Marc Vaillant

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We present a new method for computing an optimal deformation between two arbitrary surfaces embedded in Euclidean 3-dimensional space. Our main contribution is in building a norm on the space of surfaces via representation by currents of geometric measure theory. Currents are an appropriate choice for representations because they inherit natural(More)
In this paper, we present a linear setting for statistical analysis of shape and an optimization approach based on a recent derivation of a conservation of momentum law for the geodesics of diffeomorphic flow. Once a template is fixed, the space of initial momentum becomes an appropriate space for studying shape via geodesic flow since the flow at any point(More)
This paper presents a methodology and algorithm for generating diffeomorphisms of the sphere onto itself, given the displacements of a finite set of template landmarks. Deformation maps are constructed by integration of velocity fields that minimize a quadratic smoothness energy under the specified landmark constraints. We present additional formulations of(More)
This paper builds upon our previous work on elastic registration, using surface-to-surface mapping. In particular, a methodology for finding a smooth map from one cortical surface to another is presented, using constraints imposed by a number of sulcal and gyral curves. The outer cortical surface is represented by a map from the unit sphere to the surface(More)
A computer algorithm for determining optimal surgical paths in the brain is presented. The algorithm computes a cost function associated with each point on the outer brain boundary, which is treated as a candidate entry point. The cost function is determined partly based on a segmentation of the patients images into gray and white matter, and partly based(More)
This paper describes the application of large deformation diffeomorphic metric mapping to cortical surfaces based on the shape and geometric properties of subregions of the superior temporal gyrus in the human brain. The anatomical surfaces of the cortex are represented as triangulated meshes. The diffeomorphic matching algorithm is implemented by defining(More)
The cortical sulci are brain structures resembling thin convoluted ribbons embedded in three dimensions. The importance of the sulci lies primarily in their relation to the cytoarchitectonic and functional organization of the underlying cortex and in their utilization as features in non-rigid registration methods. This paper presents a methodology for(More)
Abs t rac t . We propose a methodology for extracting parametric representations of the cerebral sulci from magnetic resonance images, and we consider its application to two medical imaging problems: quantitative morphological analysis and spatial normalization and registration of brain images. Our methodology is based on deformable models utilizing(More)
In neuroimaging studies, spatial normalization and multivariate testing are central problems in characterizing group variation of functions (e.g., cortical thickness, curvature, functional response) in an atlas coordinate system across clinical populations. We present a region-of-interest (ROI)-based analysis framework for detecting such a group variation.(More)
Marc Vaillant, Christos Davatzikos and R. Nick Bryan Neuroimaging Laboratory Department of Radiology Johns Hopkins School of Medicine 600 N. Wolfe street, Baltimore MD 21287 WWW: Abstract Parametric representations of anatomical structures provide useful mathematical descriptions for many medical imaging applications, including(More)