A LogEuclidean framework for statistics on diffeomorphisms (0)

by Vincent Arsigny, Olivier Commowick, Xavier Pennec, Nicholas Ayache
Venue:in MICCAI 2006, 2006
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Diffeomorphic Demons: Efficient Non-parametric Image Registration

by Tom Vercauteren , Xavier Pennec , Aymeric Perchant , Nicholas Ayache , 2008
"... We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion’s demons algorithm. In the first part of this paper, we show that Thirion’s demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theor ..."
Abstract - Cited by 104 (13 self) - Add to MetaCart
We propose an efficient non-parametric diffeomorphic image registration algorithm based on Thirion’s demons algorithm. In the first part of this paper, we show that Thirion’s demons algorithm can be seen as an optimization procedure on the entire space of displacement fields. We provide strong theoretical roots to the different variants of Thirion’s demons algorithm. This analysis predicts a theoretical advantage for the symmetric forces variant of the demons algorithm. We show on controlled experiments that this advantage is confirmed in practice and yields a faster convergence. In the second part of this paper, we adapt the optimization procedure underlying the demons algorithm 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 displacement fields 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 gold standard, available in controlled experiments, in terms of Jacobians.
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Symmetric log-domain diffeomorphic registration: A demons-based approach

by Tom Vercauteren, Xavier Pennec, Aymeric Perchant, Nicholas Ayache - IMAG. COMPUT , 2008
"... Modern morphometric studies use non-linear image registration to compare anatomies and perform group analysis. Recently, log-Euclidean approaches have contributed to promote the use of such computational anatomy tools by permitting simple computations of statistics on a rather large class of inverti ..."
Abstract - Cited by 72 (29 self) - Add to MetaCart
Modern morphometric studies use non-linear image registration to compare anatomies and perform group analysis. Recently, log-Euclidean approaches have contributed to promote the use of such computational anatomy tools by permitting simple computations of statistics on a rather large class of invertible spatial transformations. In this work, we propose a non-linear registration algorithm perfectly fit for log-Euclidean statistics on diffeomorphisms. Our algorithm works completely in the log-domain, i.e. it uses a stationary velocity field. This implies that we guarantee the invertibility of the deformation and have access to the true inverse transformation. This also means that our output can be directly used for log-Euclidean statistics without relying on the heavy computation of the log of the spatial transformation. As it is often desirable, our algorithm is symmetric with respect to the order of the input images. Furthermore, we use an alternate optimization approach related to Thirion’s demons algorithm to provide a fast non-linear registration algorithm. First results show that our algorithm outperforms both the demons algorithm and the recently proposed diffeomorphic demons algorithm in terms of accuracy of the transformation while remaining computationally efficient.
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A Generative Model for Image Segmentation Based on Label Fusion

by Mert R. Sabuncu, B. T. Thomas Yeo, Koen Van Leemput, Bruce Fischl, Polina Golland - IEEE TRANSACTIONS IN MEDICAL IMAGING , 2010
"... We propose a nonparametric, probabilistic model for the automatic segmentation of medical images, given a training set of images and corresponding label maps. The resulting inference algorithms rely on pairwise registrations between the test image and individual training images. The training labels ..."
Abstract - Cited by 59 (3 self) - Add to MetaCart
We propose a nonparametric, probabilistic model for the automatic segmentation of medical images, given a training set of images and corresponding label maps. The resulting inference algorithms rely on pairwise registrations between the test image and individual training images. The training labels are then transferred to the test image and fused to compute the final segmentation of the test subject. Such label fusion methods have been shown to yield accurate segmentation, since the use of multiple registrations captures greater inter-subject anatomical variability and improves robustness against occasional registration failures. To the best of our knowledge, this manuscript presents the first comprehensive probabilistic framework that rigorously motivates label fusion as a segmentation approach. The proposed framework allows us to compare different label fusion algorithms theoretically and practically. In particular, recent label fusion or multiatlas segmentation
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Non-parametric Diffeomorphic Image Registration with Demons Algorithm

by Tom Vercauteren, Xavier Pennec, Aymeric Perchant, Nicholas Ayache , 2007
"... 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 diffeomorphi ..."
Abstract - Cited by 46 (9 self) - Add to MetaCart
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.
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Deformable medical image registration: A survey

by Aristeidis Sotiras, Christos Davatzikos, Nikos Paragios - IEEE TRANSACTIONS ON MEDICAL IMAGING , 2013
"... Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: i) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; ii) longitudin ..."
Abstract - Cited by 34 (1 self) - Add to MetaCart
Deformable image registration is a fundamental task in medical image processing. Among its most important applications, one may cite: i) multi-modality fusion, where information acquired by different imaging devices or protocols is fused to facilitate diagnosis and treatment planning; ii) longitudinal studies, where temporal structural or anatomical changes are investigated; and iii) population modeling and statistical atlases used to study normal anatomical variability. In this paper, we attempt to give an overview of deformable registration methods, putting emphasis on the most recent advances in the domain. Additional emphasis has been given to techniques applied to medical images. In order to study image registration methods in depth, their main components are identified and studied independently. The most recent techniques are presented in a systematic fashion. The contribution of this paper is to provide an extensive account of registration techniques in a systematic manner.
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DT-REFinD: Diffusion Tensor Registration with Exact Finite-Strain Differential

by B. T. Thomas Yeo, Tom Vercauteren, Pierre Fillard, Jean-marc Peyrat, Xavier Pennec, Polina Goll, Nicholas Ayache, Olivier Clatz - IEEE Transactions on Medical Imaging, In , 2009
"... Abstract—In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorit ..."
Abstract - Cited by 25 (9 self) - Add to MetaCart
Abstract—In this paper, we propose the DT-REFinD algorithm for the diffeomorphic nonlinear registration of diffusion tensor images. Unlike scalar images, deforming tensor images requires choosing both a reorientation strategy and an interpolation scheme. Current diffusion tensor registration algorithms that use full tensor information face difficulties in computing the differential of the tensor reorientation strategy and consequently, these methods often approximate the gradient of the objective function. In the case of the finite-strain (FS) reorientation strategy, we borrow results from the pose estimation literature in computer vision to derive an analytical gradient of the registration objective function. By utilizing the closed-form gradient and the velocity field representation of one parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. We contrast the algorithm with a traditional FS alternative
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A computational framework for the statistical analysis of cardiac diffusion tensors: Application to a small database of canine hearts

by Jean-marc Peyrat, Maxime Sermesant, Xavier Pennec, Hervé Delingette, Chenyang Xu, Elliot R. Mcveigh, Nicholas Ayache - IEEE Transactions on Medical Imaging , 2007
"... Abstract—We propose a unified computational framework to build a statistical atlas of the cardiac fiber architecture from diffusion tensor magnetic resonance images (DT-MRIs). We apply this framework to a small database of nine ex vivo canine hearts. An average cardiac fiber architecture and a measu ..."
Abstract - Cited by 24 (17 self) - Add to MetaCart
Abstract—We propose a unified computational framework to build a statistical atlas of the cardiac fiber architecture from diffusion tensor magnetic resonance images (DT-MRIs). We apply this framework to a small database of nine ex vivo canine hearts. An average cardiac fiber architecture and a measure of its variability are computed based on most recent advances in diffusion tensor statistics. This statistical analysis confirms the already established good stability of the fiber orientations and a higher variability of the laminar sheet orientations within a given species. The statistical comparison between the canine atlas and a standard human cardiac DT-MRI shows a better stability of the fiber orientations than their laminar sheet orientations between the two species. The proposed computational framework can be applied to larger databases of cardiac DT-MRIs from various species to better establish intra- and inter-species statistics on the anatomical structure of cardiac fibers. This information will be useful to guide the adjustment of average fiber models onto specific patients from in vivo anatomical imaging modalities. Index Terms—Atlas, cardiac, diffusion tensor magnetic resonance imaging, DTI, DT-MRI, fiber architecture, heart, laminar sheets, statistics. I.
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Spherical Demons: Fast Diffeomorphic Landmark-Free Surface Registration

by B. T. Thomas Yeo, Mert R. Sabuncu, Tom Vercauteren, Nicholas Ayache, Bruce Fischl, Polina Golland - IEEE TRANSACTIONS ON MEDICAL IMAGING. 29(3):650–668, 2010 , 2010
"... We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. B ..."
Abstract - Cited by 24 (5 self) - Add to MetaCart
We present the Spherical Demons algorithm for registering two spherical images. By exploiting spherical vector spline interpolation theory, we show that a large class of regularizors for the modified Demons objective function can be efficiently approximated on the sphere using iterative smoothing. Based on one parameter subgroups of diffeomorphisms, the resulting registration is diffeomorphic and fast. The Spherical Demons algorithm can also be modified to register a given spherical image to a probabilistic atlas. We demonstrate two variants of the algorithm corresponding to warping the atlas or warping the subject. Registration of a cortical surface mesh to an atlas mesh, both with more than 160k nodes requires less than 5 minutes when warping the atlas and less than 3 minutes when warping the subject on a Xeon 3.2GHz single processor machine. This is comparable to the fastest non-diffeomorphic landmarkfree surface registration algorithms. Furthermore, the accuracy of our method compares favorably to the popular FreeSurfer registration algorithm. We validate the technique in two different applications that use registration to transfer segmentation labels onto a new image: (1) parcellation of in-vivo cortical surfaces and (2) Brodmann area localization in ex-vivo cortical surfaces.

A multi-scale kernel bundle for LDDMM: Towards sparse deformation description across space and scales

by Stefan Sommer, Mads Nielsen, François Lauze, Xavier Pennec - IN: IPMI. LNCS , 2011
"... The Large Deformation Diffeomorphic Metric Mapping framework constitutes a widely used and mathematically well-founded setup for registration in medical imaging. At its heart lies the notion of the regularization kernel, and the choice of kernel greatly affects the results of registrations. This pap ..."
Abstract - Cited by 15 (7 self) - Add to MetaCart
The Large Deformation Diffeomorphic Metric Mapping framework constitutes a widely used and mathematically well-founded setup for registration in medical imaging. At its heart lies the notion of the regularization kernel, and the choice of kernel greatly affects the results of registrations. This paper presents an extension of the LDDMM framework allowing multiple kernels at multiple scales to be incorporated in each registration while preserving many of the mathematical properties of standard LDDMM. On a dataset of landmarks from lung CT images, we show by example the influence of the kernel size in standard LDDMM, and we demonstrate how our framework, LDDKBM, automatically incorporates the advantages of each scale to reach the same accuracy as the standard method optimally tuned with respect to scale. The framework, which is not limited to landmark data, thus removes the need for classical scale selection. Moreover, by decoupling the momentum across scales, it promises to provide better interpolation properties, to allow sparse descriptions of the total deformation, to remove the trade-off between match quality and regularity, and to allow for momentum based statistics using scale information.
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DTI REGISTRATION WITH EXACT FINITE-STRAIN DIFFERENTIAL

by B. T. Thomas Yeo, Tom Vercauteren, Pierre Fillard, Xavier Pennec, Polina Golland, Nicholas Ayache, Olivier Clatz , 2008
"... We propose an algorithm for the diffeomorphic registration of diffusion tensor images (DTI). Previous DTI registration algorithms using full tensor information suffer from difficulties in computing the differential of the Finite Strain tensor reorientation strategy. We borrow results from computer v ..."
Abstract - Cited by 14 (3 self) - Add to MetaCart
We propose an algorithm for the diffeomorphic registration of diffusion tensor images (DTI). Previous DTI registration algorithms using full tensor information suffer from difficulties in computing the differential of the Finite Strain tensor reorientation strategy. We borrow results from computer vision to derive an analytical gradient of the objective function. By leveraging on the closed-form gradient and the one-parameter subgroups of diffeomorphisms, the resulting registration algorithm is diffeomorphic and fast. Registration of a pair of 128 × 128 × 60 diffusion tensor volumes takes 15 minutes. We contrast the algorithm with a classic alternative that does not take into account the reorientation in the gradient computation. We show with 40 pairwise DTI registrations that using the exact gradient achieves significantly better registration.
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