Contributions to 3D Diffeomorphic Atlas Estimation: Application to Brain Images

Lecture Notes in Computer Science

Perchant

et al. 2008

285

327

Abstract. 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.

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Symmetric Log-Domain Diffeomorphic Registration: A Demons-Based Approach

Vercauteren

Lecture Notes in Computer Science

Perchant

et al. 2008

285

327

“…Both images F ′ and M ′ effectively converge toward an average shapeĨ = F • φ −1 + M • φ (similar to the approaches in [2,6]). …”

Section: Diffeomorphic Registrationmentioning

confidence: 53%

“…In the present state-of-the-art, the concept of geodesic shape averaging allows unbiased constructions of atlases through diffeomorphic methods [12,2,17], i.e., the transformation of a reference shape toward an average (the geometry of the atlas) follows a geodesic path on a Riemannian manifold (the space of diffeomorphic transformations). While the LDDMM [4,3,6] or forward scheme approaches [1,8] provide elegant mathematical frameworks for averaging shapes, these methods could be slow and find their limitations with high shape variability. Guimond et al [10] proposed a fast and efficient algorithm [19,16,26] with sequential (pairwise) registrations to a reference image.…”

Section: Introductionmentioning

confidence: 99%

Groupwise Spectral Log-Demons Framework for Atlas Construction

Lombaert

Grady

Medical Computer Vision. Recognition Techniques and Applications in Medical Imaging

et al. 2013

Abstract. We introduce a new framework to construct atlases from images with very large and complex deformations. The atlas is build in parallel with groupwise registrations by extending the symmetric Log-Demons algorithm. We describe and evaluate two forms of our framework: the Groupwise LogDemons (GL-Demons) is faster but is limited to local nonrigid deformations, and the Groupwise Spectral Log-Demons (GSL-Demons) is slower but, due to isometry-invariant representations of images, can construct atlases of organs with high shape variability. We demonstrate our framework by constructing atlases from hearts with high shape variability.

“…BCH formula for the conjugate action The Baker Campbell Haudorff (BCH) formula was introduced in the SVF diffeomorphic registration in [2] and provides an explicit way to compose diffeomorphisms by operating in the as- …”

Section: Application To Imagesmentioning

confidence: 99%

Schild’s Ladder for the Parallel Transport of Deformations in Time Series of Images

Lorenzi

Ayache

Lecture Notes in Computer Science

2011

Abstract. Follow-up imaging studies require the evaluation of the anatomical changes over time for specific clinical groups. The longitudinal changes for a specific subject can be evaluated through the non-rigid registration of successive anatomical images. However, to perform a longitudinal group-wise analysis, the subject-specific longitudinal trajectories of anatomical points need to be transported in a common reference frame. In this work, we propose the Schild's Ladder framework as an effective method to transport longitudinal deformations in time series of images in a common space using diffeomorphic registration. We illustrate the computational advantages and demonstrate the numerical accuracy of this very simple method by comparing with standard methods of transport on simulated images with progressing brain atrophy. Finally, its application to the clinical problem of the measurement of the longitudinal progression in the Alzheimer's disease suggests that an important gain in sensitivity could be expected on group-wise comparisons.