Photon-counting computed tomography (PCCT) reconstructs multiple energy-channel images to describe the same object, where there exists a strong correlation among different channel images. In addition, reconstruction of each channel image suffers photon count starving problem. To make full use of the correlation among different channel images to suppress the data noise and enhance the texture details in reconstructing each channel image, this paper proposes a tensor neural network (TNN) architecture to learn a multi-channel texture prior for PCCT reconstruction. Specifically, we first learn a spatial texture prior in each individual channel image by modeling the relationship between the center pixels and its corresponding neighbor pixels using a neural network. Then, we merge the single channel spatial texture prior into multi-channel neural network to learn the spectral local correlation information among different channel images. Since our proposed TNN is trained on a series of unpaired small spatial-spectral cubes which are extracted from one single reference multi-channel image, the local correlation in the spatial-spectral cubes is considered by TNN. To boost the TNN performance, a low-rank representation is also employed to consider the global correlation among different channel images. Finally, we integrate the learned TNN and the low-rank representation as priors into Bayesian reconstruction framework. To evaluate the performance of the proposed method, four references are considered. One is simulated images from ultra-high-resolution CT. One is spectral images from dual-energy CT. The other two are animal tissue and preclinical mouse images from a custom-made PCCT systems. Our TNN prior Bayesian reconstruction demonstrated better performance than other state-of-the-art competing algorithms, in terms of not only preserving texture feature but also suppressing image noise in each channel image.

In this study, we proposed a computer-aided diagnosis (CADx) framework under dual-energy spectral CT (DECT), which operates directly on the transmission data in the pre-log domain, called CADxDE, to explore the spectral information for lesion diagnosis. The CADxDE includes material identification and machine learning (ML) based CADx. Benefits from DECT's capability of performing virtual monoenergetic imaging with the identified materials, the responses of different tissue types (e.g., muscle, water, and fat) in lesions at each energy can be explored by ML for CADx. Without losing essential factors in the DECT scan, a pre-log domain model-based iterative reconstruction is adopted to obtain decomposed material images, which are then used to generate the virtual monoenergetic images (VMIs) at selected n energies. While these VMIs have the same anatomy, their contrast distribution patterns contain rich information along with the n energies for tissue characterization. Thus, a corresponding ML-based CADx is developed to exploit the energy-enhanced tissue features for differentiating malignant from benign lesions. Specifically, an original image-driven multi-channel three-dimensional convolutional neural network (CNN) and extracted lesion feature-based ML CADx methods are developed to show the feasibility of CADxDE. Results from three pathologically proven clinical datasets showed 4.01% to 14.25% higher AUC (area under the receiver operating characteristic curve) scores than the scores of both the conventional DECT data (high and low energy spectrum separately) and the conventional CT data. The mean gain >9.13% in AUC scores indicated that the energy spectral-enhanced tissue features from CADxDE have great potential to improve lesion diagnosis performance.

Photon-counting spectral computed tomography (CT) is capable of material characterization and can improve diagnostic performance over traditional clinical CT. However, it suffers from photon count starving for each individual energy channel which may cause severe artifacts in the reconstructed images. Furthermore, since the images in different energy channels describe the same object, there are high correlations among different channels. To make full use of the inter-channel correlations and minimize the count starving effect while maintaining clinically meaningful texture information, this paper combines a region-specific texture model with a low-rank correlation descriptor as an a priori regularization to explore a superior texture preserving Bayesian reconstruction of spectral CT. Specifically, the inter-channel correlations are characterized by the low-rank representation, and the inner-channel regional textures are modeled by a texture preserving Markov random field. In other words, this paper integrates the spectral and spatial information into a unified Bayesian reconstruction framework. The widely-used Split-Bregman algorithm is employed to minimize the objective function because of the non-differentiable property of the low-rank representation. To evaluate the tissue texture preserving performance of the proposed method for each channel, three references are built for comparison: one is the traditional CT image from energy integration detection. The second one is spectral images from dual-energy CT. The third one is individual channels images from custom-made photon-counting spectral CT. As expected, the proposed method produced promising results in terms of not only preserving texture features but also suppressing image noise in each channel, comparing to existing methods of total variation (TV), low-rank TV and tensor dictionary learning, by both visual inspection and quantitative indexes of root mean square error, peak signal to noise ratio, structural similarity and feature similarity.

Accurately classifying colorectal polyps, or differentiating malignant from benign ones, has a significant clinical impact on early detection and identifying optimal treatment of colorectal cancer. Convolution neural network (CNN) has shown great potential in recognizing different objects (e.g. human faces) from multiple slice (or color) images, a task similar to the polyp differentiation, given a large learning database. This study explores the potential of CNN learning from multiple slice (or feature) images to differentiate malignant from benign polyps from a relatively small database with pathological ground truth, including 32 malignant and 31 benign polyps represented by volumetric computed tomographic (CT) images. The feature image in this investigation is the gray-level co-occurrence matrix (GLCM). For each volumetric polyp, there are 13 GLCMs, computed from each of the 13 directions through the polyp volume. For comparison purpose, the CNN learning is also applied to the multi-slice CT images of the volumetric polyps. The comparison study is further extended to include Random Forest (RF) classification of the Haralick texture features (derived from the GLCMs). From the relatively small database, this study achieved scores of 0.91/0.93 (two-fold/leave-one-out evaluations) AUC (area under curve of the receiver operating characteristics) by using the CNN on the GLCMs, while the RF reached 0.84/0.86 AUC on the Haralick features and the CNN rendered 0.79/0.80 AUC on the multiple-slice CT images. The presented CNN learning from the GLCMs can relieve the challenge associated with relatively small database, improve the classification performance over the CNN on the raw CT images and the RF on the Haralick features, and have the potential to perform the clinical task of differentiating malignant from benign polyps with pathological ground truth.

Markov random field (MRF) has been widely used to incorporate a priori knowledge as penalty or regularizer to preserve edge sharpness while smoothing the region enclosed by the edge for pieces-wise smooth image reconstruction. In our earlier study, we proposed a type of MRF reconstruction method for low-dose CT (LdCT) scans using tissue-specific textures extracted from the same patient's previous full-dose CT (FdCT) scans as prior knowledge. It showed advantages in clinical applications. This paper aims to remove the constraint of using previous data of the same patient. We investigated the feasibility of extracting the tissue-specific MRF textures from an FdCT database to reconstruct a LdCT image of another patient. This feasibility study was carried out by experiments designed as follows. We constructed a tissue-specific MRF-texture database from 3990 FdCT scan slices of 133 patients who were scheduled for lung nodule biopsy. Each patient had one FdCT scan (120 kVp/100 mAs) and one LdCT scan (120 kVp/20 mAs) prior to biopsy procedure. When reconstructing the LdCT image of one patient among the 133 patients, we ranked the closeness of the MRF-textures from the other 132 patients saved in the database and used them as the a prior knowledge. Then, we evaluated the reconstructed image quality using Haralick texture measures. For any patient within our database, we found more than eighteen patients' FdCT MRF texures can be used without noticeably changing the Haralick texture measures on the lung nodules (to be biopsied). These experimental outcomes indicate it is promising that a sizable FdCT texture database could be used to enhance Bayesian reconstructions of any incoming LdCT scans.

The introduction of computed tomography (CT) in 1972 was among the most significant development in medical imaging since the discovery of X-rays in 1895. In addition, the innovation of computationally reconstructing tomographic images from projection data significantly influenced the development of other medical imaging modalities, such as magnetic resonance imaging and single photon and positron emission tomography. With the advent of helical and multi-detector-row CT (MDCT) scanners in the 1990s and 2000s along with innovations in cone-beam CT (CBCT) in many forms, CT gained unmatched speed and adaptability for volumetric imaging, leading to widespread use for diagnostic imaging, emergency examination, image-guided interventions, treatment planning, and monitoring of therapeutic response.

Computed tomography (CT) image recovery from low-mAs acquisitions without adequate treatment is always severely degraded due to a number of physical factors. In this paper, we formulate the low-dose CT sinogram preprocessing as a standard maximum a posteriori (MAP) estimation, which takes full consideration of the statistical properties of the two intrinsic noise sources in low-dose CT, i.e., the X-ray photon statistics and the electronic noise background. In addition, instead of using a general image prior as found in the traditional sinogram recovery models, we design a new prior formulation to more rationally encode the piecewise-linear configurations underlying a sinogram than previously used ones, like the TV prior term. As compared with the previous methods, especially the MAP-based ones, both the likelihood/loss and prior/regularization terms in the proposed model are ameliorated in a more accurate manner and better comply with the statistical essence of the generation mechanism of a practical sinogram. We further construct an efficient alternating direction method of multipliers algorithm to solve the proposed MAP framework. Experiments on simulated and real low-dose CT data demonstrate the superiority of the proposed method according to both visual inspection and comprehensive quantitative performance evaluation.

Dynamic cerebral perfusion computed tomography (DCPCT) has the ability to evaluate the hemodynamic information throughout the brain. However, due to multiple 3-D image volume acquisitions protocol, DCPCT scanning imposes high radiation dose on the patients with growing concerns. To address this issue, in this paper, based on the robust principal component analysis (RPCA, or equivalently the low-rank and sparsity decomposition) model and the DCPCT imaging procedure, we propose a new DCPCT image reconstruction algorithm to improve low-dose DCPCT and perfusion maps quality via using a powerful measure, called Kronecker-basis-representation tensor sparsity regularization, for measuring low-rankness extent of a tensor. For simplicity, the first proposed model is termed tensor-based RPCA (T-RPCA). Specifically, the T-RPCA model views the DCPCT sequential images as a mixture of low-rank, sparse, and noise components to describe the maximum temporal coherence of spatial structure among phases in a tensor framework intrinsically. Moreover, the low-rank component corresponds to the "background" part with spatial-temporal correlations, e.g., static anatomical contribution, which is stationary over time about structure, and the sparse component represents the time-varying component with spatial-temporal continuity, e.g., dynamic perfusion enhanced information, which is approximately sparse over time. Furthermore, an improved nonlocal patch-based T-RPCA (NL-T-RPCA) model which describes the 3-D block groups of the "background" in a tensor is also proposed. The NL-T-RPCA model utilizes the intrinsic characteristics underlying the DCPCT images, i.e., nonlocal self-similarity and global correlation. Two efficient algorithms using alternating direction method of multipliers are developed to solve the proposed T-RPCA and NL-T-RPCA models, respectively. Extensive experiments with a digital brain perfusion phantom, preclinical monkey data, and clinical patient data clearly demonstrate that the two proposed models can achieve more gains than the existing popular algorithms in terms of both quantitative and visual quality evaluations from low-dose acquisitions, especially as low as 20 mAs.

To continue our effort on developing magnetic resonance (MR) cystography, we introduce a novel nonrigid 3-D registration method to compensate for bladder wall motion and deformation in dynamic MR scans, which are impaired by relatively low signal-to-noise ratio in each time frame. The registration method is developed on the similarity measure of α-information, which has the potential of achieving higher registration accuracy than the commonly used mutual information (MI) measure for either monomodality or multimodality image registration. The α-information metric was also demonstrated to be superior to both the mean squares and the cross-correlation metrics in multimodality scenarios. The proposed α-registration method was applied for bladder motion compensation via real patient studies, and its effect to the automatic and accurate segmentation of bladder wall was also evaluated. Compared with the prevailing MI-based image registration approach, the presented α-information-based registration was more effective to capture the bladder wall motion and deformation, which ensured the success of the following bladder wall segmentation to achieve the goal of evaluating the entire bladder wall for detection and diagnosis of abnormality.

Image textures in computed tomography colonography (CTC) have great potential for differentiating non-neoplastic from neoplastic polyps and thus can advance the current CTC detection-only paradigm to a new level with diagnostic capability. However, image textures are frequently compromised, particularly in low-dose CT imaging. Furthermore, texture feature extraction may vary, depending on the polyp spatial orientation variation, resulting in variable results. To address these issues, this study proposes an adaptive approach to extract and analyze the texture features for polyp differentiation. Firstly, derivative (e.g. gradient and curvature) operations are performed on the CT intensity image to amplify the textures with adequate noise control. Then Haralick co-occurrence matrix (CM) is used to calculate texture measures along each of the 13 directions (defined by the first and second order image voxel neighbors) through the polyp volume in the intensity, gradient and curvature images. Instead of taking the mean and range of each CM measure over the 13 directions as the so-called Haralick texture features, Karhunen-Loeve transform is performed to map the 13 directions into an orthogonal coordinate system so that the resulted texture features are less dependent on the polyp orientation variation. These simple ideas for amplifying textures and stabilizing spatial variation demonstrated a significant impact for the differentiating task by experiments using 384 polyp datasets, of which 52 are non-neoplastic polyps and the rest are neoplastic polyps. By the merit of area under the curve of receiver operating characteristic, the innovative ideas achieved differentiation capability of 0.8016, indicating the CTC diagnostic feasibility.

Markov random field (MRF) model has been widely employed in edge-preserving regional noise smoothing penalty to reconstruct piece-wise smooth images in the presence of noise, such as in low-dose computed tomography (LdCT). While it preserves edge sharpness, its regional smoothing may sacrifice tissue image textures, which have been recognized as useful imaging biomarkers, and thus it may compromise clinical tasks such as differentiating malignant vs. benign lesions, e.g., lung nodules or colon polyps. This study aims to shift the edge-preserving regional noise smoothing paradigm to texture-preserving framework for LdCT image reconstruction while retaining the advantage of MRF's neighborhood system on edge preservation. Specifically, we adapted the MRF model to incorporate the image textures of muscle, fat, bone, lung, etc. from previous full-dose CT (FdCT) scan as a priori knowledge for texture-preserving Bayesian reconstruction of current LdCT images. To show the feasibility of the proposed reconstruction framework, experiments using clinical patient scans were conducted. The experimental outcomes showed a dramatic gain by the a priori knowledge for LdCT image reconstruction using the commonly-used Haralick texture measures. Thus, it is conjectured that the texture-preserving LdCT reconstruction has advantages over the edge-preserving regional smoothing paradigm for texture-specific clinical applications.

In the above paper (IEEE Trans. on Medical Imaging, vol. 35, no. 6, Mar. 2016, pp. 860-870), the first footnote should have noted the following information. Hao Zhang, Hao Han contributed equally to this work. Zhengrong Liang is the corresponding author.

Computer-aided detection (CADe) of pulmonary nodules is critical to assisting radiologists in early identification of lung cancer from computed tomography (CT) scans. This paper proposes a novel CADe system based on a hierarchical vector quantization (VQ) scheme. Compared with the commonly-used simple thresholding approach, the high-level VQ yields a more accurate segmentation of the lungs from the chest volume. In identifying initial nodule candidates (INCs) within the lungs, the low-level VQ proves to be effective for INCs detection and segmentation, as well as computationally efficient compared to existing approaches. False-positive (FP) reduction is conducted via rule-based filtering operations in combination with a feature-based support vector machine classifier. The proposed system was validated on 205 patient cases from the publically available online Lung Image Database Consortium database, with each case having at least one juxta-pleural nodule annotation. Experimental results demonstrated that our CADe system obtained an overall sensitivity of 82.7% at a specificity of 4 FPs/scan. Especially for the performance on juxta-pleural nodules, we observed 89.2% sensitivity at 4.14 FPs/scan. With respect to comparable CADe systems, the proposed system shows outperformance and demonstrates its potential for fast and adaptive detection of pulmonary nodules via CT imaging.

Previous studies have shown that by minimizing the total variation (TV) of the to-be-estimated image with some data and/or other constraints, a piecewise-smooth X-ray computed tomography image can be reconstructed from sparse-view projection data. However, due to the piecewise constant assumption for the TV model, the reconstructed images are frequently reported to suffer from the blocky or patchy artifacts. To eliminate this drawback, we present a total variation-stokes-projection onto convex sets (TVS-POCS) reconstruction method in this paper. The TVS model is derived by introducing isophote directions for the purpose of recovering possible missing information in the sparse-view data situation. Thus the desired consistencies along both the normal and the tangent directions are preserved in the resulting images. Compared to the previous TV-based image reconstruction algorithms, the preserved consistencies by the TVS-POCS method are expected to generate noticeable gains in terms of eliminating the patchy artifacts and preserving subtle structures. To evaluate the presented TVS-POCS method, both qualitative and quantitative studies were performed using digital phantom, physical phantom and clinical data experiments. The results reveal that the presented method can yield images with several noticeable gains, measured by the universal quality index and the full-width-at-half-maximum merit, as compared to its corresponding TV-based algorithms. In addition, the results further indicate that the TVS-POCS method approaches to the gold standard result of the filtered back-projection reconstruction in the full-view data case as theoretically expected, while most previous iterative methods may fail in the full-view case because of their artificial textures in the results.

In the above-named article [ibid., vol. 33, no. 3, pp. 749-763, Mar. 2014], Y. Liu was incorrectly listed as the corresponding author. Z. Liang should have been indicated as the corresponding author.

This paper proposes an adaptive window-setting scheme for noninvasive detection and segmentation of bladder tumor surface in T(1)-weighted magnetic resonance (MR) images. The inner border of the bladder wall is first covered by a group of ball-shaped detecting windows with different radii. By extracting the candidate tumor windows and excluding the false positive (FP) candidates, the entire bladder tumor surface is detected and segmented by the remaining windows. Different from previous bladder tumor detection methods that are mostly focusing on the existence of a tumor, this paper emphasizes segmenting the entire tumor surface in addition to detecting the presence of the tumor. The presented scheme was validated by ten clinical T(1)-weighted MR image datasets (five volunteers and five patients). The bladder tumor surfaces and the normal bladder wall inner borders in the ten datasets were covered by 223 and 10,491 windows, respectively. Such a large number of the detecting windows makes the validation statistically meaningful. In the FP reduction step, the best feature combination was obtained by using receiver operating characteristics or ROC analysis. The validation results demonstrated the potential of this presented scheme in segmenting the entire tumor surface with high sensitivity and low FP rate. This study inherits our previous results of automatic segmentation of the bladder wall and will be an important element in our MR-based virtual cystoscopy or MR cystography system.

In this paper, we propose a coupled level set (LS) framework for segmentation of bladder wall using T(1)-weighted magnetic resonance (MR) images with clinical applications to virtual cystoscopy (i.e., MR cystography). The framework uses two collaborative LS functions and a regional adaptive clustering algorithm to delineate the bladder wall for the wall thickness measurement on a voxel-by-voxel basis. It is significantly different from most of the pre-existing bladder segmentation work in four aspects. First of all, while most previous work only segments the inner border of the wall or at most manually segments the outer border, our framework extracts both the inner and outer borders automatically except that the initial seed point is given by manual selection. Secondly, it is adaptive to T(1)-weighted images with decreased intensities in urine, as opposed to enhanced intensities in T(2)-weighted scenario and computed tomography. Thirdly, by considering the image global intensity distribution and local intensity contrast, the defined image energy function in the framework is more immune to inhomogeneity effect, motion artifacts and image noise. Finally, the bladder wall thickness is measured by the length of integral path between the two borders which mimic the electric field line between two iso-potential surfaces. The framework was tested on six datasets with comparison to the well-known Chan-Vese (C-V) LS model. Five experts blindly scored the segmented inner and outer borders of the presented framework and the C-V model. The scores demonstrated statistically the improvement in detecting the inner and outer borders.

This work presents an iterative expectation-maximization (EM) approach to the maximum a posteriori (MAP) solution of segmenting tissue mixtures inside each image voxel. Each tissue type is assumed to follow a normal distribution across the field-of-view (FOV). Furthermore, all tissue types are assumed to be independent from each other. Under these assumptions, the summation of all tissue mixtures inside each voxel leads to the image density mean value at that voxel. The summation of all the tissue mixtures' unobservable random processes leads to the observed image density at that voxel, and the observed image density value also follows a normal distribution (image data are observed to follow a normal distribution in many applications). By modeling the underlying tissue distributions as a Markov random field across the FOV, the conditional expectation of the posteriori distribution of the tissue mixtures inside each voxel is determined, given the observed image data and the current-iteration estimation of the tissue mixtures. Estimation of the tissue mixtures at next iteration is computed by maximizing the conditional expectation. The iterative EM approach to a MAP solution is achieved by a finite number of iterations and reasonable initial estimate. This MAP-EM framework provides a theoretical solution to the partial volume effect, which has been a major cause of quantitative imprecision in medical image processing. Numerical analysis demonstrated its potential to estimate tissue mixtures accurately and efficiently.

The author affiliations in the first footnote of the above-named work are corrected.

This paper presents a model-based approach to correct for both partial volume effect and inhomogeneity in segmenting tissue mixtures inside each voxel of magnetic resonance images. A maximum a posteriori probability (MAP) solution is sought. In calculating the solution, the well-known expectation maximization (EM) algorithm is employed. The models of data likelihood and Markov priors for tissue mixture and bias field in establishing this MAP-EM framework are described in details. A preliminary test is presented

Reconstructing low-dose X-ray computed tomography (CT) images is a noise problem. This work investigated a penalized weighted least-squares (PWLS) approach to address this problem in two dimensions, where the WLS considers first- and second-order noise moments and the penalty models signal spatial correlations. Three different implementations were studied for the PWLS minimization. One utilizes a Markov random field (MRF) Gibbs functional to consider spatial correlations among nearby detector bins and projection views in sinogram space and minimizes the PWLS cost function by iterative Gauss-Seidel algorithm. Another employs Karhunen-Loeve (KL) transform to de-correlate data signals among nearby views and minimizes the PWLS adaptively to each KL component by analytical calculation, where the spatial correlation among nearby bins is modeled by the same Gibbs functional. The third one models the spatial correlations among image pixels in image domain also by a MRF Gibbs functional and minimizes the PWLS by iterative successive over-relaxation algorithm. In these three implementations, a quadratic functional regularization was chosen for the MRF model. Phantom experiments showed a comparable performance of these three PWLS-based methods in terms of suppressing noise-induced streak artifacts and preserving resolution in the reconstructed images. Computer simulations concurred with the phantom experiments in terms of noise-resolution tradeoff and detectability in low contrast environment. The KL-PWLS implementation may have the advantage in terms of computation for high-resolution dynamic low-dose CT imaging

Fan-beam collimators are designed to improve the system sensitivity and resolution for imaging small objects such as the human brain and breasts in single photon emission computed tomography (SPECT). Many reconstruction algorithms have been studied and applied to this geometry to deal with every kind of degradation factor. This paper presents a new reconstruction approach for SPECT with circular orbit, which demonstrated good performance in terms of both accuracy and efficiency. The new approach compensates for degradation factors including noise, scatter, attenuation, and spatially variant detector response. Its uniform attenuation approximation strategy avoids the additional transmission scan for the brain attenuation map, hence reducing the patient radiation dose and furthermore simplifying the imaging procedure. We evaluate and compare this new approach with the well-established ordered-subset expectation-maximization iterative method, using Monte Carlo simulations. We perform quantitative analysis with regional bias-variance, receiver operating characteristics, and Hotelling trace studies for both methods. The results demonstrate that our reconstruction strategy has comparable performance with a significant reduction of computing time.

This paper investigates an accurate reconstruction method to invert the attenuated Radon transform in nonparallel beam (NPB) geometries. The reconstruction method contains three major steps: 1) performing one-dimensional phase-shift rebinning; 2) implementing nonuniform Hilbert transform; and 3) applying Novikov's explicit inversion formula. The method seems to be adaptive to different settings of fan-beam geometry from very long to very short focal lengths without sacrificing reconstruction accuracy. Compared to the conventional bilinear rebinning technique, the presented method showed a better spatial resolution, as measured by modulation transfer function. Numerical experiments demonstrated its computational efficiency and stability to different levels of Poisson noise. Even with complicated geometries such as varying focal-length and asymmetrical fan-beam collimation, the presented method achieved nearly the same reconstruction quality of parallel-beam geometry. This effort can facilitate quantitative reconstruction of single photon emission computed tomography for cardiac imaging, which may need NPB collimation geometries and require high computational efficiency.

The developmental dysplasia of the hip (DDH) is a congenital malformation of the acetabulum with different degrees. Leaving it partially treated or untreated is a major cause of disability. In this paper, we implemented a computer-aided system for the diagnosis and treatment planning of DDH. Instead of labeling each voxel with a unique label or tissue type, the percentage of different tissues within each voxel, which we call a mixture, was considered in establishing a maximum a posterior probability (MAP) framework for more accurate segmentation. A graphical module displayed the segmented bone in a 3D view to show the spatial relationship between acetabulum and femurs. This virtual image, together with quantitative measurement indexes, helps physicians make diagnosis. The system also provides physicians a virtual treatment planning on screen for acetabular and femoral osteotomy. It is currently under clinical trial on patient datasets.

Virtual endoscopy (VE) is an itegration of medical imaging and virtual reality. VE gives a computer-based alternative to standard radiological image viewing and to traditional fiberoptic endoscopy for examining the interior structures of human organs. It has evolved rapidly in the past decade, as high-resolution helical spiral computed tomography (CT) has evolved for clinical use. A total of 22 submissions were received, covering modalities of virtual colonoscopy, virtual bronchoscopy, and virtual angioscopy, with technical focus on image segmentation, registration, dynamical modeling, flight path planning, fast volumetric rendering, interactive and active navigation, and CAD.

In this paper, we introduce a concise and concrete definition of an accurate colon centerline and provide an efficient automatic means to extract the centerline and its associated branches (caused by a forceful touching of colon and small bowel or a deep fold in twisted colon lumen). We further discuss its applications on fly-through path planning and endoscopic simulation, as well as its potential to solve the challenging touching and colon collapse problems in virtual colonoscopy. Experimental results demonstrated its centeredness, robustness, and efficiency.

Virtual endoscopy is a computerized, noninvasive procedure for detecting anomalies inside human organs. Several preliminary studies have demonstrated the benefits and effectiveness of this modality. Unfortunately, previous work cannot guarantee that an existing anomaly will be detected, especially for complex organs with multiple branches. In this paper, we introduce the concept of reliable navigation, which ensures the interior organ surface is fully examined by the physician performing the virtual endoscopy procedure. To achieve this, we propose computing a reliable fly-through path that ensures no blind areas during the navigation. Theoretically, we discuss the criteria of evaluating a reliable path and prove that the problem of generating an optimal reliable path for virtual endoscopy is NP-complete. In practice, we develop an efficient method for the calculation of an effective reliable path. First, a small set of center observation points are automatically located inside the hollow organ. For each observation point, there exists at least one patch of interior surface visible to it, but that cannot be seen from any of the other observation points. These chosen points are then linked with a path that stays in the center of the organ. Finally, new points inside the organ are recursively selected and connected into the path until the entire organ surface is visible from the path. We present encouraging results from experiments on several data sets. For a medium-size volumetric model with several hundred thousand inner voxels, an effective reliable path can be generated in several minutes.

An automatic method has been developed for segmentation of abdominal computed tomography (CT) images for virtual colonoscopy obtained after a bowel preparation of a low-residue diet with ingested contrast solutions to enhance the image intensities of residual colonic materials. Removal of the enhanced materials was performed electronically by a computer algorithm. The method is a multistage approach that employs a modified self-adaptive on-line vector quantization technique for a low-level image classification and utilizes a region-growing strategy for a high-level feature extraction. The low-level classification labels each voxel based on statistical analysis of its three-dimensional intensity vectors consisting of nearby voxels. The high-level processing extracts the labeled stool, fluid and air voxels within the colon, and eliminates bone and lung voxels which have similar image intensities as the enhanced materials and air, but are physically separated from the colon. This method was evaluated by volunteer studies based on both objective and subjective criteria. The validation demonstrated that the method has a high reproducibility and repeatability and a small error due to partial volume effect. As a result of this electronic colon cleansing, routine physical bowel cleansing prior to virtual colonoscopy may not be necessary.

We present an interactive navigation system for virtual colonoscopy, which is based solely on high performance volume rendering. Previous colonic navigation systems have employed either a surface rendering or a Z-buffer-assisted volume rendering method that depends on the surface rendering results. Our method is a fast direct volume rendering technique that exploits distance information stored in the potential field of the camera control model, and is parallelized on a multiprocessor. Experiments have been conducted on both a simulated pipe and patients' data sets acquired with a CT scanner.

A variety of inversions of exponential Radon transform has been derived based on the circular harmonic transform in Fourier space by several research groups. However, these inversions cannot be directly applied to deal with the reconstruction for fan-beam or variable-focal-length fan-beam collimator geometries in single photon emission computed tomography (SPECT). In this paper, we derived a Cormack-type inversion of the exponential Radon transform by employing the circular harmonic transform directly in the projection space and the image space instead of the Fourier space. Thus, a unified reconstruction framework is established for parallel-, fan-, and variable-focal-length fan-beam collimator geometries. Compared to many existing algorithms, the presented one greatly mitigates the difficulty of image reconstruction due to the complicated collimator geometry and significantly reduces the computational burden of the special functions, such as Chebyshev or Bessel functions. By the well-established fast-Fourier transform (FFT), our algorithm is very efficient, as demonstrated by several numerical simulations.

A new technique for matching a 2-D or 3-D image to a translated, rotated, and uniformly scaled reference image is proposed. This method comprises three steps: (1) calculating the Radon transform of the reference image and the images to be matched, (2) calculating the Fourier invariant (FI) descriptor for each 1-D projection image, and (3) matching the FI descriptor in the projection space. The theory shows that information about translation, rotation and uniform scaling of a 2-D or 3-D image can be represented in its 1-D projections; thus a 2-D or 3-D matching can be accomplished as a set of 1-D operations. In particular, the presented technique provides a way to address the 3-D recognition problem when rigid motion is assumed.

Spatially varying focal length fan-beam collimators can be used in single photon emission computed tomography to improve detection efficiency and to reduce reconstruction artifacts resulting from the truncation of projection data. It has been proven that there exists no convolution backprojection algorithm for this type of collimator, so a complicated interpolation between two nonparallel projection rays is necessary for existing algorithms. The interpolation may generate blurring and artifacts in the reconstructed images. Based on a harmonic decomposition technique and the translation property of Fourier series, a semifrequency resampling technique is proposed to avoid the above mentioned interpolations. By this technique, the harmonic decomposition of projection data for spatially varying focal length fan-beam collimators has the same form as that for parallel-beam collimators in the semifrequency domain (Fourier transform with respect to angular variables only). An alternative version of the inverse Cormack transform is then proposed to reconstruct the images. The derived reconstruction algorithm was implemented in a Pentium II/266 PC computer. Numerical simulations demonstrated its efficiency (3 s for 128 x 128 reconstruction arrays) and its robust performance (compared to the existing algorithms).

3D virtual colonoscopy has recently been proposed as a non-invasive alternative procedure for the visualization of the human colon. Surface rendering is sufficient for implementing such a procedure to obtain an overview of the interior surface of the colon at interactive rendering speeds. Unfortunately, physicians can not use it to explore tissues beneath the surface to differentiate between benign and malignant structures. In this paper, we present a direct volume rendering approach based on perspective ray casting, as a supplement to the surface navigation. To accelerate the rendering speed, surface-assistant techniques are used to adapt the resampling rates by skipping the empty space inside the colon. In addition, a parallel version of the algorithm has been implemented on a shared-memory multiprocessing architecture. Experiments have been conducted on both simulation and patient data sets.

Fan-beam collimators with spatially varying focal lengths are used in single photon emission computed tomography (SPECT) to improve the imaging sensitivity and to reduce the reconstruction artifacts resulting from the truncation of projection data. An angular representation of the detector coordinates for the projection data is adopted to investigate several aspects of the reconstruction problem for this type of collimation. A rebinning reconstruction algorithm is derived. We prove a conjecture posed by Zeng and Gullberg and obtain a simplified form of their backprojection filtering algorithm. Some computer simulations are presented to investigate the performance of the rebinning algorithm.

A mathematical method was studied to model the detector response of high spatial-resolution positron emission tomography systems consisting of close-packed small crystals, and to restore the resolution deteriorated due to crystal penetration and/or nonuniform sampling across the field-of-view (FOV). The simulated detector system had 600 bismuth germanate crystals of 3.14 mm width and 30 mm length packed on a single ring of 60 cm diameter. The space between crystals was filled up with lead (i.e., septa). Each crystal was in coincidence with 200 opposite crystals so that the FOV had a radius of 30 cm. The detector response was modeled based on the attenuating properties of the crystals and the septa, as well as the geometry of the detector system. The modeled detector-response function was used to restore the projections from the sinogram of the ring-detector system. The restored projections had a uniform sampling of 1.57 mm across the FOV. The crystal penetration and/or the nonuniform sampling were compensated in the projections. A penalized maximum-likelihood algorithm was employed to accomplish the restoration. The restored projections were then filtered and backprojected to reconstruct the image. A chest phantom with a few small circular "cold" objects ( approximately 4 mm diameter) located at the center and near the periphery of FOV was computer generated and used to test the restoration. The reconstructed images from the restored projections demonstrated resolution improvement off the FOV center, while preserving the resolution near the center.

A statistical method is developed to classify tissue types and to segment the corresponding tissue regions from relaxation time T(1 ), T(2), and proton density P(D) weighted magnetic resonance images. The method assumes that the distribution of image intensities associated with each tissue type can be expressed as a multivariate likelihood function of three weighted signal intensity values (T(1), T(2), P(D)) at each location within that tissue regions. The method further assumes that the underlying tissue regions are piecewise contiguous and can be characterized by a Markov random field prior. In classifying the tissue types, the method models the likelihood of realizing the images as a finite multivariate-mixture function. The class parameters associated with the tissue types (i.e. the weighted intensity means, variances and correlation coefficients of the multivariate function, as well as the number of voxels within regions of the tissue types of are estimated by maximum likelihood. The estimation fits the class parameters to the image data via the expectation-maximization algorithm. The number of classes associated with the tissue types is determined by the information criterion of minimum description length. The method segments the tissue regions, given the estimated class parameters, by maximum a posteriori probability. The prior is constructed by the tissue-region membership of the first- and second-order neighborhood. The method is tested by a few sets of T(1), T(2), and P(D) weighted images of the brain acquired with a 1.5 Tesla whole body scanner. The number of classes and the associated class parameters are automatically estimated. The regions of different brain tissues are satisfactorily segmented.