Automated 3-D PDM construction from segmented images using deformable models

In recent years, several methods have been proposed for constructing statistical shape models to aid image analysis tasks by providing a priori knowledge. Examples include principal component analysis of manually or semiautomatically placed corresponding landmarks on the learning shapes [point distribution models (PDMs)], which is time consuming and subjective. However, automatically establishing surface correspondences continues to be a difficult problem. This paper presents a novel method for the automated construction of three-dimensional PDM from segmented images. Corresponding surface landmarks are established by adapting a triangulated learning shape to segmented volumetric images of the remaining shapes. The adaptation is based on a novel deformable model technique. We illustrate our approach using computed tomography data of the vertebra and the femur. We demonstrate that our method accurately represents and predicts shapes.     

Registration-assisted segmentation of real-time 3-D echocardiographic data using deformable models

Real-time three-dimensional (3-D) echocardiography is a new imaging modality that presents the unique opportunity to visualize the complex 3-D shape and motion of the left ventricle (LV) in vivo and to measure the associated global and local function parameters. To take advantage of this opportunity in routine clinical practice, automatic segmentation of the LV in the 3-D echocardiographic data, usually hundreds of megabytes large, is essential. We report a new segmentation algorithm for this task. Our algorithm has two distinct stages, initialization of a deformable model and its refinement, which are connected by a dual "voxel + wiremesh" template. In the first stage, mutual-information-based registration of the voxel template with the image to be segmented helps initialize the wiremesh template. In the second stage, the wiremesh is refined iteratively under the influence of external and internal forces. The internal forces have been customized to preserve the nonsymmetric shape of the wiremesh template in the absence of external forces, defined using the gradient vector flow approach. The algorithm was validated against expert-defined segmentation and demonstrated acceptable accuracy. Our segmentation algorithm is fully automatic and has the potential to be used clinically together with real-time 3-D echocardiography for improved cardiovascular disease diagnosis.     

Turning images into 3-D models

In this article developments and performance analysis of image matching for detailed surface reconstruction of heritage objects is discussed. Three dimensional image-based modeling of heritages is a very interesting topic with many possible applications. In this article we propose a multistage image-based modeling approach that requires only a limited amount of human interactivity and is capable of capturing the fine geometric details with similar accuracy as close-range active range sensors. It can also cope with wide baselines using several advancements over standard stereo matching techniques. Our approach is sequential, starting from a sparse basic segmented model created with a small number of interactively measured points. This model, specifically the equation of each surface, is then used as a guide to automatically add the fine details. The following three techniques are used, each where best suited, to retrieve the details: 1) for regularly shaped patches such as planes, cylinders, or quadrics, we apply a fast relative stereo matching technique. 2) For more complex or irregular segments with unknown shape, we use a global multi-image geometrically constrained technique. 3) For segments unsuited for stereo matching, we employ depth from shading (DFS). The goal is not the development of a fully automated procedure for 3D object reconstruction from image data or a sparse stereo approach, but we aim at the digital reconstruction of detailed and accurate surfaces from calibrated and oriented images for practical daily documentation and digital conservation of wide variety of heritage objects.     

Neighbor-constrained segmentation with level set based 3-D deformable models

A novel method for the segmentation of multiple objects from three-dimensional (3-D) medical images using interobject constraints is presented. Our method is motivated by the observation that neighboring structures have consistent locations and shapes that provide configurations and context that aid in segmentation. We define a maximum a posteriori (MAP) estimation framework using the constraining information provided by neighboring objects to segment several objects simultaneously. We introduce a representation for the joint density function of the neighbor objects, and define joint probability distributions over the variations of the neighboring shape and position relationships of a set of training images. In order to estimate the MAP shapes of the objects, we formulate the model in terms of level set functions, and compute the associated Euler-Lagrange equations. The contours evolve both according to the neighbor prior information and the image gray level information. This method is useful in situations where there is limited interobject information as opposed to robust global atlases. In addition, we compare our level set representation of the object shape to the point distribution model. Results and validation from experiments on synthetic data and medical imagery in two-dimensional and 3-D are demonstrated.     

Estimation of 3-D left ventricular deformation from medical images using biomechanical models

The quantitative estimation of regional cardiac deformation from three-dimensional (3-D) image sequences has important clinical implications for the assessment of viability in the heart wall. We present here a generic methodology for estimating soft tissue deformation which integrates image-derived information with biomechanical models, and apply it to the problem of cardiac deformation estimation. The method is image modality independent. The images are segmented interactively and then initial correspondence is established using a shape-tracking approach. A dense motion field is then estimated using a transversely isotropic, linear-elastic model, which accounts for the muscle fiber directions in the left ventricle. The dense motion field is in turn used to calculate the deformation of the heart wall in terms of strain in cardiac specific directions. The strains obtained using this approach in open-chest dogs before and after coronary occlusion, exhibit a high correlation with strains produced in the same animals using implanted markers. Further, they show good agreement with previously published results in the literature. This proposed method provides quantitative regional 3-D estimates of heart deformation.     

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     

3-D face structure extraction and recognition from images using 3-D morphing and distance mapping

We describe a novel approach for creating a three-dimensional (3-D) face structure from multiple image views of a human face taken at a priori unknown poses by appropriately morphing a generic 3-D face. A cubic explicit polynomial in 3-D is used to morph a generic face into the specific face structure. The 3-D face structure allows for accurate pose estimation as well as the synthesis of virtual images to be matched with a test image for face identification. The estimation of a 3-D person's face and pose estimation is achieved through the use of a distance map metric. This distance map residual error (geometric-based face classifier) and the image intensity residual error are fused in identifying a person in the database from one or more arbitrary image view(s). Experimental results are shown on simulated data in the presence of noise, as well as for images of real faces, and promising results are obtained.     

Automated 3-D reconstruction of vascular structures from highdefinition casts

Three-dimensional reconstruction and computer modeling is becoming recognized as a powerful tool for studying vascular structures. The computational approach, as well as the computer hardware selected for the task, however, depend upon the information desired. For the modeling of surface geometry, as in the case of the aortic valve, a surface formation technique is favorable over the more computationally demanding volume rendering approach. Automated surface formation, however, requires good quality, high contrast images. We therefore present a technique for producing high contrast images from high definition casts. We also describe the methodology used for automatic contour tracing, generating a mesh of variable density, and the schemes used to reconstruct bifurcating objects. With this approach, 98 mbytes of imaging data could be reduced to 180 kbytes of polygon vertices, and manipulated at near real-time speed on a medium performance graphics workstation. Such a system is therefore well suited for detailed, quantitative analyses of the reconstructed structures. Overall, this paper outlines the procedures used to create a high definition, three-dimensional computer model of any vascular structure.     

Registration of 3-D images using weighted geometrical features

The authors present a weighted geometrical feature (WGF) registration algorithm. Its efficacy is demonstrated by combining points and a surface. The technique is an extension of Besl and McKay's (1992) iterative closest point (ICP) algorithm. The authors use the WGF algorithm to register X-ray computed tomography (CT) and T2-weighted magnetic resonance (MR) volume head images acquired from eleven patients that underwent craniotomies in a neurosurgical clinical trial. Each patient had five external markers attached to transcutaneous posts screwed into the outer table of the skull. The authors define registration error as the distance between positions of corresponding markers that are not used for registration. The CT and MR images are registered using fiducial paints (marker positions) only, a surface only, and various weighted combinations of points and a surface. The CT surface is derived from contours corresponding to the inner surface of the skull. The MR surface is derived from contours corresponding to the cerebrospinal fluid (CSF)-dura interface. Registration using points and a surface is found to be significantly more accurate then registration using only points or a surface     

3-D active appearance models: segmentation of cardiac MR and ultrasound images

A model-based method for three-dimensional image segmentation was developed and its performance assessed in segmentation of volumetric cardiac magnetic resonance (MR) images and echocardiographic temporal image sequences. Comprehensive design of a three-dimensional (3-D) active appearance model (AAM) is reported for the first time as an involved extension of the AAM framework introduced by Cootes et al. The model's behavior is learned from manually traced segmentation examples during an automated training stage. Information about shape and image appearance of the cardiac structures is contained in a single model. This ensures a spatially and/or temporally consistent segmentation of three-dimensional cardiac images. The clinical potential of the 3-D AAM is demonstrated in short-axis cardiac MR images and four-chamber echocardiographic sequences. The method's performance was assessed by comparison with manually identified independent standards in 56 clinical MR and 64 clinical echo image sequences. The AAM method showed good agreement with the independent standard using quantitative indexes of border positioning errors, endo- and epicardial volumes, and left ventricular mass. In MR, the endocardial volumes, epicardial volumes, and left ventricular wall mass correlation coefficients between manual and AAM were R2 = 0.94, 0.97, 0.82, respectively. For echocardiographic analysis, the area correlation was R2 = 0.79. The AAM method shows high promise for successful application to MR and echocardiographic image analysis in a clinical setting.     

Small vessel enhancement in MRA images using local maximum meanprocessing

The enhancement of small vessels in MRA imaging is an important problem. In this paper, we propose using local maximum mean (LMM) processing to enhance the detectability of small vessels. At each voxel in the original three-dimensional (3-D) data set, the LMM over the line segments in the cube centered at the voxel is taken and used to form the 3-D LMM data set. The maximum intensity projection (MIP) is then applied to the LMM data to produce the two-dimensional (2-D) LMM-MIP image. Through LMM processing, the variance of background tissue is reduced, thus increasing the detectability of small vessels. Moreover, the single bright voxels are suppressed and the disconnected small vessels can be connected. However, the LMM processing widens the larger, brighter vessels. To keep the advantages provided by both the LMM-MIP and MIP images, it is proposed that weight functions be used to combine them. The performance of the LMM-MIP algorithm is analyzed and compared with the performance of the MIP algorithm under three measures: The vessel voxel projection probability, the vessel receiver operating characteristic (ROC) curve and the vessel-tissue contrast-to-noise ratio (CNR). Closed forms of the three measures are obtained. It is shown that the LMM-MIP algorithm improves the detectability of small vessels under all three measures. The longer the projection path and the larger the CNR of the original data, then the greater the improvement. Confirming the theoretical analysis, results of an experiment utilizing practical MRA data demonstrate the improved visual quality of small vessels.     

Object classification in 3-D images using alpha-trimmed mean radialbasis function network

We propose a pattern classification based approach for simultaneous three-dimensional (3-D) object modeling and segmentation in image volumes. The 3-D objects are described as a set of overlapping ellipsoids. The segmentation relies on the geometrical model and graylevel statistics. The characteristic parameters of the ellipsoids and of the graylevel statistics are embedded in a radial basis function (RBF) network and they are found by means of unsupervised training. A new robust training algorithm for RBF networks based on alpha-trimmed mean statistics is employed in this study. The extension of the Hough transform algorithm in the 3-D space by employing a spherical coordinate system is used for ellipsoidal center estimation. We study the performance of the proposed algorithm and we present results when segmenting a stack of microscopy images.     

Extraction of the hepatic vasculature in rats using 3-D micro-CT images

High-resolution micro-computed tomography (CT) scanners now exist for imaging small animals. In particular, such a scanner can generate very large three-dimensional (3-D) digital images of the rat's hepatic vasculature. These images provide data on the overall structure and function of such complex vascular trees. Unfortunately, human operators have extreme difficulty in extracting the extensive vasculature contained in the images. Also, no suitable tree representation exists that permits straight-forward structural analysis and information retrieval. This work proposes an automatic procedure for extracting and representing such a vascular tree. The procedure is both computation and memory efficient and runs on current PCs. As the results demonstrate, the procedure faithfully follows human-defined measurements and provides far more information than can be defined interactively.     

Noise characteristics of 3-D and 2-D PET images

The authors analyzed the noise characteristics of two-dimensional (2-D) and three-dimensional (3-D) images obtained from the GE Advance positron emission tomography (PET) scanner. Three phantoms were used: a uniform 20-cm phantom, a 3-D Hoffman brain phantom, and a chest phantom with heart and lung inserts. Using gated acquisition, the authors acquired 20 statistically equivalent scans of each phantom in 2-D and 3-D modes at several activity levels. From these data, they calculated pixel normalized standard deviations (NSD's), scaled to phantom mean, across the replicate scans, which allowed them to characterize the radial and axial distributions of pixel noise. The authors also performed sequential measurements of the phantoms in 2-D and 3-D modes to measure noise (from interpixel standard deviations) as a function of activity. To compensate for the difference in axial slice width between 2-D and 3-D images (due to the septa and reconstruction effects), they developed a smoothing kernel to apply to the 2-D data. After matching the resolution, the ratio of image-derived NSD values (NSD_2D/NSD_3D)² averaged throughout the uniform phantom was in good agreement with the noise equivalent count (NEC) ratio (NEC_3D/NEC_2D). By comparing different phantoms, the authors showed that the attenuation and emission distributions influence the spatial noise distribution. The estimates of pixel noise for 2-D and 3-D images produced here can be applied in the weighting of PET kinetic data and may be useful in the design of optimal dose and scanning requirements for PET studies. The accuracy of these phantom-based noise formulas should be validated for any given imaging situation, particularly in 3-D, if there is significant activity outside the scanner field of view     

Semiautomatic 3-D prostate segmentation from TRUS images using spherical harmonics

Prostate brachytherapy quality assessment procedure should be performed while the patient is still on the operating table since this would enable physicians to implant additional seeds immediately into the prostate if necessary thus reducing the costs and increasing patient outcome. Seed placement procedure is readily performed under fluoroscopy and ultrasound guidance. Therefore, it has been proposed that seed locations be reconstructed from fluoroscopic images and prostate boundaries be identified in ultrasound images to perform dosimetry in the operating room. However, there is a key hurdle that needs to be overcome to perform the ultrasound and fluoroscopy-based dosimetry: it is highly time-consuming for physicians to outline prostate boundaries in ultrasound images manually, and there is no method that enables physicians to identify three-dimensional (3-D) prostate boundaries in postimplant ultrasound images in a fast and robust fashion. In this paper, we propose a new method where the segmentation is defined in an optimization framework as fitting the best surface to the underlying images under shape constraints. To derive these constraints, we modeled the shape of the prostate using spherical harmonics of degree eight and performed statistical analysis on the shape parameters. After user initialization, our algorithm identifies the prostate boundaries on the average in 2 min. For algorithm validation, we collected 30 postimplant prostate volume sets, each consisting of axial transrectal ultrasound images acquired at 1-mm increments. For each volume set, three experts outlined the prostate boundaries first manually and then using our algorithm. By treating the average of manual boundaries as the ground truth, we computed the segmentation error. The overall mean absolute distance error was 1.26 +/- 0.41 mm while the percent volume overlap was 83.5 +/- 4.2. We found the segmentation error to be slightly less than the clinically-observed interobserver variability.     

Alignment of sparse freehand 3-D ultrasound with preoperative images of the liver using models of respiratory motion and deformation

We present a method for alignment of an interventional plan to optically tracked two-dimensional intraoperative ultrasound (US) images of the liver. Our clinical motivation is to enable the accurate transfer of information from three-dimensional preoperative imaging modalities [magnetic resonance (MR) or computed tomography (CT)] to intraoperative US to aid needle placement for thermal ablation of liver metastases. An initial rigid registration to intraoperative coordinates is obtained using a set of US images acquired at maximum exhalation. A preprocessing step is applied to both the preoperative images and the US images to produce evidence of corresponding structures. This yields two sets of images representing classification of regions as vessels. The registration then proceeds using these images. The preoperative images and plan are then warped to correspond to a single US slice acquired at an unknown point in the breathing cycle where the liver is likely to have moved and deformed relative to the preoperative image. Alignment is constrained using a patient-specific model of breathing motion and deformation. Target registration error is estimated by carrying out simulation experiments using resliced MR volumes to simulate real US and comparing the registration results to a "bronze-standard" registration performed on the full MR volume. Finally, the system is tested using real US and verified using visual inspection.     

3-D IIR filtering using decimated DFT-polyphase filter bank structures

Two three-dimensional (3-D) under-decimated uniform discrete Fourier transform polyphase filter bank structures are proposed along with two applications: first, the sub-pixel motion discrimination of two-dimensional spatial objects moving with approximately constant local velocity in a noisy 3-D spatio-temporal image sequence and, second, the selective filtering of 3-D spatio-temporal broad-band plane waves based on their directions of arrival. The desired 3-D filter passband shapes are realized utilizing combinations of highly selective first-order 3-D infinite-impulse response frequency-planar filters in each band between the analysis and synthesis sections. Measured spatio-temporal performance confirms the high-quality broad-band transmission of passband signals, high directional selectivity and low computational complexity.     

Analysis of 3-D interconnect structures with PEEC using SPICE

This paper discusses the possibilities of using the circuit simulation program, simulation program with integrated circuit emphasis (SPICE) for the simulation of partial element equivalent circuit (PEEC) models. After an introduction into the PEEC method, the simulation of quasi-stationary models is considered. An enhancement of SPICE is described, allowing the simulation of retarded PEEC models. This enables the computation of electric fields radiated from an interconnection structure. With the modified SPICE simulator it is possible to use existing SPICE models and combine them with full wave PEEC models