Accurate reconstruction of the three-dimensional (3D) geometry of a myocardial infarct from two-dimensional (2D) multi-slice image sequences has important applications in the clinical evaluation and treatment of patients with ischemic cardiomyopathy. However, this reconstruction is challenging because the resolution of common clinical scans used to acquire infarct structure, such as short-axis, late-gadolinium enhanced cardiac magnetic resonance (LGE-CMR) images, is low, especially in the out-of-plane direction. In this study, we propose a novel technique to reconstruct the 3D infarct geometry from low resolution clinical images. Our methodology is based on a function called logarithm of odds (LogOdds), which allows the broader class of linear combinations in the LogOdds vector space as opposed to being limited to only a convex combination in the binary label space. To assess the efficacy of the method, we used high-resolution LGE-CMR images of 36 human hearts in vivo, and 3 canine hearts ex vivo. The infarct was manually segmented in each slice of the acquired images, and the manually segmented data were downsampled to clinical resolution. The developed method was then applied to the downsampled image slices, and the resulting reconstructions were compared with the manually segmented data. Several existing reconstruction techniques were also implemented, and compared with the proposed method. The results show that the LogOdds method significantly outperforms all the other tested methods in terms of region overlap.
In this study we develop a methodology to accurately extract and visualize cardiac microstructure from experimental
Diffusion Tensor (DT) data. First, a test model was constructed using an image-based model generation technique on
Diffusion Tensor Magnetic Resonance Imaging (DT-MRI) data. These images were derived from a dataset having
122x122x500 um3 voxel resolution. De-noising and image enhancement was applied to this high-resolution dataset to
clearly define anatomical boundaries within the images. The myocardial tissue was segmented from structural images
using edge detection, region growing, and level set thresholding. The primary eigenvector of the diffusion tensor for each
voxel, which represents the longitudinal direction of the fiber, was calculated to generate a vector field. Then an
advanced locally regularizing nonlinear anisotropic filter, termed Perona-Malik (PEM), was used to regularize this vector
field to eliminate imaging artifacts inherent to DT-MRI from volume averaging of the tissue with the surrounding
medium. Finally, the vector field was streamlined to visualize fibers within the segmented myocardial tissue to compare
the results with unfiltered data. With this technique, we were able to recover locally regularized (homogenized) fibers
with a high accuracy by applying the PEM regularization technique, particularly on anatomical surfaces where imaging
artifacts were most apparent. This approach not only aides in the visualization of noisy complex 3D vector fields
obtained from DT-MRI, but also eliminates volume averaging artifacts to provide a realistic cardiac microstructure for
use in electrophysiological modeling studies.
Automatic segmentation is an essential problem in biomedical imaging. It is still an open problem to automatically
segment biomedical images with complex structures and compositions. This paper proposes a novel algorithm called
Gradient-Intensity Clusters and Expanding Boundaries (GICEB). The algorithm attempts to solve the problem with
considerations of the image properties in intensity, gradient, and spatial coherence in the image space. The solution is
achieved through a combination of using a two-dimensional histogram, domain connectivity in the image space, and
segment region growing. The algorithm has been tested on some real images and the results have been evaluated.
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.
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.
Studies in experimental neuroscience have found some evidence showing that the shapes of cortical surfaces of human brains might have certain connection with the neural functioning. This paper presents a morphological study of the cortical surfaces. The work consists of four major elements. First, we collect a sufficient number of 3D MRI datasets of brains that belong to different categories of people. Second, we extract the cortical surfaces from the 3D MRI datasets. Third, we apply statistical analysis to characterize the morphological features of the cortical surfaces. The last component is 3D visualization to illustrate the shapes and characteristics of cortical surfaces in an interactive environment.
In this paper, we propose a computer-assisted approach for spectral design and synthesis. This approach starts with some initial spectrum, modifies it interactively, evaluates the change, and decides the optimal spectrum. Given a requested change as function of wavelength, we model the change function using a Gaussian function. When there is the metameric constraint, from the Gaussian function of request change, we propose a method to generate the change function such that the result spectrum has the same color as the initial spectrum. We have tested the proposed method with different initial spectra and change functions, and implemented an interactive graphics environment for spectral design and synthesis. The proposed approach and graphics implementation for spectral design and synthesis can be helpful for a number of applications such as lighting of building interiors, textile coloration, and pigment development of automobile paints, and spectral computer graphics.
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. 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 Fourier expansion vanish and therefore we only need to keep the cosine coefficients. These make our method not only accurate, but also compact. We have tested the method with a large number of real spectra of various types, and compared with the existing methods such as direct Fourier expansion and linear model. The numerical results have confirmed the advantages of the proposed method.