268 research outputs found
Unified Heat Kernel Regression for Diffusion, Kernel Smoothing and Wavelets on Manifolds and Its Application to Mandible Growth Modeling in CT Images
We present a novel kernel regression framework for smoothing scalar surface
data using the Laplace-Beltrami eigenfunctions. Starting with the heat kernel
constructed from the eigenfunctions, we formulate a new bivariate kernel
regression framework as a weighted eigenfunction expansion with the heat kernel
as the weights. The new kernel regression is mathematically equivalent to
isotropic heat diffusion, kernel smoothing and recently popular diffusion
wavelets. Unlike many previous partial differential equation based approaches
involving diffusion, our approach represents the solution of diffusion
analytically, reducing numerical inaccuracy and slow convergence. The numerical
implementation is validated on a unit sphere using spherical harmonics. As an
illustration, we have applied the method in characterizing the localized growth
pattern of mandible surfaces obtained in CT images from subjects between ages 0
and 20 years by regressing the length of displacement vectors with respect to
the template surface.Comment: Accepted in Medical Image Analysi
BrainPrint: Identifying Subjects by Their Brain
Introducing BrainPrint, a compact and discriminative representation of anatomical structures in the brain. BrainPrint captures shape information of an ensemble of cortical and subcortical structures by solving the 2D and 3D Laplace-Beltrami operator on triangular (boundary) and tetrahedral (volumetric) meshes. We derive a robust classifier for this representation that identifies the subject in a new scan, based on a database of brain scans. In an example dataset containing over 3000 MRI scans, we show that BrainPrint captures unique information about the subject’s anatomy and permits to correctly classify a scan with an accuracy of over 99.8%. All processing steps for obtaining the compact representation are fully automated making this processing framework particularly attractive for handling large datasets.Alexander von Humboldt-StiftungAthinoula A. Martinos Center for Biomedical Imaging (P41-RR014075)Athinoula A. Martinos Center for Biomedical Imaging (P41-EB015896)National Alliance for Medical Image Computing (U.S.) (U54-EB005149)Neuroimaging Analysis Center (U.S.) (P41-EB015902
A sub-Riemannian model of the visual cortex with frequency and phase
In this paper we present a novel model of the primary visual cortex (V1) based on orientation, frequency and phase selective behavior of the V1 simple cells. We start from the first level mechanisms of visual perception: receptive profiles. The model interprets V1 as a fiber bundle over the 2-dimensional retinal plane by introducing orientation, frequency and phase as intrinsic variables. Each receptive profile on the fiber is mathematically interpreted as a rotated, frequency modulated and phase shifted Gabor function. We start from the Gabor function and show that it induces in a natural way the model geometry and the associated horizontal connectivity modeling the neural connectivity patterns in V1. We provide an image enhancement algorithm employing the model framework. The algorithm is capable of exploiting not only orientation but also frequency and phase information existing intrinsically in a 2-dimensional input image. We provide the experimental results corresponding to the enhancement algorithm
Multi-scale and multi-spectral shape analysis: from 2d to 3d
Shape analysis is a fundamental aspect of many problems in computer graphics and computer vision, including shape matching, shape registration, object recognition and classification. Since the SIFT achieves excellent matching results in 2D image domain, it inspires us to convert the 3D shape analysis to 2D image analysis using geometric maps. However, the major disadvantage of geometric maps is that it introduces inevitable, large distortions when mapping large, complex and topologically complicated surfaces to a canonical domain. It is demanded for the researchers to construct the scale space directly on the 3D shape.
To address these research issues, in this dissertation, in order to find the multiscale processing for the 3D shape, we start with shape vector image diffusion framework using the geometric mapping. Subsequently, we investigate the shape spectrum field by introducing the implementation and application of Laplacian shape spectrum. In order to construct the scale space on 3D shape directly, we present a novel idea to solve the diffusion equation using the manifold harmonics in the spectral point of view. Not only confined on the mesh, by using the point-based manifold harmonics, we rigorously derive our solution from the diffusion equation which is the essential of the scale space processing on the manifold. Built upon the point-based manifold harmonics transform, we generalize the diffusion function directly on the point clouds to create the scale space. In virtue of the multiscale structure from the scale space, we can detect the feature points and construct the descriptor based on the local neighborhood. As a result, multiscale shape analysis directly on the 3D shape can be achieved
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