Combining a morphological interpolation approach with a surface reconstruction method for the 3-D representation of tomographic data

In this paper, a new interpolation scheme, based on Mathematical Morphology and a modified Marching Cubes (MC) Algorithm to reconstruct 3-D anatomical structures is presented. The proposed interpolation technique is implemented using morphological operations and incorporates a distance function to improve the computational effectiveness of the technique. The morphological interpolation technique is compared to an existing shape based interpolation method and its advantages include superiority capability on handling various cases such as the branching and holes problem (appearance and disappearance of information) and more accurate volume estimation. Furthermore, the morphological technique is companied with a 3-D reconstruction algorithm capable of representing any anatomical structure from real 3-D medical data. Introducing a novel general rule, the algorithm triangulates all standard cube configurations introduced from the standard MC algorithm, without producing topologically incoherent surfaces or holes. Finally, the technique is implemented in JAVA and its output is in VRML 1.0 format; therefore it can be executed over the internet and implemented for telemedicine applications.     

Dyslexia diagnostics by 3-D shape analysis of the corpus callosum

Dyslexia severely impairs learning abilities; therefore, improved diagnostic methods are needed. Neuropathological studies have revealed an abnormal anatomy of the corpus callosum (CC) in dyslexic brains. We propose a new approach for the quantitative analysis of 3-D magnetic resonance images (MRI) of the brain that ensures a more accurate quantification of anatomical differences between the CC of dyslexic and control subjects. The proposed approach consists of three main processing steps: 1) segmenting the CC from a given 3-D MRI using the learned CC shape and visual appearance; 2) extracting the centerline of the CC; and 3) cylindrical mapping of the CC surface for its comparative analysis. Validation on 3-D simulated phantoms demonstrates the ability of the proposed approach to accurately detect the shape variability between two 3-D surfaces. Experimental results revealed significant differences (at the 95% confidence level) between 14 normal and 16 dyslexic subjects in all four anatomical divisions, i.e., splenium, rostrum, genu, and body of their CCs. Moreover, the initial classification results based on the centerline length and CC thickness suggest that the proposed shape analysis is a promising supplement to the current techniques for diagnosing dyslexia.     

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.     

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     

Modeling of 3-D Surface Roughness Effects With Application to μ-Coaxial Lines

Effects of 3-D surface roughness on the propagation constant of transverse electromagnetic transmission lines are calculated using finite-element method software by solving for the fields inside conductors. The modeling is validated by comparison with available literature results for the special case of 2-D surface roughness and by simulations using the finite-integration technique. Results for cubical, semiellipsoidal, and pyramidal indentations, as well as rectangular, semicircular, and triangular grooves in conductor surfaces are presented. A developed surface roughness model is applied to rectangular mu-coaxial lines. It is shown that roughness contributes up to 9.2% to their overall loss for frequencies below 40 GHz     

光纤-混凝土复合体三维非线性有限元分析

对光纤-混凝土间的微观力学行为进行了分析。考虑了双接触面摩擦接触,通过试验确定了接触面力学参数;对光纤-混凝土复合体进行了三维非线性数值分析,得出光纤-混凝土复合体不同受载状况下微观应力应变分布状态及其接触面滑移状态,从理论上验证了光纤涂覆层对其传感灵敏度的影响及光纤布置方式的选择。     

基于PC机的断层图象序列3-D表面重建

由断层图象序列重建三维物体模型及其可见表面显示是目前国际上十分活跃的研究课题。本文对X射线CT图象序列重建三维对象模型,以及可见表面3-D显示进行了研究。提出一种给定分段点数的轮廓多边形近似方法,继而提出一种快速断面图象间轮廊插值方法。对重建出的人体肝脏体元阵列,用深度和梯度明暗显示方法进行显示,肝脏可见表面的3-D显示结果令人满意。全部软件都是在以PC/AT为主机,配以PC-VISION图象处理板的微机图象处理系统上,用C语言编程实现的。     

Reconstruction of 3-D horizons from 3-D seismic datasets

We propose a method for extracting automatically and simultaneously the quasi-horizontal surfaces in three-dimensional (3-D) seismic data. The proposed algorithm identifies connected sets of points which form surfaces in 3-D space. To improve reliability, this algorithm takes into consideration the relative positions of all horizons, and uses globally self-consistent connectivity criteria which respect the temporal order of horizon creation. The first stage of the algorithm consists of the preliminary estimation of the local direction of each horizon at each point of the 3-D space. The second stage consists of smoothing the signal along the detected layer structure to reduce noise. The last stage consists of the simultaneous building of all 3-D horizons. The output of the processing is a set of 3-D horizons represented by a series of triangulated surfaces.     

Reconstruction of 3-D geometry using 2-D profiles and a geometric prior model

A method has been developed to reconstruct three-dimensional (3-D) surfaces from two-dimensional (2-D) projection data. It is used to produce individualized boundary element models, consisting of thorax and lung surfaces, for electro- and magnetocardiographic inverse problems. Two orthogonal projections are utilized. A geometrical prior model, built using segmented magnetic resonance images, is deformed according to profiles segmented from projection images. In the authors' method, virtual X-ray images of the prior model are first constructed by simulating real X-ray imaging. The 2-D profiles of the model are segmented from the projections and elastically matched with the profiles segmented from patient data. The displacement vectors produced by the elastic 2-D matching are back projected onto the 3-D surface of the prior model. Finally, the model is deformed, using the back-projected vectors. Two different deformation methods are proposed. The accuracy of the method is validated by a simulation. The average reconstruction error of a thorax and lungs was 1.22 voxels, corresponding to about 5 mm     

Interpolation of 3-D binary images based on morphological skeletonization

In this paper, the morphological skeleton interpolation (MSI) algorithm is presented. It is an efficient, shape-based interpolation method used for interpolating slices in a three-dimensional (3-D) binary object. It is based on morphological skeletonization, which is used for two-dimensional (2-D) slice representation. The proposed morphological skeleton matching process provides translation, rotation, and scaling information at the same time. The interpolated slices preserve the shape of the original object slices, when the slices have similar shapes. It can also modify the shape of an object when the successive slices do not have similar shapes. Applications on artificial and real data are also presented.     

Fault Surface Detection in 3-D Seismic Data

A novel approach to the automatic extraction of geological faults from three-dimensional (3-D) seismic data is described, and qualitative and quantitative comparisons of manually and automatically picked fault geometries interpreted from both high and medium quality 3-D seismic datasets are presented. An algorithm has been developed that allows semiautomated identification, extraction, and modeling of fault surfaces imaged in 3-D seismic datasets. Based on a multistage approach, the algorithm operates initially at a small spatial scale, identifying local discontinuities in the seismic horizons, and then gradually considers larger and larger segments of fault surfaces until a set of complete fault surfaces are identified. A large portion of the work involves merging of segments of fault surfaces, performed using a highest confidence first (HCF) stratagem, taking into consideration the context of the resultant fault geometry. We show that results from the automated fault picker compare favorably with a manually labeled set of faults surfaces interpreted from a high-quality dataset. Last, we present an estimate of the savings in human operator time that can be made by using the automated approach, indicating savings of multiple person-days for the multigigabyte datasets that typify the petroleum industry.     

3维曲面振镜激光加工FPLSCM算法实践

为了高质量地将目标图像标刻在任意曲面上, 需要将计算机中排版的2维数据转换为3维数据从而形成具体振镜加工轨迹数据。在大量激光标刻实验测量与计算的基础上, 采用一种对任意自由曲面进行最小化失真展开的区域重点最小二乘共形展开(FPLSCM)算法, 完成了实用的3维振镜激光加工系统软件设计, 并进行了理论分析和实验验证, 取得了大量标刻测量数据。结果表明, 在z轴上下300mm范围内, 本算法能有效将由于高度与待加工表面形状差异带来的标刻畸变控制在1%左右, 并且在各类3维曲面上都得到了很好的加工效果。此研究成功实现了在自由3维曲面上利用动态聚焦技术完成各种表面加工的工作, 并通过优化算法有效减少了畸变。     

Vision processing for realtime 3-D data acquisition based on coded structured light

Structured light vision systems have been successfully used for accurate measurement of 3-D surfaces in computer vision. However, their applications are mainly limited to scanning stationary objects so far since tens of images have to be captured for recovering one 3-D scene. This paper presents an idea for real-time acquisition of 3-D surface data by a specially coded vision system. To achieve 3-D measurement for a dynamic scene, the data acquisition must be performed with only a single image. A principle of uniquely color-encoded pattern projection is proposed to design a color matrix for improving the reconstruction efficiency. The matrix is produced by a special code sequence and a number of state transitions. A color projector is controlled by a computer to generate the desired color patterns in the scene. The unique indexing of the light codes is crucial here for color projection since it is essential that each light grid be uniquely identified by incorporating local neighborhoods so that 3-D reconstruction can be performed with only local analysis of a single image. A scheme is presented to describe such a vision processing method for fast 3-D data acquisition. Practical experimental performance is provided to analyze the efficiency of the proposed methods.     

一种管道内3维形貌检测系统

为了解决常见结构光管道内3维形貌检测系统存在光线遮挡引起测量误差和盲区的问题,采用了一种新改进的圆结构光垂直照明、用两个互补金属氧化物半导体摄像机同步拍摄的管道内3维形貌检测系统,建立了适合该系统的图像处理和系统标定方法,完成了检测实验。结果表明,该系统可以很好地解决盲区问题,减小了测量误差,系统的标准差为0.50mm,并能得到完整的管道内壁3维形貌信息。     

Vessels as 4-D curves: global minimal 4-D paths to extract 3-D tubular surfaces and centerlines

In this paper, we propose an innovative approach to the segmentation of tubular structures. This approach combines all of the benefits of minimal path techniques such as global minimizers, fast computation, and powerful incorporation of user input, while also having the capability to represent and detect vessel surfaces directly which so far has been a feature restricted to active contour and surface techniques. The key is to represent the trajectory of a tubular structure not as a 3-D curve but to go up a dimension and represent the entire structure as a 4-D curve. Then we are able to fully exploit minimal path techniques to obtain global minimizing trajectories between two user supplied endpoints in order to reconstruct tubular structures from noisy or low contrast 3-D data without the sensitivity to local minima inherent in most active surface techniques. In contrast to standard purely spatial 3-D minimal path techniques, however, we are able to represent a full tubular surface rather than just a curve which runs through its interior. Our representation also yields a natural notion of a tube's "central curve." We demonstrate and validate the utility of this approach on magnetic resonance (MR) angiography and computed tomography (CT) images of coronary arteries.     

Compact encoding of 3-D voxel surfaces based on pattern code representation

We propose a lossless compression algorithm for three-dimensional (3-D) binary voxel surfaces, based on the pattern code representation (PCR). In PCR, a voxel surface is represented by a series of pattern codes. The pattern of a voxel v is defined as the 3 /spl times/ 3 /spl times/ 3 array of voxels, centered on v. Therefore, the pattern code for v informs of the local shape of the voxel surface around v. The proposed algorithm can achieve the coding gain, since the patterns of adjacent voxels are highly correlated to each other. The performance of the proposed algorithm is evaluated using various voxel surfaces, which are scan-converted from triangular mesh models. It is shown that the proposed algorithm requires only 0.5/spl sim/1 bits per black voxel (bpbv) to store or transmit the voxel surfaces.     

Automatic construction of 3-D statistical deformation models of the brain using nonrigid registration

In this paper, we show how the concept of statistical deformation models (SDMs) can be used for the construction of average models of the anatomy and their variability. SDMs are built by performing a statistical analysis of the deformations required to map anatomical features in one subject into the corresponding features in another subject. The concept of SDMs is similar to statistical shape models (SSMs) which capture statistical information about shapes across a population, but offers several advantages over SSMs. First, SDMs can be constructed directly from images such as three-dimensional (3-D) magnetic resonance (MR) or computer tomography volumes without the need for segmentation which is usually a prerequisite for the construction of SSMs. Instead, a nonrigid registration algorithm based on free-form deformations and normalized mutual information is used to compute the deformations required to establish dense correspondences between the reference subject and the subjects in the population class under investigation. Second, SDMs allow the construction of an atlas of the average anatomy as well as its variability across a population of subjects. Finally, SDMs take the 3-D nature of the underlying anatomy into account by analysing dense 3-D deformation fields rather than only information about the surface shape of anatomical structures. We show results for the construction of anatomical models of the brain from the MR images of 25 different subjects. The correspondences obtained by the nonrigid registration are evaluated using anatomical landmark locations and show an average error of 1.40 mm at these anatomical landmark positions. We also demonstrate that SDMs can be constructed so as to minimize the bias toward the chosen reference subject.     

Registration of real-time 3-D ultrasound images of the heart for novel 3-D stress echocardiography

Stress echocardiography is a routinely used clinical procedure to diagnose cardiac dysfunction by comparing wall motion information in prestress and poststress ultrasound images. Incomplete data, complicated imaging protocols and misaligned prestress and poststress views, however, are known limitations of conventional stress echocardiography. We discuss how the first two limitations are overcome via the use of real-time three-dimensional (3-D) ultrasound imaging, an emerging modality, and have called the new procedure "3-D stress echocardiography." We also show that the problem of misaligned views can be solved by registration of prestress and poststress 3-D image sequences. Such images are misaligned because of variations in placing the ultrasound transducer and stress-induced anatomical changes. We have developed a technique to temporally align 3-D images of the two sequences first and then to spatially register them to rectify probe placement error while preserving the stress-induced changes. The 3-D spatial registration is mutual information-based. Image registration used in conjunction with 3-D stress echocardiography can potentially improve the diagnostic accuracy of stress testing.