Tooth segmentation of dental study models using range images

The accurate segmentation of the teeth from the digitized representation of a dental study model is an important component in computer-based algorithms for orthodontic feature detection and measurement and in the simulation of orthodontic procedures such as tooth rearrangement. This paper presents an automated method for tooth segmentation from the three-dimensional (3-D) digitized image captured by a laser scanner. We avoid the complexity of directly processing 3-D mesh data by proposing the innovative idea of detecting features on two range images computed from the 3-D image. The dental arch is first obtained from the plan-view range image. Using the arch as the reference, a panoramic range image of the dental model can be computed. The interstices between the teeth are detected separately in the two range images, and results from both views are combined for a determination of interstice locations and orientations. Finally, the teeth are separated from the gums by delineating the gum margin. The algorithm was tested on 34 dental models representing a variety of malocclusions and was found to be robust and accurate.     

A 3-D reconstruction system for the human jaw using a sequence of optical images

This paper presents a model-based vision system for dentistry that will assist in diagnosis, treatment planning, and surgical simulation. Dentistry requires an accurate three-dimensional (3-D) representation of the teeth and jaws for diagnostic and treatment purposes. The proposed integrated computer vision system constructs a 3-D model of the patient's dental occlusion using an intraoral video camera. A modified shape from shading (SFS) technique, using perspective projection and camera calibration, extracts the 3-D information from a sequence of two-dimensional (2-D) images of the jaw. Data fusion of range data and 3-D registration techniques develop the complete jaw model. Triangulation is then performed, and a solid 3-D model is reconstructed. The system performance is investigated using ground truth data, and the results show acceptable reconstruction accuracy.     

Urban object reconstruction using airborne laser elevation image and aerial image

Creating three-dimensional (3-D) models of real urban objects is an important goal in a wide variety of applications. This paper describes a method that utilizes airborne laser elevation images and aerial images for the 3-D reconstruction of urban objects. Our modeling approach uses the vertical geometric pattern analysis of elevation images. These patterns correspond to object contours and, thus, enable the extraction of the object. In addition, to provide realistic textured details, textures are cut from aerial images and mapped onto 3-D models. Our texture-mapping approach can avoid geometry mismatching and enable the automatic registration to determine the most reliable correspondence between projected outlines of 3-D models and contours of real objects shown in aerial images. Edge pairs, which are matched with projected outlines, are detected from aerial images. In order to minimize mismatching, we apply the voting technique based on the generalized Hough transform. Experimental results show that 3-D reconstruction of urban objects is generally successful.     

Measurements of dental cast profile and three-dimensional toothmovement during orthodontic treatment

We have developed a system for measuring three-dimensional profiles of dental casts and three-dimensional tooth movement during orthodontic treatment. The profile measurement is based on the triangulation method which detects a laser sport on a cast using an image sensor. The system is computer-controlled and designed to achieve the depth and lateral resolutions of 0.05 and 0.1 mm, respectively, within a depth range of 25 mm. We have applied our system to measuring three-dimensional movement of teeth, including rotations, during orthodontic treatment. The movements have been obtained by means of three-dimensional registration of tooth profiles using a computer between casts serially taken at different stages of the treatment. Measurements over periods of 41 to 190 days on patients have revealed that this technique is capable of quantifying the difference in movements due to orthodontic therapeutics.     

Three-dimensional statistical model for gingival contour reconstruction

Optimal gingival contours around restored teeth and implants are of critical importance for restorative success and esthetics. This paper describes a novel computer-aided methodology for building a 3-D statistical model of gingival contours from a 3-D scan dental dataset and reconstructing missing gingival contours in partially edentulous patients. The gingival boundaries were first obtained from the 3-D dental model through a discrete curvature analysis and shortest path searching algorithm. Based on the gingival shape differential characteristics, the boundaries were demarcated to construct the gingival contour of each individual tooth. Through B-spline curve approximation to each gingival contour, the control points of the B-spline curves are used as the shape vector for training the model. Statistical analysis results demonstrate that the method can give a simple but compact model that effectively capture the most important variations in arch width and shape as well as gingival morphology and position. Within this statistical model, the morphologically plausible missing contours can be inferred based on a nonlinear optimization fitting from the global similarity transformation, the model shape deformation and a Mahalanobis prior. The reconstruction performance is evaluated through large simulated experimental data and a real patient case, which demonstrates the effectiveness of this approach.     

Computational geometry for patient-specific reconstruction and meshing of blood vessels from MR and CT angiography

Investigation of three-dimensional (3-D) geometry and fluid-dynamics in human arteries is an important issue in vascular disease characterization and assessment. Thanks to recent advances in magnetic resonance (MR) and computed tomography (CT), it is now possible to address the problem of patient-specific modeling of blood vessels, in order to take into account interindividual anatomic variability of vasculature. Generation of models suitable for computational fluid dynamics is still commonly performed by semiautomatic procedures, in general based on operator-dependent tasks, which cannot be easily extended to a significant number of clinical cases. In this paper, we overcome these limitations making use of computational geometry techniques. In particular, 3-D modeling was carried out by means of 3-D level sets approach. Model editing was also implemented ensuring harmonic mean curvature vectors distribution on the surface, and model geometric analysis was performed with a novel approach, based on solving Eikonal equation on Voronoi diagram. This approach provides calculation of central paths, maximum inscribed sphere estimation and geometric characterization of the surface. Generation of adaptive-thickness boundary layer finite elements is finally presented. The use of the techniques presented here makes it possible to introduce patient-specific modeling of blood vessels at clinical level.     

Initial results for automated computational modeling ofpatient-specific electromagnetic hyperthermia

Developments in finite-difference time-domain (FD-TD) computational modeling of Maxwell's equations, super-computer technology, and computed tomography (CT) imagery open the possibility of accurate numerical simulation of electromagnetic (EM) wave interactions with specific, complex, biological tissue structures. One application of this technology is in the area of treatment planning for EM hyperthermia. In this paper, we report the first highly automated CT image segmentation and interpolation scheme applied to model patient-specific EM hyperthermia. This novel system is based on sophisticated tools from the artificial intelligence, computer vision, and computer graphics disciplines. It permits CT-based patient-specific hyperthermia models to be constructed without tedious manual contouring on digitizing pads or CRT screens. The system permits in principle near real-time assistance in hyperthermia treatment planning. We apply this system to interpret actual patient CT data, reconstructing a 3-D model of the human thigh from a collection of 29 serial CT images at 10 mm intervals. Then, using FD-TD, we obtain 2-D and 3-D models of EM hyperthermia of this thigh due to a waveguide applicator. We find that different results are obtained from the 2-D and 3-D models, and conclude that full 3-D tissue models are required for future clinical usage.     

Parallelized Bayesian inversion for three-dimensional dental X-ray imaging

Diagnostic and operational tasks based on dental radiology often require three-dimensional (3-D) information that is not available in a single X-ray projection image. Comprehensive 3-D information about tissues can be obtained by computerized tomography (CT) imaging. However, in dental imaging a conventional CT scan may not be available or practical because of high radiation dose, low-resolution or the cost of the CT scanner equipment. In this paper, we consider a novel type of 3-D imaging modality for dental radiology. We consider situations in which projection images of the teeth are taken from a few sparsely distributed projection directions using the dentist's regular (digital) X-ray equipment and the 3-D X-ray attenuation function is reconstructed. A complication in these experiments is that the reconstruction of the 3-D structure based on a few projection images becomes an ill-posed inverse problem. Bayesian inversion is a well suited framework for reconstruction from such incomplete data. In Bayesian inversion, the ill-posed reconstruction problem is formulated in a well-posed probabilistic form in which a priori information is used to compensate for the incomplete information of the projection data. In this paper we propose a Bayesian method for 3-D reconstruction in dental radiology. The method is partially based on Kolehmainen et al. 2003. The prior model for dental structures consist of a weighted /spl lscr//sup 1/ and total variation (TV)-prior together with the positivity prior. The inverse problem is stated as finding the maximum a posteriori (MAP) estimate. To make the 3-D reconstruction computationally feasible, a parallelized version of an optimization algorithm is implemented for a Beowulf cluster computer. The method is tested with projection data from dental specimens and patient data. Tomosynthetic reconstructions are given as reference for the proposed method.     

Optimal CT scanning plan for long-bone 3-D reconstruction

Digital computed tomographic (CT) data are widely used in three-dimensional (3-D) construction of bone geometry and density features for 3-D modelling purposes. During in vivo CT data acquisition the number of scans must be limited in order to protect patients from the risks related to X-ray absorption. The aim of this work is to automatically define, given a finite number of CT slices, the scanning plan which returns the optimal 3-D reconstruction of a bone segment from in vivo acquired CT images. An optimization algorithm based on a Discard-Insert-Exchange technique has been developed. In the proposed method the optimal scanning sequence is searched by minimizing the overall reconstruction error of a two-dimensional (2-D) prescanning image: an anterior-posterior (AP) X-ray projection of the bone segment. This approach has been validated in vitro on 3 different femurs. The 3-D reconstruction errors obtained through the optimization of the scanning plan on the 3-D prescanning images and on the corresponding 3-D data sets have been compared. 2-D and 3-D data sets have been reconstructed by linear interpolation along the longitudinal axis. Results show that direct 3-D optimization yields root mean square reconstruction errors which are only 4%-7% lower than the 2-D-optimized plan, thus proving that 2-D-optimization provides a good suboptimal scanning plan for 3-D reconstruction. Further on, 3-D reconstruction errors given by the optimized scanning plan and a standard radiological protocol for long bones have been compared. Results show that the optimized plan yields 20%-50% lower 3-D reconstruction errors     

Development of a vertebral endplate 3-D reconstruction technique

The increase of low back problems has stimulated the development of different analysis and evaluation techniques. Among these methods, the direct linear transformation (DLT) technique is commonly used to reconstruct the spine in three dimensions by means of its known image coordinates on radiographs. Despite its efficiency and precision, general reconstruction of some standard anatomical landmarks does not give all the necessary data for a detailed analysis of the intrinsic geometrical characteristics of lumbar vertebrae. Thus, in order to obtain such geometrical information a three-dimensional (3-D) reconstruction vertebral endplate contour technique has been developed. This technique involves: (1) iterative optimization and reconstruction processes of the vertebral endplate centroid; and (2) 3-D reconstruction of vertebral endplate contour. Validation based on mathematical simulations demonstrated that two or three iterations are necessary to correct (within 2 mm) the endplate centroid position for simulated error higher than 10 mm. Other validations based on 3-D reconstructions of a chamfered tube and a dry vertebra contours of known dimensions have given mean errors of 2 mm. Application on a healthy subject demonstrated the potential of this 3-D reconstruction technique. Finally, 3-D data obtained on vertebral endplates would allow the development of new clinical measurements that could be used to evaluate the lumbar spine geometrical behavior and orthoses biomechanical effects     

3-D/2-D registration of CT and MR to X-ray images

A crucial part of image-guided therapy is registration of preoperative and intraoperative images, by which the precise position and orientation of the patient's anatomy is determined in three dimensions. This paper presents a novel approach to register three-dimensional (3-D) computed tomography (CT) or magnetic resonance (MR) images to one or more two-dimensional (2-D) X-ray images. The registration is based solely on the information present in 2-D and 3-D images. It does not require fiducial markers, intraoperative X-ray image segmentation, or timely construction of digitally reconstructed radiographs. The originality of the approach is in using normals to bone surfaces, preoperatively defined in 3-D MR or CT data, and gradients of intraoperative X-ray images at locations defined by the X-ray source and 3-D surface points. The registration is concerned with finding the rigid transformation of a CT or MR volume, which provides the best match between surface normals and back projected gradients, considering their amplitudes and orientations. We have thoroughly validated our registration method by using MR, CT, and X-ray images of a cadaveric lumbar spine phantom for which "gold standard" registration was established by means of fiducial markers, and its accuracy assessed by target registration error. Volumes of interest, containing single vertebrae L1-L5, were registered to different pairs of X-ray images from different starting positions, chosen randomly and uniformly around the "gold standard" position. CT/X-ray (MR/ X-ray) registration, which is fast, was successful in more than 91% (82% except for L1) of trials if started from the "gold standard" translated or rotated for less than 6 mm or 17 degrees (3 mm or 8.6 degrees), respectively. Root-mean-square target registration errors were below 0.5 mm for the CT to X-ray registration and below 1.4 mm for MR to X-ray registration.     

X-ray computed tomography for medical imaging

The article looks at reconstruction in 2-D and 3-D tomography. We have not dealt with some of the issues in reconstruction such as sampling and aliasing artifacts, finite detector aperture artifacts, beam hardening artifacts, etc., in greater detail since these are beyond the scope of an introductory tutorial. We examine the physical and mathematical concepts of the Radon (1917) transform, and the basic parallel beam reconstruction algorithms are discussed. We also develop the algorithms for fan-beam CT, and discuss the mathematical principles of cone-beam CT     

Three-dimensional (3-D) reconstruction of the spine from a single X-ray image and prior vertebra models

The lateral bending test is routinely used by clinicians for the preoperative assessment of spinal mobility. The evaluation of bending motion is usually based on the qualitative analysis of a two-dimensional (2-D) antero-posterior X-ray image. The aim of this paper is to introduce a novel three-dimensional (3-D) reconstruction technique that is a prerequisite for the quantitative 3-D analysis of lateral bending motion. An algorithm was developed for the 3-D reconstruction of the spine from a single X-ray image. The X-ray is calibrated using a small calibration object and an explicit calibration algorithm. The information contained in the single X-ray is completed by registering a priori 3-D geometric models of individual vertebrae. Part of the error yielded by the 3-D/2-D registration is corrected by a vertebral alignment constraint that aims to minimize intervertebral dislocations. Three-dimensional models of 15 different scoliosis patients, obtained from a standard stereo-radiographic 3-D reconstruction, were used in simulation and validation experiments. Experimental results show that the new method is robust and accurate. With pessimistic levels of simulated noise, the average root mean square reconstruction error is 2.89 mm, which is appropriate for common clinical applications.     

Towards cardiac C-arm computed tomography

Cardiac interventional procedures would benefit tremendously from sophisticated three-dimensional image guidance. Such procedures are typically performed with C-arm angiography systems, and tomographic imaging is currently available only by using preprocedural computed tomography (CT) or magnetic resonance imaging (MRI) scans. Recent developments in C-arm CT (Angiographic CT) allow three-dimensional (3-D) imaging of low contrast details with angiography imaging systems for noncardiac applications. We propose a new approach for cardiac imaging that takes advantage of this improved contrast resolution and is based on intravenous contrast injection. The method is an analogue to multisegment reconstruction in cardiac CT adapted to the much slower rotational speed of C-arm CT. Motion of the heart is considered in the reconstruction process by retrospective electrocardiogram (ECG)-gating, using only projections acquired at a similar heart phase. A series of N almost identical rotational acquisitions is performed at different heart phases to obtain a complete data set at a minimum temporal resolution of 1/N of the heart cycle time. First results in simulation, using an experimental phantom, and in preclinical in vivo studies showed that excellent image quality can be achieved.     

Binary reconstruction of the heart chambers from biplane angiographic image sequences

The aim of this work is the three-dimensional (3-D) reconstruction of the left or right heart chamber from digital biplane angiograms. The approach used, the binary reconstruction, exploits the density information of subtracted ventriculograms from two orthogonal views in addition to the ventricular contours. The ambiguity of the problem is largely reduced by incorporating a priori knowledge of human ventricles. A model-based reconstruction program is described that is applicable to routinely acquired biplane ventriculographic studies. Prior to reconstruction, several geometric and densitometric imaging errors are corrected. The finding of corresponding density profiles and anatomical landmarks is supported by a biplane image pairing procedure that takes the movement of the gantry system into account. Absolute measurements are based on geometric isocenter calibration and a slice-wise density calibration technique. The reconstructed ventricles allow 3-D visualization and regional wall motion analysis independently of the gantry setting. The method is applied to clinical angiograms and tested in left- and right-ventricular phantoms yielding a well shape conformity even with few model information. The results indicate that volumes of binary reconstructed ventricles are less projection-dependent compared to volume data derived by purely contour-based methods. A limitation is that the heart chamber must not be superimposed by other dye-filled structures in both projections.     

Feldkamp-type cone-beam tomography in the wavelet framework

X-ray computed tomography (CT) is in transition from fan-beam to cone-beam geometry. For cone-beam volumetric imaging, reduction of radiation exposure remains an important issue. Because the wavelet approach was shown to be effective and flexible for two-dimensional (2-D) local region reconstruction, we are motivated to perform wavelet local CT in cone-beam geometry. In this paper, we formulate the Feldkamp cone-beam reconstruction from the wavelet perspective, derive both full-scan and half-scan Feldkamp-type formulas for either global or local reconstruction, and demonstrate the feasibility and utility in synthetic and real data. It is found that using the wavelet Feldkamp approach, a three-dimensional (3-D) region of interest (ROI) can be reconstructed with neither severe image artifacts nor any significant constant bias in our simulation and experiments.     

Iterative image reconstruction using inverse Fourier rebinning for fully 3-D PET

We describe a fast forward and back projector pair based on inverse Fourier rebinning for use in iterative image reconstruction for fully 3-D positron emission tomography (PET). The projector pair is used as part of a factored system matrix that takes into account detector-pair response by using shift-variant sinogram blur kernels, thereby combining the computational advantages of Fourier rebinning with iterative reconstruction using accurate system models. The forward projector consists of a 2-D projector, which maps 3-D images into 2-D direct sinograms, followed by exact inverse rebinning which maps the 2-D into fully 3-D sinograms. The back projector is implemented as the transpose of the forward projector and differs from the true exact rebinning operator in the sense that it does not require reprojection to compute missing lines of response (LORs). We compensate for two types of inaccuracies that arise in a cylindrical PET scanner when using inverse Fourier rebinning: 1) nonuniform radial sampling and 2) nonconstant oblique angles in the radial direction in a single oblique sinogram. We examine the effects of these corrections on sinogram accuracy and reconstructed image quality. We evaluate performance of the new projector pair for maximum a posteriori (MAP) reconstruction of simulated and in vivo data. The new projector results in only a small loss in resolution towards the edge of the field-of-view when compared to the fully 3-D geometric projector and requires an order of magnitude less computation.     

3-D reconstruction of tissue components for atherosclerotic human arteries using ex vivo high-resolution MRI

Automatic computer-based methods are well suited for the image analysis of the different components in atherosclerotic plaques. Although several groups work on such analysis some of the methods used are oversimplified and require improvements when used within a computational framework for predicting meaningful stress and strain distributions in the heterogeneous arterial wall under various loading conditions. Based on high-resolution magnetic resonance imaging of excised atherosclerotic human arteries and a series of two-dimensional (2-D) contours we present a segmentation tool that permits a three-dimensional (3-D) reconstruction of the most important tissue components of atherosclerotic arteries. The underlying principle of the proposed approach is a model-based snake algorithm for identifying 2-D contours, which uses information about the plaque composition and geometric data of the tissue layers. Validation of the computer-generated tissue boundaries is performed with 100 MR images, which are compared with the results of a manual segmentation performed by four experts. Based on the Hausdorff distance and the average distance for computer-to-expert differences and the interexpert differences for the outer boundary of the adventitia, the adventitia-media, media-intima, intima-lumen and calcification boundaries are less than 1 pixel (0.234 mm). The percentage statistic shows similar results to the modified Williams index in terms of accuracy. Except for the identification of lipid-rich regions the proposed algorithm is automatic. The nonuniform rational B-spline-based computer-generated 3-D models of the individual tissue components provide a basis for clinical and computational analysis.     

Automatic fusion of freehand endoscopic brain images to three-dimensional surfaces: creating stereoscopic panoramas

A major limitation of the use of endoscopes in minimally invasive surgery is the lack of relative context between the endoscope and its surroundings. The purpose of this work was to fuse images obtained from a tracked endoscope to surfaces derived from three-dimensional (3-D) preoperative magnetic resonance or computed tomography (CT) data, for assistance in surgical planning, training and guidance. We extracted polygonal surfaces from preoperative CT images of a standard brain phantom and digitized endoscopic video images from a tracked neuro-endoscope. The optical properties of the endoscope were characterized using a simple calibration procedure. Registration of the phantom (physical space) and CT images (preoperative image space) was accomplished using fiducial markers that could be identified both on the phantom and within the images. The endoscopic images were corrected for radial lens distortion and then mapped onto the extracted surfaces via a two-dimensional 2-D to 3-D mapping algorithm. The optical tracker has an accuracy of about 0.3 mm at its centroid, which allows the endoscope tip to be localized to within 1.0 mm. The mapping operation allows multiple endoscopic images to be "painted" onto the 3-D brain surfaces, as they are acquired, in the correct anatomical position. This allows panoramic and stereoscopic visualization, as well as navigation of the 3-D surface, painted with multiple endoscopic views, from arbitrary perspectives.     

Incorporating Patient-Specific Variability in the Simulation of Realistic Whole-Body $^{18}{hbox{F-FDG}}$ Distributions for Oncology Applications

The purpose of the work described in this paper was the development of a framework for the creation of a realistic positron emission tomography (PET) simulated database incorporating patient-specific variability. The ground truth used was therefore based on clinical PET/computed tomography (CT) data of oncology patients. In the first step, the NURBS-based cardiac-torso phantom was adapted to the patient's CT acquisitions to reproduce their specific anatomy while the corresponding PET acquisitions were used to derive the activity distribution of each organ of interest. Secondly, realistic tumor shapes with homogeneous or heterogeneous activity distributions were modeled based on segmentation of the PET tumor volume and incorporated in the patient-specific models obtained at the first step. Lastly, patient-specific respiratory motion was also modeled. The derived patient-specific models were subsequently combined with the PET SORTEO Monte Carlo simulation tool for the simulation of the whole-body PET acquisition process. The accuracy of the simulated datasets was assessed in comparison to the original clinical patient images. In addition, a couple of applications for such simulated images were also demonstrated. Future work will focus on the creation of a comprehensive database of simulated raw data and reconstructed whole-body images, facilitating the rigorous evaluation of image-processing algorithms in PET for oncology applications.