Spectral Demons – Image Registration via Global Spectral Correspondence

Lombaert, Hervé; Grady, Leo; Pennec, Xavier; Ayache, Nicholas; Cheriet, Foued

doi:10.1007/978-3-642-33709-3_3

Cited by 20 publications

(14 citation statements)

References 29 publications

(34 reference statements)

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“…This analysis on harmonic weights contrasts with conventional approaches where surface values are typically coupled with surface points. Possible extensions to images [32,33] may be also provide new applications. To conclude, our method, Brain Transfer, offers a better formulation for spectral methods by enabling the spectral transfer of intrinsic geometrical properties across surfaces.…”

Section: Resultsmentioning

confidence: 99%

Brain Transfer: Spectral Analysis of Cortical Surfaces and Functional Maps

Lombaert

Arcaro

Ayache

2015

Lecture Notes in Computer Science

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International audienceThe study of brain functions using fMRI often requires an accuratematching of cortical surface data for comparing brain activation acrossa population. In this context, several tasks are critical, such as surface in-flation for cortical visualizations and measurements, surface matching andalignment of functional data for group-level analyses. Present methods typicallytreat each task separately and can be computationally expensive. It takesfor example several hours to smooth and match a single pair of cortical surfaces.Furthermore, conventional methods rely on anatomical features to drivethe alignment of functional data across individuals, whereas their relation tofunction can vary across a population. To address these issues, we proposeBrain Transfer, a spectral framework that unifies cortical smoothing, pointmatching with confidence regions, and transfer of functional maps, all withinminutes of computation. Spectral methods have the advantage of decomposingshapes into intrinsic geometrical harmonics, but suffer from the inherentinstability of these harmonics. This limits their direct comparison in surfacematching, and prevents the spectral transfer of functions. Our contributionsconsist of, first, the optimization of a spectral transformation matrix, whichcombines both, point correspondence and change of eigenbasis, and second,a localized spectral decomposition of functional data, via focused harmonics.Brain Transfer enables the transfer of surface functions across interchangeablecortical spaces, accounts for localized confidence, and gives a new way toperform statistics on surfaces. We illustrate the benefits of spectral transfersby exploring the shape and functional variability of retinotopy, which remainschallenging with conventional methods. We find a higher degree of accuracyin the alignment of retinotopy, exceeding those of conventional methods

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Section: Resultsmentioning

confidence: 99%

Brain Transfer: Spectral Analysis of Cortical Surfaces and Functional Maps

Lombaert

Arcaro

Ayache

2015

Lecture Notes in Computer Science

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“…Model D. Finally Thirion [21] introduced the so-called demon registration method where every pixel in the image acts as the demons that force a pulling and pushing action in a similar way to what Maxwell did for solving the Gibbs paradox in thermodynamics. The original demon registration model is a special case of diffusion registration but it has been much studied and improved since 1998; see [17,15,25,14]. The energy functional for the basic demon method is given by…”

Section: Review Of Non-parametric Image Registrationmentioning

confidence: 99%

“…So, when this ratio is large (indicating possibly a noise presence), the total variation model reduces it and hence removes noise. However, important features of u which have a large level set ratio are removed also and so not preserved by the total variation model (14).…”

Section: Advantages Of a Gaussian Curvaturementioning

confidence: 99%

A novel variational model for image registration using Gaussian curvature

Ibrahim

Chen

Brito‐Loeza

2014

Geometry, Imaging and Computing

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Image registration is one important task in many image processing applications. It aims to align two or more images so that useful information can be extracted through comparison, combination or superposition. This is achieved by constructing an optimal transformation which ensures that the template image becomes similar to a given reference image. Although many models exist, designing a model capable of modelling a large and smooth deformation field continues to pose a challenge. This paper proposes a novel variational model for image registration using the Gaussian curvature as a regulariser. The model is motivated by the surface restoration work in geometric processing [Elsey and Esedoglu, Multiscale Model. Simul., (2009), pp. 1549-1573]. An effective numerical solver is provided for the model using an augmented Lagrangian method. Numerical experiments can show that the new model outperforms three competing models based on, respectively, a linear curvature [Fischer and Modersitzki, J. Math. Imaging Vis., (2003), pp. 81-85], the mean curvature [Chumchob, Chen and Brito, Multiscale Model. Simul., (2011), pp. 89-128] and the diffeomorphic demon model [Vercauteren at al., NeuroImage, (2009), pp. 61-72] in terms of robustness and accuracy.

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“…We now describe a new update scheme based on spectral correspondence [21,11,18,14,13] that will enable the construction of atlases with large deformations. Let us first consider I Ω , the portion of an image I bounded by a contour Ω.…”

Section: Spectral Correspondencementioning

confidence: 99%

“…However, as in most registration methods, transformation updates based on the image gradients are inherently limited by their local scope. Secondly, we introduce a new update scheme for groupwise registration based on the spectral decomposition of graph Laplacians [7,23,13], that is invariant to shape isometry and is capable of capturing large deformations during the construction of the atlas. We provide two forms of our groupwise registration framework that we name the Groupwise Log-Demons (GL-Demons, faster and suited for local nonrigid deformations), and the Groupwise Spectral Log-Demons (GSL-Demons, slower but capable of capturing very large deformations).…”

Section: Introductionmentioning

confidence: 99%

Groupwise Spectral Log-Demons Framework for Atlas Construction

Lombaert

Grady

Pennec

et al. 2013

Medical Computer Vision. Recognition Techniques and Applications in Medical Imaging

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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.

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Spectral Demons – Image Registration via Global Spectral Correspondence

Cited by 20 publications

References 29 publications

Brain Transfer: Spectral Analysis of Cortical Surfaces and Functional Maps

Brain Transfer: Spectral Analysis of Cortical Surfaces and Functional Maps

A novel variational model for image registration using Gaussian curvature

Groupwise Spectral Log-Demons Framework for Atlas Construction

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