can handle both normal and tangential velocities, large deformations, shocks, rarefactions and topological changes. The possible applications of our approach include scientific visualization, computer graphics and image processing.

Unfolding the Cerebral Cortex Using Level Set Methods

Level set methods provide a robust way to implement geometric flows, but they suffer from two problems which are relevant when using smoothing flows to unfold the cortex: the lack of point-correspondence between scales and the inability to implement tangential velocities. In this paper, we suggest to solve these problems by driving the nodes of a mesh with an ordinary Differential equation. We state that this approach does not suffer from the known problems of Lagrangian methods since all geometrical properties are computed on the fixed (Eulerian) grid. Additionally, tangential velocities can be given to the nodes, allowing the mesh to follow general evolution equations, which could be crucial to achieving the final goal of minimizing local metric distortions. To experiment with this approach, we derive area and volume preserving mean curvature flows and use them to unfold surfaces extracted from MRI data of the human brain.

Dixon Sequence with Superimposed Model-Based Bone Compartment Provides Highly Accurate PET/MR Attenuation Correction of the Brain.

Simultaneous PET/MR of the brain is a promising technology for characterizing patients with suspected cognitive impairment or epilepsy. Unlike CT, however, MR signal intensities do not correlate directly with PET photon attenuation correction (AC), and inaccurate radiotracer SUV estimation can limit future PET/MR clinical applications. We tested a novel AC method that supplements standard Dixon-based tissue segmentation with a superimposed model-based bone compartment. Methods: We directly compared SUV estimation between MR-based AC and reference CT AC in 16 patients undergoing same-day PET/CT and PET/MR with a single 18F-FDG dose for suspected neurodegeneration. Three Dixon-based MR AC methods were compared with CT: standard Dixon 4-compartment segmentation alone, Dixon with a superimposed model-based bone compartment, and Dixon with a superimposed bone compartment and linear AC optimized specifically for brain tissue. The brain was segmented using a 3-dimensional T1-weighted volumetric MR sequence, and SUV estimations were compared with CT AC for whole-image, whole-brain, and 91 FreeSurfer-based regions of interest. Results: Modifying the linear AC value specifically for brain and superimposing a model-based bone compartment reduced the whole-brain SUV estimation bias of Dixon-based PET/MR AC by 95% compared with reference CT AC (P < 0.05), resulting in a residual −0.3% whole-brain SUVmean bias. Further, brain regional analysis demonstrated only 3 frontal lobe regions with an SUV estimation bias of 5% or greater (P < 0.05). These biases appeared to correlate with high individual variability in frontal bone thickness and pneumatization. Conclusion: Bone compartment and linear AC modifications result in a highly accurate MR AC method in subjects with suspected neurodegeneration. This prototype MR AC solution appears equivalent to other recently proposed solutions and does not require additional MR sequences and scanning time. These data also suggest that exclusively model-based MR AC approaches may be adversely affected by common individual variations in skull anatomy.

Application and assessment of a robust elastic motion correction algorithm to dynamic MRI

The purpose of this study was to assess the performance of a new motion correction algorithm. Twenty-five dynamic MR mammography (MRM) data sets and 25 contrast-enhanced three-dimensional peripheral MR angiographic (MRA) data sets which were affected by patient motion of varying severeness were selected retrospectively from routine examinations. Anonymized data were registered by a new experimental elastic motion correction algorithm. The algorithm works by computing a similarity measure for the two volumes that takes into account expected signal changes due to the presence of a contrast agent while penalizing other signal changes caused by patient motion. A conjugate gradient method is used to find the best possible set of motion parameters that maximizes the similarity measures across the entire volume. Images before and after correction were visually evaluated and scored by experienced radiologists with respect to reduction of motion, improvement of image quality, disappearance of existing lesions or creation of artifactual lesions. It was found that the correction improves image quality (76% for MRM and 96% for MRA) and diagnosability (60% for MRM and 96% for MRA).