Brain structural mapping using a novel hybrid implicit/explicit framework based on the level-set method

Leow, Alex D.; Yu, Cheng‐Wei; Lee, S. J.; Huang, Sung‐Cheng; Protas, Hillary; Nicolson, Rob; Hayashi, Kiralee M.; Toga, Arthur W.; Thompson, Paul M.

doi:10.1016/j.neuroimage.2004.09.022

Cited by 58 publications

(42 citation statements)

References 43 publications

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“…Overall, finding diffeomorphic mappings between brain surfaces is an important but difficult problem. In most cases, extra regulations, such as inverse consistency [9,16], have to be enforced to ensure a diffeomorphism. Since the proposed work offers a harmonic map based scheme for diffeomorphisms which guarantees a perfect landmark curve registration via enforced boundary matching, the novelty of the proposed work is that it facilitates diffeomorphic mapping between general surfaces with delineated landmark curves.…”

Section: Previous Workmentioning

confidence: 99%

Hyperbolic Harmonic Brain Surface Registration with Curvature-Based Landmark Matching

Zeng

Wang

et al. 2013

Lecture Notes in Computer Science

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Abstract. Brain Cortical surface registration is required for inter-subject studies of functional and anatomical data. Harmonic mapping has been applied for brain mapping, due to its existence, uniqueness, regularity and numerical stability. In order to improve the registration accuracy, sculcal landmarks are usually used as constraints for brain registration. Unfortunately, constrained harmonic mappings may not be diffeomorphic and produces invalid registration. This work conquers this problem by changing the Riemannian metric on the target cortical surface to a hyperbolic metric, so that the harmonic mapping is guaranteed to be a diffeomorphism. With landmarks delineated as boundary condition, it is possible to be integrated with landmark matching. The computational algorithms are based on the Ricci flow method and hyperbolic heat diffusion. Experimental results demonstrate that, by changing the Riemannian metric, the registrations have higher qualities in terms of landmark alignment, curvature matching, area distortion and overlapping of region of interests.

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Section: Previous Workmentioning

confidence: 99%

Hyperbolic Harmonic Brain Surface Registration with Curvature-Based Landmark Matching

Zeng

Wang

et al. 2013

Lecture Notes in Computer Science

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“…A simple approach to obtain such a map is to parameterize each pair of curves with arc length and establish correspondences between points on the two curves by uniform sampling. One can also establish the mapping between curves using the method in (Leow et al, 2005).…”

Section: A Variational Frameworkmentioning

confidence: 99%

Direct cortical mapping via solving partial differential equations on implicit surfaces

Shi

Thompson

Dinov

et al. 2007

Medical Image Analysis

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In this paper, we propose a novel approach for cortical mapping that computes a direct map between two cortical surfaces while satisfying constraints on sulcal landmark curves. By computing the map directly, we can avoid conventional intermediate parameterizations and help simplify the cortical mapping process. The direct map in our method is formulated as the minimizer of a flexible variational energy under landmark constraints. The energy can include both a harmonic term to ensure smoothness of the map and general data terms for the matching of geometric features. Starting from a properly designed initial map, we compute the map iteratively by solving a partial differential equation (PDE) defined on the source cortical surface. For numerical implementation, a set of adaptive numerical schemes are developed to extend the technique of solving PDEs on implicit surfaces such that landmark constraints are enforced. In our experiments, we show the flexibility of the direct mapping approach by computing smooth maps following landmark constraints from two different energies. We also quantitatively compare the metric preserving property of the direct mapping method with a parametric mapping method on a group of 30 subjects. Finally, we demonstrate the direct mapping method in the brain mapping applications of atlas construction and variability analysis.

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“…Thus, a more natural way to proceed consists of calculating the unsigned distance functions T y (ϕ(., 1)) between the ϕ(x i , 1) and the associated structure in the study. This method was used in the plane by Leow et al [1], and is extended to the sphere in this paper.…”

Section: Landmark Matching On the Spherementioning

confidence: 99%

“…Within this framework, the transformation ϕ satisfies (1) where The final solution is given by ϕ(x, 1). Here the coordinate x is taken in a fixed reference frame, while the image deforms in time.…”

Section: Introductionmentioning

confidence: 99%

“…In the context of large deformations, Leow et al [1] used the smoothness constraint described in [7] in the plane, while replacing their matching term by a sum of the backward and forward distance functions at the final positions of the template landmarks. This method was shown to significantly improve the results, relative to unidirectional matching.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Landmark matching on the sphere using distance functions

Leporé¹,

Leow²,

Thompson³

3rd IEEE International Symposium on Biomedical Imaging: Macro to Nano, 2006.

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Nonlinear registration of 3D surfaces is important in many medical imaging applications, including the mapping of longitudinal changes in anatomy, or of multi-subject functional MRI data to a canonical surface for comparison and integration. To register 3D surfaces, such as the cortical surface of the brain, one approach is to transform them first to planar or spherical objects. Internal landmarks can then be matched on these simpler parameter domains. Here we study the diffeomorphic matching of landmarks on the sphere. Our method builds on the level set technique of Leow et al. [1] for the plane. Both forward and backward matching terms are included, thus ensuring the invertibility of the representation. We demonstrate our technique on a pair of lines on the sphere. The overall approach improves on earlier work in cortical matching by allowing the matching energy to be relaxed along sulcal landmarks, minimizing distortion, and also enables point and curve landmarks to be aligned in the same general framework as densely-defined scalar fields, such as curvature or cortical thickness maps.

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Brain structural mapping using a novel hybrid implicit/explicit framework based on the level-set method

Cited by 58 publications

References 43 publications

Hyperbolic Harmonic Brain Surface Registration with Curvature-Based Landmark Matching

Hyperbolic Harmonic Brain Surface Registration with Curvature-Based Landmark Matching

Direct cortical mapping via solving partial differential equations on implicit surfaces

Landmark matching on the sphere using distance functions

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