Three-dimensional PET emission scan registration and transmissionscan synthesis

The duration of a positron emission tomography (PET) imaging scan can be reduced if the transmission scan of one patient which is used for emission correction can be synthesized by using the reference transmission scan of another patient. In this paper, we propose a new intersubjects PET emission scan registration method and PET transmission synthesis method by using the boundary information of the body or brain scan of the PET emission scans. The PET emission scans have poor image quality and different intensity statistics so that we preprocess the emission scans to have a similar histogram and then apply the point distribution model (PDM) to extract the contours of the emission scan. The extracted boundary contour of every slice is used to reconstruct the three-dimensional (3-D) surface of the reference set and the target set. Our registration is 3-D surface-based which uses the normal flow method to find the correspondence vector field between two 3-D reconstructed surfaces. Since it is difficult to analyze internal organs using PET emission scan imaging without correction, we assume that the deformation of internal organ is homogeneous. With the corresponding vector field between the two emission scans and the transmission scan of the reference set, we can synthesize the transmission scan of the target set     

Brain surface conformal parameterization using Riemann surface structure

In medical imaging, parameterized 3-D surface models are useful for anatomical modeling and visualization, statistical comparisons of anatomy, and surface-based registration and signal processing. Here we introduce a parameterization method based on Riemann surface structure, which uses a special curvilinear net structure (conformal net) to partition the surface into a set of patches that can each be conformally mapped to a parallelogram. The resulting surface subdivision and the parameterizations of the components are intrinsic and stable (their solutions tend to be smooth functions and the boundary conditions of the Dirichlet problem can be enforced). Conformal parameterization also helps transform partial differential equations (PDEs) that may be defined on 3-D brain surface manifolds to modified PDEs on a two-dimensional parameter domain. Since the Jacobian matrix of a conformal parameterization is diagonal, the modified PDE on the parameter domain is readily solved. To illustrate our techniques, we computed parameterizations for several types of anatomical surfaces in 3-D magnetic resonance imaging scans of the brain, including the cerebral cortex, hippocampi, and lateral ventricles. For surfaces that are topologically homeomorphic to each other and have similar geometrical structures, we show that the parameterization results are consistent and the subdivided surfaces can be matched to each other. Finally, we present an automatic sulcal landmark location algorithm by solving PDEs on cortical surfaces. The landmark detection results are used as constraints for building conformal maps between surfaces that also match explicitly defined landmarks.     

A computational framework for approximating boundary surfaces in 3-D biomedical images.

We propose a new method for detecting and approximating the boundary surfaces in three-dimensional (3-D) biomedical images. Using this method, each boundary surface in the original 3-D image is normalized as a zero-value isosurface of a new 3-D image transformed from the original 3-D image. A novel computational framework is proposed to perform such an image transformation. According to this framework, we first detect boundary surfaces from the original 3-D image and compute discrete samplings of the boundary surfaces. Based on these discrete samplings, a new 3-D image is constructed for each boundary surface such that the boundary surface can be well approximated by a zero-value isosurface in the new 3-D image. In this way, the complex problem of reconstructing boundary surfaces in the original 3-D image is converted into a task to extract a zero-value isosurface from the new 3-D image. The proposed technique is not only capable of adequately reconstructing complex boundary surfaces in 3-D biomedical images, but it also overcomes vital limitations encountered by the isosurface-extracting method when the method is used to reconstruct boundary surfaces from 3-D images. The performances and advantages of the proposed computational framework are illustrated by many examples from different 3-D biomedical images.     

Genus zero surface conformal mapping and its application to brain surface mapping

We developed a general method for global conformal parameterizations based on the structure of the cohomology group of holomorphic one-forms for surfaces with or without boundaries (Gu and Yau, 2002), (Gu and Yau, 2003). For genus zero surfaces, our algorithm can find a unique mapping between any two genus zero manifolds by minimizing the harmonic energy of the map. In this paper, we apply the algorithm to the cortical surface matching problem. We use a mesh structure to represent the brain surface. Further constraints are added to ensure that the conformal map is unique. Empirical tests on magnetic resonance imaging (MRI) data show that the mappings preserve angular relationships, are stable in MRIs acquired at different times, and are robust to differences in data triangulation, and resolution. Compared with other brain surface conformal mapping algorithms, our algorithm is more stable and has good extensibility.     

Three-dimensional attenuation map reconstruction using geometrical models and free-form deformations

We address the issue of using deformable models to reconstruct an unknown attenuation map of the torso from a set of transmission scans. We assume the three-dimensional (3-D) distribution of attenuation coefficients to be piecewise uniform. We represent the unknown distribution by a set of closed surfaces defining regions having the same attenuating properties. The methods of reconstruction published so far tend to directly deform the surfaces, the parameters being the surface elements. Rather than deforming the surfaces, we explore the possibility of deforming the space in which the geometrical primitives are contained. We focus on the use of free-form deformations (FFD's) to describe the continuous transformation of space used to match a set of transmission measurements. We illustrate this approach by reconstructing realistically simulated transmission scans of the torso with various noise levels and compare the results to standard reconstruction methods.     

Curvature and torsion feature extraction from free-form 3-D meshesat multiple scales

A novel technique is presented for multi-scale curvature computation on a smoothed 3-D surface. This is achieved by convolving local parameterisations of the surface iteratively with 2-D Gaussian filters. In the technique, each vertex of the mesh becomes a local origin around which semi-geodesic co-ordinates are constructed. A geodesic from the origin is first constructed in an arbitrary direction, typically the direction of one of the incident edges. The smoothing eliminates surface noise and slowly erodes small surface detail, resulting in gradual simplification of the object shape. The surface Gaussian and mean curvature values are estimated accurately at multiple scales, together with curvature zero-crossing contours. For better visualisation, the curvature values are then mapped to colours and displayed directly on the surface. Furthermore local maxima of Gaussian and mean curvatures, as well as the torsion maxima of the zero-crossing contours of Gaussian and mean curvatures are also located and displayed on the surface. These features can be utilised by later processes for robust surface matching and object recognition. The technique is independent of the underlying triangulation and is more efficient than volumetric diffusion techniques since 2-D rather than 3-D convolutions are employed. Another advantage is that it is applicable to incomplete surfaces which arise during occlusion or to surfaces with holes     

基于链码匹配的断层间复杂轮廓线的三角片曲面重构

基于断层间轮廓线进行曲面重构是科学计算可视化的一个重要内容。本文利用链码理论对已获取的层间轮廓线进行编码,将二维的轮廓曲线转化为包含轮廓形状信息的一维链码;采用链码匹配技术完成相邻层轮廓特征点的匹配,将复杂轮廓线分割为若干简单的曲线段,最后,重构的曲面由这些分片构造的三角片曲面拼接而成。我们首先对模式识别中链码的串匹配算法作一个简要介绍,并详细分析讨论了其中的关键难点:编码,代价函数,链间距离,使其能够适用于我们的工作。实验表明该算法能够找出复杂轮廓线上恰当的对应特征点,从而构造出较真实的曲面。     

Evolutionary computation applied to the reconstruction of 3-D surface topography in the SEM

A genetic algorithm has been applied to the line profile reconstruction from the signals of the standard secondary electron (SE) and/or backscattered electron detectors in a scanning electron microscope. This method solves the topographical surface reconstruction problem as one of combinatorial optimization. To extend this optimization approach for three-dimensional (3-D) surface topography, this paper considers the use of a string coding where a 3-D surface topography is represented by a set of coordinates of vertices. We introduce the Delaunay triangulation, which attains the minimum roughness for any set of height data to capture the fundamental features of the surface being probed by an electron beam. With this coding, the strings are processed with a class of hybrid optimization algorithms that combine genetic algorithms and simulated annealing algorithms. Experimental results on SE images are presented.     

Sparse brain network recovery under compressed sensing

Partial correlation is a useful connectivity measure for brain networks, especially, when it is needed to remove the confounding effects in highly correlated networks. Since it is difficult to estimate the exact partial correlation under the small- n large- p situation, a sparseness constraint is generally introduced. In this paper, we consider the sparse linear regression model with a l(1)-norm penalty, also known as the least absolute shrinkage and selection operator (LASSO), for estimating sparse brain connectivity. LASSO is a well-known decoding algorithm in the compressed sensing (CS). The CS theory states that LASSO can reconstruct the exact sparse signal even from a small set of noisy measurements. We briefly show that the penalized linear regression for partial correlation estimation is related to CS. It opens a new possibility that the proposed framework can be used for a sparse brain network recovery. As an illustration, we construct sparse brain networks of 97 regions of interest (ROIs) obtained from FDG-PET imaging data for the autism spectrum disorder (ASD) children and the pediatric control (PedCon) subjects. As validation, we check the network reproducibilities by leave-one-out cross validation and compare the clustered structures derived from the brain networks of ASD and PedCon.     

A Novel Surface Reconstruction and Display Method for Cardiac PET Imaging

Positron emission tomography (PET) allows the in vivo assessment of biochemical activity in humans. The newer PET cameras can create several imaging planes, or slices, through an organ inside the body. The interpretation of two-dimensional (2-D) slices of an organ is often difficult for the clinician since he or she has to form a three-dimensional (3-D) mental composite of the structure of interest. We have developed a set of algorithms to reconstruct a functional three-dimensional surface model of the cardiac left ventricle from a set of two-dimensional cross-sectional image slices generated by PET. The theoretical techniques for this reconstruction method are applicable to most organs provided that the appropriate models for the organs are considered. An automatic boundary detection algorithm outlines the surface of the left ventricle from the 2-D images and assigns intensity values to the surface points whose level is proportional to the local activity. A 3-D surface of the intensity levels, with pseudocolor enhancement, is then displayed with the long axis of the heart in a vertical position. Such a display allows the 3-D myocardial tracer uptake to be clearly visualized by the clinician for better diagnosis.     

任意稀疏结构的多量测向量快速稀疏重构算法研究

目前的稀疏重构算法求解多量测向量时存在两个问题:一是计算复杂度高;二是不能实现任意稀疏结构的多量测向量重构.为此,本文提出一种多量测向量快速重构算法.该算法首先构建矩阵平滑零范数法,实现对具有任意稀疏结构的多量测向量的重构,并获得多量测向量的初始支撑集;其次根据稀疏度与量测维度的关系,对初始支撑集进行筛选获得预选支撑集;然后采用贝叶斯组检验方式得到信号重构所需的最终支撑集;最后通过最终支撑集实现信号的重构.该算法充分利用了矩阵平滑零范数法的高效性以及贝叶斯组检验对冗余支撑集的剔除功能,不但实现了稀疏位置随机变化的多量测向量的高效重构,而且保证了算法的精度,并对噪声具有一定的鲁棒性,基于实测数据的ISAR成像实验验证了所提算法的有效性.     

Three-dimensional elastic matching of volumes

Registering volumes that have been deformed with respect to each other involves recovery of the deformation. A 3-D elastic matching algorithm has been developed to use surface information for registering volumes. Surface extraction is performed in two steps: extraction of contours in 2-D image planes using active contours, and forming triangular patch surface models from the stack of 2-D contours. One volume is modeled as being deformed with respect to another goal volume. Correspondences between surfaces in the two image volumes are used to warp the deformed volume towards its goal. This process of contour extraction, surface formation and matching, and warping is repeated a number of times, with decreasing image volume stiffness. As the iterations continue the stretched volume is refined towards its goal volume. Registration examples of deformed volumes are presented.     

Digital stereo image analyzer for generating automated 3-D measures of optic disc deformation in glaucoma

The major limitations of precise evaluation of retinal structures in present clinical situations are the lack of standardization, the inherent subjectivity involved in the interpretation of retinal images, and intra- as well as interobserver variability. While evaluating optic disc deformation in glaucoma, these limitations could be overcome by using advanced digital image analysis techniques to generate precise metrics from stereo optic disc image pairs. A digital stereovision system for visualizing the topography of the optic nerve head from stereo optic disc images is presented. We have developed an algorithm, combining power cepstrum and zero-mean-normalized cross correlation techniques, which extracts depth information using coarse-to-fine disparity between corresponding windows in a stereo pair. The gray level encoded sparse disparity matrix is subjected to a cubic B-spline operation to generate smooth representations of the optic cup/disc surfaces and new three-dimensional (3-D) metrics from isodisparity contours. Despite the challenges involved in 3-D surface recovery, the robustness of our algorithm in finding disparities within the constraints used has been validated using stereo pairs with known disparities. In a preliminary longitudinal study of glaucoma patients, a strong correlation is found between the computer-generated quantitative cup/disc volume metrics and manual metrics commonly used in a clinic. The computer generated new metrics, however, eliminate the subjective variability and greatly reduce the time and cost involved in manual metric generation in follow-up studies of glaucoma.     

Registration of 3-D intraoperative MR images of the brain using a finite-element biomechanical model

We present a new algorithm for the nonrigid registration of three-dimensional magnetic resonance (MR) intraoperative image sequences showing brain shift. The algorithm tracks key surfaces of objects (cortical surface and the lateral ventricles) in the image sequence using a deformable surface matching algorithm. The volumetric deformation field of the objects is then inferred from the displacements at the boundary surfaces using a linear elastic biomechanical finite-element model. Two experiments on synthetic image sequences are presented, as well as an initial experiment on intraoperative MR images showing brain shift. The results of the registration algorithm show a good correlation of the internal brain structures after deformation, and a good capability of measuring surface as well as subsurface shift. We measured distances between landmarks in the deformed initial image and the corresponding landmarks in the target scan. Cortical surface shifts of up to 10 mm and subsurface shifts of up to 6 mm were recovered with an accuracy of 1 mm or less and 3 mm or less respectively.     

GPR phase-based techniques for profiling rough surfaces and detecting small, low-contrast landmines under flat ground

We present a new technique whereby phase variation signatures are used to profile two-dimensional (2-D) rough surfaces and to discern shallowly buried, small, low-contrast landmines under a flat ground. The method has been tested using data measured over a composite surface containing two rough dielectric surface patches, and over a flat ground under which small, low-contrast antipersonnel landmines are shallowly buried. The results show that the phase-based technique is capable of profiling rough surfaces and of detecting small, low-contrast landmines with different internal structures buried underneath a flat ground.     

基于图像块整体稀疏性与流形投影的压缩成像

如何利用自然图像本身固有的先验知识来提高重构图像质量是压缩成像系统的一个关键问题.本文在压缩成像系统中融合图像块整体稀疏性与流形特性,提出了一种高质量压缩成像算法.在该算法中,图像块由字典稀疏表示,同时还可由一组与图像块位于同一低维流形上的近邻点线性逼近,从而使稀疏重建信号分布在原始信号所处的流形附近.另外本文充分利用了图像中任意位置处图像块的稀疏性先验知识,使得压缩成像算法在低采样率下能重构出质量较高的图像.     

多层单道电弧增材表面3-D重构方法研究

为了研究多层单道电弧增材表面3-D成形特征，采用激光视觉传感系统采集电弧增材制造表面条纹图像。提出基于边界约束条件的感兴趣区域(ROI)提取法对焊缝特征曲线进行定位，获取ROI的激光条纹像素坐标。进行了理论分析和实验验证，得到电弧增材表面的3-D离散点数据，采用Delaunay三角剖分对离散点拟合形成3-D实体表面。结果表明，锯齿靶标的线性标定方法，3-D重构精度在0.2mm以内; 基于边界约束条件的ROI提取方法能准确定位电弧增材上表面和侧表面的条纹特征曲线。这一结果对电弧增材表面的3-D成形检测是有帮助的。     

Efficient segmentation by sparse pixel classification

Segmentation methods based on pixel classification are powerful but often slow. We introduce two general algorithms, based on sparse classification, for optimizing the computation while still obtaining accurate segmentations. The computational costs of the algorithms are derived, and they are demonstrated on real 3-D magnetic resonance imaging and 2-D radiograph data. We show that each algorithm is optimal for specific tasks, and that both algorithms allow a speedup of one or more orders of magnitude on typical segmentation tasks.     

Denoising for 3-D Photon-Limited Imaging Data Using Nonseparable Filterbanks

In this paper, we present a novel frame-based denoising algorithm for photon-limited 3-D images. We first construct a new 3-D nonseparable filterbank by adding elements to an existing frame in a structurally stable way. In contrast with the traditional 3-D separable wavelet system, the new filterbank is capable of using edge information in multiple directions. We then propose a data-adaptive hysteresis thresholding algorithm based on this new 3-D nonseparable filterbank. In addition, we develop a new validation strategy for denoising of photon-limited images containing sparse structures, such as neurons (the structure of interest is less than 5% of total volume). The validation method, based on tubular neighborhoods around the structure, is used to determine the optimal threshold of the proposed denoising algorithm. We compare our method with other state-of-the-art methods and report very encouraging results on applications utilizing both synthetic and real data.