Yinlong Sun

STATISTICAL ANALYSIS OF MORPHOLOGICAL DIFFERENCES BETWEEN BRAINS

Recent study in neuroscience has observed evidence that the anatomic structures in human brains might have certain connection with the functioning. This triggers the interest in morphological study of cortical surfaces and in comparison of different ethnic groups. This article compares the MRI brain datasets of 10 Chinese and 10 Caucasians. A statistical analysis was applied to the white matter volumes in these datasets and evaluate the dissimilarities between the two groups using various intuitive measures. This analysis has revealed systematic morphological differences between the two ethnic groups.

Statistically-based reflection model for rough surfaces

Modeling light reflection from rough surfaces is an essential problem in computer graphics, computational vision, and multispectral imaging. Existing methods commonly separate the total reflection into diffuse and specular components, but this leads to the nonphysical arbitrariness in choosing the relative weights for the two components. There also lacks a sufficient model for the self-shadowing effect, which is important for rough surfaces. To eliminate these drawbacks, we propose a new reflection model entirely using physical parameters. The surfaces are assumed homogeneous, isotropic, and microscopically smooth, and their height probability densities are assumed Gaussian. Thus we derive the one-bounce reflection through Fresnel coefficient, self-shadowing factor, and probability function for surface orientation. The shadowing factor is calculated analytically from the statistical properties of a rough surface, including the height probability density and correlation function, and it agrees well with numerical simulation. Since all involved parameters in this model are physical, it can be easily verified with measurement. Besides, as a single term, this model generates a sharp specular highlight when a surface is smooth and shows diffuse behavior when the surface is rough. This advantage will be shown through rendered images.

GPU-based visualization techniques for 3D microscopic imaging data

Three-dimensional (3D) microscopic imaging techniques such as confocal microscopy have become a common tool in measuring cellular structures. While computer volume visualization has advanced into a sophisticated level in medical applications, much fewer studies have been made on data acquired by the 3D microscopic imaging techniques. To optimize the visualization of such data, it is important to consider the data characteristics such as thin data volume. It is also interesting to apply the new GPU (graphics processing unit) technology to interactive volume rendering of the data. In this paper, we discuss several texture-based techniques to visualize confocal microscopy data by considering the data characteristics and with support of GPU. One simple technique generates one set of 2D textures along the axial direction of image acquisition. An improved technique uses three sets of 2D textures in the three principal directions, and creates the rendered image via a weighted sum of the images generated by blending the individual texture sets. In addition, we propose a new approach based on stencil such that textures are blended based on a stencil control. Given the viewing condition, a texel needs to be drawn only when its corresponding projection on the image plane is inside a stencil area. Finally, we have explored the use of multiple-channel datasets for flexible classification of objects. These studies are useful to optimize the visualization of 3D microscopic imaging data.

EMBRIOSS: ELECTROMAGNETIC BRAIN IMAGING BY OPTIMIZATION IN SPECTRAL SPACE

We propose a new method called electromagnetic brain imaging by optimization in spectral space (EMBRIOSS) for electromagnetic source imaging of the human brain. The method incorporates the physiological knowledge that electrical activities in the brain are spatially coherent and often sparse. For spatial coherency, we confine the solution to a subspace spanned by the low-frequency eigenvectors of a Laplacian of the cortical surface mesh. For sparseness, we apply a p-norm regularization with p < 2. The resulting nonlinear regularization problem is solved efficiently using half-quadratic programming. Through realistic simulations, we have compared our method with existing approaches. The results show that our method performs better

Interactive volume visualization of cellular structures

Modern optical imaging techniques such as confocal and multi-photon microscopy can acquire volumetric datasets of cellular structures. In this paper we propose an approach for interactive volume rendering of such cellular datasets. In the first stage, we create a set of 2D textures corresponding to the image stacks in the original dataset. These textures are generated through a transfer function that maps voxel intensities to colors and opacities, and stored in the texture memory in computer. In the second stage, by blending the textures with hardware support, we can achieve interactive volume rendering including rotation and zooming on regular PCs. Besides, to generate good images for viewing in lateral directions, we use two additional sets of 2D textures for two orthogonal lateral directions and the texture resolutions can be adapted to the rendering requirement and computer hardware. This approach offers an effective visualization environment for biologists to better understand and analyze measured cellular structures.

POSS: efficient nonlinear optimization for parameterization methods

We propose a new, generic method called POSS (Parameterization by Optimization in Spectral Space) to efficiently obtain parameterizations with low distortions for 3D surface meshes. Given a mesh, first we compute a valid initial parameterization using an available method and then express the optimal solution as a linear combination of the initial parameterization and an unknown displacement term. The displacement term is approximated by a linear combination of the eigenvectors with the smallest eigenvalues of a mesh Laplacian. This approximation considerably reduces the number of unknowns while minimizing the deviation from the optimality. Finally, we find a valid parameterization with low distortion using a standard constrained nonlinear optimization procedure. POSS is fast, flexible, generic, and hierarchical. Its advantage has been confirmed by its application to planar parameterizations of surface meshes that represent complex human cortical surfaces. This method has a promising potential to improve the efficiency of all parameterization techniques which involve constrained nonlinear optimization.

Elastic surface registration by parameterization optimization in spectral space

This paper proposes a novel method to register 3D surfaces. Given two surface meshes, we formulate the registration as a problem of optimizing the parameterization of one mesh for the other. The optimal parameterization of the mesh is achieved in two steps. First, we find an initial solution close to the optimal solution. Second, we elastically modify the parameterization to minimize the cost function. The modification of the parameterization is expressed as a linear combination of a relatively small number of low-frequency eigenvectors of an appropriate mesh Laplacian. The minimization of the cost function uses a standard nonlinear optimization procedure that determines the coefficients of the linear combination. Constraints are added so that the parameterization validity is preserved during the optimization. The proposed method extends parametric registration of 2D images to the domain of 3D surfaces. This method is generic and capable of elastically registering surfaces with arbitrary geometry. It is also very efficient and can be fully automatic. We believe that this paper for the first time introduces eigenvectors of mesh Laplacians into the problem of surface registration. We have conducted experiments using real meshes that represent human cortical surfaces and the results are promising.

Representing spectral functions using symmetric extension

This paper proposes an accurate, compact, and generic method for representing spectral functions. The focus is on smooth functions, the case of most natural spectra. While pursuing the idea of using Fourier series expansion for its advantage in representation generality, we attempt to remove the problem of Gibbs phenomenon. The solution that we propose is a new method called symmetric extension. In this method, given a smooth spectral function S1, we first generate a new function S2 which is a mirror reflection of S1 about the upper bound of the wavelength domain. Then we create another function U that merges S1 and S2, and apply Fourier expansion to U. Because the values of U at its boundaries are equal, Gibbs oscillation is largely reduced. Besides, since U is self symmetric, all sine terms in its Fourier expansion vanish and therefore we only need to keep the coefficients for the cosine bases. These properties make our method not only accurate, but also compact. We have tested the new method with a large number of real spectra of various types, and compared the results to those using the existing models such as direct Fourier expansion and linear model. The numerical results have confirmed the advantages of the proposed method.

Representing scattering functions with spherical harmonics of spectral Fourier components

A fundamental problem in imaging science and engineering is to characterize wave scattering from a small region of surface or volume. This behavior is generally described by a multidimensional scattering function. This paper proposes a new representation method of scattering functions to optimize data compression. Our method first performs a Fourier transform in the wavelength dimension and then spherical harmonic transform for each Fourier coefficient in the dimensions for spatial directions. The representation errors are studied numerically for using different levels of spherical harmonics and different numbers of Fourier components. This method has the advantage of efficiently storing data of scattering functions and has a great potential of applications in imaging science and engineering.

Approximation of optimal surface parameterizations and the application in cerebral cortex mapping

Optimal parameterizations of surface meshes are useful in the mapping and visualization of the cerebral cortex, the outer layer of the human brain. We propose two new methods to compute approximations of the optimal parameterizations, and apply these methods to human cortical surface meshes extracted from magnetic resonance images. Our methods approximate the parameterizations in a low-dimensional subspace spanned by the coordinate vectors of an initial parameterization and the low-frequency eigenvectors of a mesh Laplacian. This low-dimensional approximation reduces the computational complexity while minimizing the error.