Rule-based detection of intrathoracic airway trees

New sensitive and reliable methods for assessing alterations in regional lung structure and function are critically important for the investigation and treatment of pulmonary diseases. Accurate identification of the airway tree will provide an assessment of airway structure and will provide a means by which multiple volumetric images of the lung at the same lung volume over time can be used to assess regional parenchymal changes. The authors describe a novel rule-based method for the segmentation of airway trees from three-dimensional (3-D) sets of computed tomography (CT) images, and its validation. The presented method takes advantage of a priori anatomical knowledge about pulmonary airway and vascular trees and their interrelationships. The method is based on a combination of 3-D seeded region growing that is used to identify large airways, rule-based two-dimensional (2-D) segmentation of individual CT slices to identify probable locations of smaller diameter airways, and merging of airway regions across the 3-D set of slices resulting in a tree-like airway structure. The method was validated in 40 3-mm-thick CT sections from five data sets of canine lungs scanned via electron beam CT in vivo with lung volume held at a constant pressure. The method's performance was compared with that of the conventional 3-D region growing method. The method substantially outperformed an existing conventional approach to airway tree detection.     

Three-dimensional path planning for virtual bronchoscopy

Multidetector computed-tomography (MDCT) scanners provide large high-resolution three-dimensional (3-D) images of the chest. MDCT scanning, when used in tandem with bronchoscopy, provides a state-of-the-art approach for lung-cancer assessment. We have been building and validating a lung-cancer assessment system, which enables virtual-bronchoscopic 3-D MDCT image analysis and follow-on image-guided bronchoscopy. A suitable path planning method is needed, however, for using this system. We describe a rapid, robust method for computing a set of 3-D airway-tree paths from MDCT images. The method first defines the skeleton of a given segmented 3-D chest image and then performs a multistage refinement of the skeleton to arrive at a final tree structure. The tree consists of a series of paths and branch structural data, suitable for quantitative airway analysis and smooth virtual navigation. A comparison of the method to a previously devised path-planning approach, using a set of human MDCT images, illustrates the efficacy of the method. Results are also presented for human lung-cancer assessment and the guidance of bronchoscopy.     

Segmentation and analysis of the human airway tree from three-dimensional X-ray CT images

The lungs exchange air with the external environment via the pulmonary airways. Computed tomography (CT) scanning can be used to obtain detailed images of the pulmonary anatomy, including the airways. These images have been used to measure airway geometry, study airway reactivity, and guide surgical interventions. Prior to these applications, airway segmentation can be used to identify the airway lumen in the CT images. Airway tree segmentation can be performed manually by an image analyst, but the complexity of the tree makes manual segmentation tedious and extremely time-consuming. We describe a fully automatic technique for segmenting the airway tree in three-dimensional (3-D) CT images of the thorax. We use grayscale morphological reconstruction to identify candidate airways on CT slices and then reconstruct a connected 3-D airway tree. After segmentation, we estimate airway branchpoints based on connectivity changes in the reconstructed tree. Compared to manual analysis on 3-mm-thick electron-beam CT images, the automatic approach has an overall airway branch detection sensitivity of approximately 73%.     

Registration of 3-D CT and 2-D Flat Images of Mouse via Affine Transformation

It is difficult to directly coregister the 3-D fluorescence molecular tomography (FMT) image of a small tumor in a mouse whose maximal diameter is only a few millimeters with a larger CT image of the entire animal that spans about 10 cm. This paper proposes a new method to register 2-D flat and 3-D CT image first to facilitate the registration between small 3-D FMT images and large 3-D CT images. A novel algorithm combining differential evolution and improved simplex method for the registration between the 2-D flat and 3-D CT images is introduced and validated with simulated images and real images of mice. The visualization of the alignment of the 3-D FMT and CT image through 2-D registration shows promising results.      

Automatic lung segmentation for accurate quantitation of volumetricX-ray CT images

Segmentation of pulmonary X-ray computed tomography (CT) images is a precursor to most pulmonary image analysis applications. This paper presents a fully automatic method for identifying the lungs in three-dimensional (3-D) pulmonary X-ray CT images. The method has three main steps. First, the lung region is extracted from the CT images by gray-level thresholding. Then, the left and right lungs are separated by identifying the anterior and posterior junctions by dynamic programming. Finally, a sequence of morphological operations is used to smooth the irregular boundary along the mediastinum in order to obtain results consistent with those obtained by manual analysis, in which only the most central pulmonary arteries are excluded from the lung region. The method has been tested by processing 3-D CT data sets from eight normal subjects, each imaged three times at biweekly intervals with lungs at 90% vital capacity. We present results by comparing our automatic method to manually traced borders from two image analysts. Averaged over all volumes, the root mean square difference between the computer and human analysis is 0.8 pixels (0.54 mm). The mean intrasubject change in tissue content over the three scans was 2.75% +/- 2.29% (mean +/- standard deviation).     

$n$ -SIFT: $n$ -Dimensional Scale Invariant Feature Transform

We propose the $n$ -dimensional scale invariant feature transform ( $n$-SIFT) method for extracting and matching salient features from scalar images of arbitrary dimensionality, and compare this method's performance to other related features. The proposed features extend the concepts used for 2-D scalar images in the computer vision SIFT technique for extracting and matching distinctive scale invariant features. We apply the features to images of arbitrary dimensionality through the use of hyperspherical coordinates for gradients and multidimensional histograms to create the feature vectors. We analyze the performance of a fully automated multimodal medical image matching technique based on these features, and successfully apply the technique to determine accurate feature point correspondence between pairs of 3-D MRI images and dynamic $3{rm D} + {rm time}$ CT data.      

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.     

Medical image compression by using three-dimensional wavelet transformation

This paper proposes a three-dimensional (3-D) medical image compression method for computed tomography (CT) and magnetic resonance (MR) that uses a separable nonuniform 3-D wavelet transform. The separable wavelet transform employs one filter bank within two-dimensional (2-D) slices and then a second filter bank on the slice direction. CT and MR image sets normally have different resolutions within a slice and between slices. The pixel distances within a slice are normally less than 1 mm and the distance between slices can vary from 1 mm to 10 mm. To find the best filter bank in the slice direction, the authors use the various filter banks in the slice direction and compare the compression results. The results from the 12 selected MR and CT image sets at various slice thickness show that the Haar transform in the slice direction gives the optimum performance for most image sets, except for a CT image set which has 1 mm slice distance. Compared with 2-D wavelet compression, compression ratios of the 3-D method are about 70% higher for CT and 35% higher for MR image sets at a peak signal to noise ratio (PSNR) of 50 dB, In general, the smaller the slice distance, the better the 3-D compression performance.     

Alignment of 3-D optical coherence tomography scans to correct eye movement using a particle filtering

Eye movement artifacts occurring during 3-D optical coherence tomography (OCT) scanning is a well-recognized problem that may adversely affect image analysis and interpretation. A particle filtering algorithm is presented in this paper to correct motion in a 3-D dataset by considering eye movement as a target tracking problem in a dynamic system. The proposed particle filtering algorithm is an independent 3-D alignment approach, which does not rely on any reference image. 3-D OCT data is considered as a dynamic system, while the location of each A-scan is represented by the state space. A particle set is used to approximate the probability density of the state in the dynamic system. The state of the system is updated frame by frame to detect A-scan movement. The proposed method was applied on both simulated data for objective evaluation and experimental data for subjective evaluation. The sensitivity and specificity of the x-movement detection were 98.85% and 99.43%, respectively, in the simulated data. For the experimental data (74 3-D OCT images), all the images were improved after z-alignment, while 81.1% images were improved after x-alignment. The proposed algorithm is an efficient way to align 3-D OCT volume data and correct the eye movement without using references.     

3-D/2-D registration by integrating 2-D information in 3-D

In image-guided therapy, high-quality preoperative images serve for planning and simulation, and intraoperatively as "background", onto which models of surgical instruments or radiation beams are projected. The link between a preoperative image and intraoperative physical space of the patient is established by image-to-patient registration. In this paper, we present a novel 3-D/2-D registration method. First, a 3-D image is reconstructed from a few 2-D X-ray images and next, the preoperative 3-D image is brought into the best possible spatial correspondence with the reconstructed image by optimizing a similarity measure (SM). Because the quality of the reconstructed image is generally low, we introduce a novel SM, which is able to cope with low image quality as well as with different imaging modalities. The novel 3-D/2-D registration method has been evaluated and compared to the gradient-based method (GBM) using standardized evaluation methodology and publicly available 3-D computed tomography (CT), 3-D rotational X-ray (3DRX), and magnetic resonance (MR) and 2-D X-ray images of two spine phantoms, for which gold standard registrations were known. For each of the 3DRX, CT, or MR images and each set of X-ray images, 1600 registrations were performed from starting positions, defined as the mean target registration error (mTRE), randomly generated and uniformly distributed in the interval of 0-20 mm around the gold standard. The capture range was defined as the distance from gold standard for which the final TRE was less than 2 mm in at least 95% of all cases. In terms of success rate, as the function of initial misalignment and capture range the proposed method outperformed the GBM. TREs of the novel method and the GBM were approximately the same. For the registration of 3DRX and CT images to X-ray images as few as 2-3 X-ray views were sufficient to obtain approximately 0.4 mm TREs, 7-9 mm capture range, and 80%-90% of successful registrations. To obtain similar results for MR to X-ray registrations, an image, reconstructed from at least 11 X-ray images was required. Reconstructions from more than 11 images had no effect on the registration results.     

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.     

Automated anatomical labeling of the bronchial branch and its application to the virtual bronchoscopy system

This paper describes a method for the automated anatomical labeling of the bronchial branch extracted from a three-dimensional (3-D) chest X-ray CT image and its application to a virtual bronchoscopy system (VBS). Automated anatomical labeling is necessary for implementing an advanced computer-aided diagnosis system of 3-D medical images. This method performs the anatomical labeling of the bronchial branch using the knowledge base of the bronchial branch name. The knowledge base holds information on the bronchial branch as a set of rules for its anatomical labeling. A bronchus region is automatically extracted from a given 3-D CT image. A tree structure representing the essential structure of the extracted bronchus is recognized from the bronchus region. Anatomical labeling is performed by comparing this tree structure of the bronchus with the knowledge base. As an application, we implemented the function to automatically present the anatomical names of the branches that are shown in the currently rendered image in real time on the VBS. The result showed that the method could segment about 57% of the branches from CT images and extracted a tree structure of about 91% in branches in the segmented bronchus. The anatomical labeling method could assign the correct branch name to about 93% of the branches in the extracted tree structure. Anatomical names were appropriately displayed in the endoscopic view.     

Reversible decorrelation method for progressive transmission of 3-Dmedical image

In this paper, the authors present a new reversible decorrelation method of three-dimensional (3-D) medical images for progressive transmission. Progressive transmission of an image permits gradual improvement of image quality while being displayed. When the amount of image data is very large, as a 3-D medical image, the progressive transmission plays an important role in viewing or browsing the image. The data structure presented in this paper takes account of interframe correlation as well as intraframe correlation of the 3-D image. This type of data structure has been termed the 3-D hierarchy embedded differential image (3-D-HEDI) as was derived from the earlier HEDI structure (Kim et al., 1995). Experiments were conducted to verify the performance of 3-D HEDI in terms of the decorrelation efficiency as well as the progressive transmission efficiency. It is compared with those of conventional hierarchy interpolation (HINT), two-dimensional (2-D) HEDI and differential pulse code modulation (DPCM). Experimental results indicate that 3-D HEDI outperforms HINT, 2-D HEDI and DPCM in both decorrelation efficiency as well as the progressive transmission efficiency on 3-D medical images     

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.     

Computation of 3-D velocity fields from 3-D cine CT images of a human heart

A method of computing the three-dimensional (3-D) velocity field from 3-D cine computer tomographs (CTs) of a beating heart is proposed. Using continuum theory, the authors develop two constraints on the 3-D velocity field generated by a beating heart. With these constraints, the computation of the 3-D velocity field is formulated as an optimization problem and a solution to the optimization problem is developed using the Euler-Lagrange method. The solution is then discretized for computer implementation. The authors present the results for both simulated images and clinical cine CT images of a beating heart.     

An efficient Fourier method for 3-D radon inversion in exactcone-beam CT reconstruction

The radial derivative of the three-dimensional (3-D) radon transform of an object is an important intermediate result in many analytically exact cone-beam reconstruction algorithms. The authors briefly review Grangeat's (1991) approach for calculating radon derivative data from cone-beam projections and then present a new, efficient method for 3-D radon inversion, i.e., reconstruction of the image from the radial derivative of the 3-D radon transform, called direct Fourier inversion (DFI). The method is based directly on the 3-D Fourier slice theorem. From the 3-D radon derivative data, which is assumed to be sampled on a spherical grid, the 3-D Fourier transform of the object is calculated by performing fast Fourier transforms (FFTs) along radial lines in the radon space. Then, an interpolation is performed from the spherical to a Cartesian grid using a 3-D gridding step in the frequency domain. Finally, this 3-D Fourier transform is transformed back to the spatial domain via 3-D inverse FFT. The algorithm is computationally efficient with complexity in the order of N ³ log N. The authors have done reconstructions of simulated 3-D radon derivative data assuming sampling conditions and image quality requirements similar to those in medical computed tomography (CT)     

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     

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.     

Nonlinear filtering approach to 3-D gray-scale image interpolation

Three-dimensional (3-D) images are now common in radiology. A 3-D image is formed by stacking a contiguous sequence of two-dimensional cross-sectional images, or slices. Typically, the spacing between known slices is greater than the spacing between known points on a slice. Many visualization and image-analysis tasks, however, require the 3-D image to have equal sample spacing in all directions. To meet this requirement, one applies an interpolation technique to the known 3-D image to generate a new uniformly sampled 3-D image. The authors propose a nonlinear-filter-based approach to gray-scale interpolation of 3-D images. The method, referred to as column-fitting interpolation, is reminiscent of the maximum-homogeneity filter used for image enhancement. The authors also draw upon the paradigm of relaxation labeling to devise an improved column-fitting interpolator. Both methods are typically more effective than traditional gray-scale interpolation techniques.     

Statistical distributions of DCT coefficients and their application to an interframe compression algorithm for 3-D medical images

Displacement estimated interframe (DEI) coding, a coding scheme for 3-D medical image data sets such as X-ray computed tomography (CT) or magnetic resonance (MR) images, is presented. To take advantage of the correlation between contiguous slices, a displacement-compensated difference image based on the previous image is encoded. The best fitting distribution functions for the discrete cosine transform (DCT) coefficients obtained from displacement compensated difference images are determined and used in allocating bits and optimizing quantizers for the coefficients. The DEI scheme is compared with 2-D block discrete cosine transform (DCT) as well as a full-frame DCT using the bit allocation technique of S. Lo and H.K. Huang (1985). For X-ray CT head images, the present bit allocation and quantizer design, using an appropriate distribution model, resulted in a 13-dB improvement in the SNR compared to the full-frame DCT using the bit allocation technique. For an image set with 5-mm slice thickness, the DEI method gave about 5% improvement in the compression ratio on average and less blockiness at the same distortion. The performance gain increases to about 10% when the slice thickness decreases to 3 mm.