Shape Modeling with Front Propagation: A Level Set Approach
IEEE Transactions on Pattern Analysis and Machine Intelligence
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Diffeomorphic statistical shape models
Image and Vision Computing
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MICCAI '08 Proceedings of the 11th International Conference on Medical Image Computing and Computer-Assisted Intervention, Part II
A Schrödinger Equation for the Fast Computation of Approximate Euclidean Distance Functions
SSVM '09 Proceedings of the Second International Conference on Scale Space and Variational Methods in Computer Vision
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International Journal of Computer Vision
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MICCAI '09 Proceedings of the 12th International Conference on Medical Image Computing and Computer-Assisted Intervention: Part I
Optimization of mutual information for multiresolution image registration
IEEE Transactions on Image Processing
Fast shape-based nearest-neighbor search for brain MRIs using hierarchical feature matching
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part II
Mixture of segmenters with discriminative spatial regularization and sparse weight selection
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part III
3d segmentation of rodent brain structures using hierarchical shape priors and deformable models
MICCAI'11 Proceedings of the 14th international conference on Medical image computing and computer-assisted intervention - Volume Part III
3D anatomical shape atlas construction using mesh quality preserved deformable models
MeshMed'12 Proceedings of the 2012 international conference on Mesh Processing in Medical Image Analysis
3D anatomical shape atlas construction using mesh quality preserved deformable models
Computer Vision and Image Understanding
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This paper proposes a novel technique for constructing a neuroanatomical shape complex atlas using an information geometry framework. A shape complex is a collection of shapes in a local neighborhood. We represent the boundary of the entire shape complex using the zero level set of a distance function S(x). The spatial relations between the different anatomical structures constituting the shape complex are captured via the distance transform. We then leverage the well known relationship between the stationary state wave function ψ(x) of the Schrödinger equation -h2∇2ψ + ψ = 0 and the eikonal equation ||∇S|| = 1 satisfied by any distance function S(x). This leads to a one-to-one map between ψ(x) and S(x) and allows for recovery of S(x) from ψ(x) through an explicit mathematical relationship. Since the wave function can be regarded as a square-root density function, we are able to exploit this connection and convert shape complex distance transforms into probability density functions. Furthermore, square-root density functions can be seen as points on a unit hypersphere whose Riemannian structure is fully known. A shape complex atlas is constructed by first computing the Karcher mean ψ(x) of the wave functions, followed by an inverse mapping of the estimated mean back to the space of distance transforms in order to realize the atlas. We demonstrate the shape complex atlas computation via a set of experiments on a population of brain MRI scans. We also present modes of variation from the computed atlas for the control population to demonstrate the shape complex variability.