Abstract Additive Manufacturing (AM) has emerged as a manufacturing process that allows the direct production of samples from digital models. To ensure that quality standards are met in all samples of a batch, X-ray computed tomography (X-CT) is often used in combination with automated anomaly detection. For the latter, deep learning (DL) anomaly detection techniques are increasingly used, as they can be trained to be robust to the material being analysed and resilient to poor image quality. Unfortunately, most recent and popular DL models have been developed for 2D image processing, thereby disregarding valuable volumetric information. Additionally, there is a notable absence of comparisons between supervised and unsupervised models for voxel-wise pore segmentation tasks. This study revisits recent supervised (UNet, UNet++, UNet 3+, MSS-UNet, ACC-UNet) and unsupervised (VAE, ceVAE, gmVAE, vqVAE, RV-VAE) DL models for porosity analysis of AM samples from X-CT images and extends them to accept 3D input data with a 3D-patch approach for lower computational requirements, improved efficiency and generalisability. The supervised models were trained using the Focal Tversky loss to address class imbalance that arises from the low porosity in the training datasets. The output of the unsupervised models was post-processed to reduce misclassifications caused by their inability to adequately represent the object surface. The findings were cross-validated in a 5-fold fashion and include: a performance benchmark of the DL models, an evaluation of the post-processing algorithm, an evaluation of the effect of training supervised models with the output of unsupervised models. In a final performance benchmark on a test set with poor image quality, the best performing supervised model was UNet++ with an average precision of 0.751 ± 0.030, while the best unsupervised model was the post-processed ceVAE with 0.830 ± 0.003. Notably, the ceVAE model, with its post-processing technique, exhibited superior capabilities, endorsing unsupervised learning as the preferred approach for the voxel-wise pore segmentation task.

X-ray Computed Tomography (CT) is a commonly used imaging technique for non-destructive inspection of manufactured objects. However, a full CT scan requires a long acquisition time, making this method unsuitable for inline applications. In contrast to X-ray CT, inspection can be performed directly in the projection space, using simulated X-ray projections of a reference model of the manufactured object. However, to effectively compare simulated and measured projections, an accurate 3D pose estimation of the object and consequent alignment between the measured object and the reference model are crucial. In this paper, we present a fast method to estimate the 3D pose of a measured object based on convolutional neural networks (CNNs). Through experiments on synthetic and measured data, we demonstrate that our method allows estimating the 3D pose of the object with sub-pixel accuracy. Even if very few projections are available, our approach is comparable to CT-based methods for registration, and outperforms state-of-the-art deep learning methods for radiograph-based pose estimation.

Abstract In X-ray computed tomography, discrete tomography (DT) algorithms have been successful at reconstructing objects composed of only a few distinct materials. Many DT-based methods rely on a divide-and-conquer procedure to reconstruct the volume in parts, which improves their run-time and reconstruction quality. However, this procedure is based on static rules, which introduces redundant computation and diminishes the efficiency. In this work, we introduce an update strategy framework that allows for dynamic rules and increases control for divide-and-conquer methods for DT. We illustrate this framework by introducing Tabu-DART, which combines our proposed framework with the Discrete Algebraic Reconstruction Technique (DART). Through simulated and real data reconstruction experiments, we show that our approach yields similar or improved reconstruction quality compared to DART, with substantially lower computational complexity.

Due to the rapid nucleation and bubble deformation processes that occur during a foam formation process, 4D-CT scans can only record a small number of X-ray projections per rotation. Current dynamic CT imaging methods compute a series of 3D images, which requires a high number of projections per rotation and thus limits the temporal resolution. In this work, we present a new reconstruction method that directly reconstructs a 4D dynamic image, by adapting a set of spherical meshes, representing the foam bubbles, such that the projection distance to the measured projections is minimized. Our method requires little memory, is robust against noise, and yields accurate reconstructions even when only few projections are available, as demonstrated by several experiments on simulated and real data.

High density materials, such as metals, strongly scatter X-ray photons during X-ray Computed Tomography (CT) scans, which is detrimental to the quality of the reconstructed images. In this study, a scatter compensation method for X-ray CT, based on Monte-Carlo (MC) simulations from the object’s CAD model, is presented and employed in conjunction with polychromatic reconstructions. The estimation of the scatter contributions is accelerated by 1) reducing the number of simulated projections accordingly to the Nyquist theorem, 2) noise reduction 3) angular interpolation. The method was applied to enhance CT images of a steel object produced via Additive Manufacturing, whose CAD model is known. Results show that, in conjunction with polychromatic reconstruction, our method can efficiently reduce beam hardening, scattering artifacts and increase the contrast of defects within the object.

X-ray 3D Computed Tomography (3DCT) has great potential for inspection of industrial products. Unfortunately, conventional CT-based workflows to inspect objects created from a CAD model involve a time-consuming acquisition process, computationally expensive image reconstruction, and multiple postprocessing steps, preventing them from inline usage. In this paper, we propose DynaPose, a fast and yet accurate workflow for 3D X-ray inspection of objects created from a CAD model. By exploiting prior knowledge of the CAD model, and relying on only very few radiographs, inspection can be performed in real-time. The DynaPose method allows automated 3D pose estimation of the object to be inspected while dynamically acquiring radiographs that are optimal for the detection task. Through simulation and real experiments, we show that our approach paves the way for inline inspection of manufactured objects.

mapping. The RIM is a neural network framework that learns an iterative inference process based on the signal model, similar to conventional statistical methods for quantitative MRI (QMRI), such as the Maximum Likelihood Estimator (MLE). This framework combines the advantages of both data-driven and model-based methods, and, we hypothesize, is a promising tool for QMRI. Previously, RIMs were used to solve linear inverse reconstruction problems. Here, we show that they can also be used to optimize non-linear problems and estimate relaxometry maps with high precision and accuracy. The developed RIM framework is evaluated in terms of accuracy and precision and compared to an MLE method and an implementation of the Residual Neural Network (ResNet). The results show that the RIM improves the quality of estimates compared to the other techniques in Monte Carlo experiments with simulated data, test-retest analysis of a system phantom, and in-vivo scans. Additionally, inference with the RIM is 150 times faster than the MLE, and robustness to (slight) variations of scanning parameters is demonstrated. Hence, the RIM is a promising and flexible method for QMRI. Coupled with an open-source training data generation tool, it presents a compelling alternative to previous methods.

In this paper, we study the influence of the beam shape of Terahertz (THz) radiation on the image formation in THz computed tomography and how to account for it in the reconstruction process. This is accomplished by first considering the beam shape in the forward projection using a modified Radon transform and then inverting this transform to construct new inversion techniques. Simulation experiments show that, compared to conventional back projection, directly incorporating the beam shape in the Radon transform can significantly improve image quality in terms of the mean squared error and the Structural Similarity Index.

In this paper, we present an approach to realistically simulate terahertz (THz) transmission mode imaging. We model the THz beam shape and account for the refraction of the THz beam at the different media interfaces using ray optics. Our approach does not require prior knowledge on the interfaces, instead it utilizes the refractive index scalar field. We study the beam shape and refraction effects separately by comparing resulting sinograms with the ones simulated by a Gaussian beam model, as well as with a real acquisition of a plastic object. The proposed forward projection can be utilized in iterative reconstruction algorithms to improve the quality of THz CT images.

Most lab-based X-ray sources are polychromatic, making the acquisition follow a non-linear model. However, widespread reconstruction algorithms, such as FBP and SIRT, assume the reconstruction to be a linear problem, leading to artefacts in the reconstructions. We propose a non-linear optimization technique, Newton-Krylov, to minimize a polychromatic objective function instead. The objective function can also easily be extended with regularisation terms, in a mathematically sound framework. Results on Monte-Carlo simulated projection data show a lower error in the data fidelity term, as well as improved reconstruction quality.

X-ray Computed Laminography (CL) is a well-known computed tomography technique to image the internal structure of flat objects. High-quality CL imaging requires, however, a large number of X-ray projections, resulting in long acquisition times. Reducing the number of acquired projections allows to speed up the acquisition process but decreases the quality of the reconstructed images. In this work, we investigate the use of Convolutional Neural Networks for processing volumes reconstructed from only four X-ray projections acquired at an inline CL scanning setup.

Magnetic resonance imaging (MRI) based T1 mapping allows spatially resolved quantification of the tissue-dependent spin-lattice relaxation time constant T1, which is a potential biomarker of various neurodegenerative diseases, including Multiple Sclerosis, Alzheimer disease, and Parkinson’s disease . In conventional T1 MR relaxometry, a quantitative T1 map is obtained from a series of T1-weighted MR images. Acquiring such a series, however, is time consuming. This has sparked the development of more efficient T1 mapping methods, one of which is a super-resolution reconstruction (SRR) framework in which a set of low resolution (LR) T1-weighted images is acquired and from which a high resolution (HR) T1 map is directly estimated. In this paper, the SRR T1 mapping framework is augmented with motion estimation. That is, motion between the acquisition of the LR T1-weighted images is modeled and the motion parameters are estimated simultaneously with the T1 parameters. Based on Monte Carlo simulation experiments, we show that such an integrated motion/relaxometry estimation approach yields more accurate T1 maps compared to a previously reported SRR based T1 mapping approach.

Abstract We present visual analysis methods for the evaluation of tomographic fiber reconstruction algorithms by means of analysis, visual debugging and comparison of reconstructed fibers in materials science. The methods are integrated in a tool (FIAKER) that supports the entire workflow. It enables the analysis of various fiber reconstruction algorithms, of differently parameterized fiber reconstruction algorithms and of individual steps in iterative fiber reconstruction algorithms. Insight into the performance of fiber reconstruction algorithms is obtained by a list‐based ranking interface. A 3D view offers interactive visualization techniques to gain deeper insight, e.g., into the aggregated quality of the examined fiber reconstruction algorithms and parameterizations. The tool was designed in close collaboration with researchers who work with fiber‐reinforced polymers on a daily basis and develop algorithms for tomographic reconstruction and characterization of such materials. We evaluate the tool using synthetic datasets as well as tomograms of real materials. Five case studies certify the usefulness of the tool, showing that it significantly accelerates the analysis and provides valuable insights that make it possible to improve the fiber reconstruction algorithms. The main contribution of the paper is the well‐considered combination of methods and their seamless integration into a visual tool that supports the entire workflow. Further findings result from the analysis of (dis‐)similarity measures for fibers as well as from the discussion of design decisions. It is also shown that the generality of the analytical methods allows a wider range of applications, such as the application in pore space analysis.

In quantitative magnetic resonance mapping, the variable flip angle (VFA) steady state spoiled gradient recalled echo (SPGR) imaging technique is popular as it provides a series of high resolution weighted images in a clinically feasible time. Fast, linear methods that estimate maps from these weighted images have been proposed, such as DESPOT1 and iterative re-weighted linear least squares. More accurate, non-linear least squares (NLLS) estimators are in play, but these are generally much slower and require careful initialization. In this paper, we present NOVIFAST, a novel NLLS-based algorithm specifically tailored to VFA SPGR mapping. By exploiting the particular structure of the SPGR model, a computationally efficient, yet accurate and precise map estimator is derived. Simulation and in vivo human brain experiments demonstrate a twenty-fold speed gain of NOVIFAST compared with conventional gradient-based NLLS estimators while maintaining a high precision and accuracy. Moreover, NOVIFAST is eight times faster than the efficient implementations of the variable projection (VARPRO) method. Furthermore, NOVIFAST is shown to be robust against initialization.

In computed tomography (CT), motion and deformation during the acquisition lead to streak artefacts and blurring in the reconstructed images. To remedy these artefacts, we introduce an efficient algorithm to estimate and correct for global affine deformations directly on the cone beam projections. The proposed technique is data driven and thus removes the need for markers and/or a tracking system. A relationship between affine transformations and the cone beam transform is proved and used to correct the projections. The deformation parameters that describe deformation perpendicular to the projection direction are estimated for each projection by minimizing a plane-based inconsistency criterion. The criterion compares each projection of the main scan with all projections of a fast reference scan, which is acquired prior or posterior to the main scan. Experiments with simulated and experimental data show that the proposed affine deformation estimation method is able to substantially reduce motion artefacts in cone beam CT images.

In quantitative MR T1mapping, the spin-lattice relaxation time T1of tissues is estimated from a series of T1-weighted images. As the T1estimation is a voxel-wise estimation procedure, correct spatial alignment of the T1-weighted images is crucial. Conventionally, the T1-weighted images are first registered based on a general-purpose registration metric, after which the T1map is estimated. However, as demonstrated in this paper, such a two-step approach leads to a bias in the final T1map. In our work, instead of considering motion correction as a preprocessing step, we recover the motion-free T1map using a unified estimation approach. In particular, we propose a unified framework where the motion parameters and the T1map are simultaneously estimated with a Maximum Likelihood (ML) estimator. With our framework, the relaxation model, the motion model as well as the data statistics are jointly incorporated to provide substantially more accurate motion and T1parameter estimates. Experiments with realistic Monte Carlo simulations show that the proposed unified ML framework outperforms the conventional two-step approach as well as state-of-the-art model-based approaches, in terms of both motion and T1map accuracy and mean-square error. Furthermore, the proposed method was additionally validated in a controlled experiment with real T1-weighted data and with two in vivo human brain T1-weighted data sets, showing its applicability in real-life scenarios.

An important factor influencing the quality of magnetic resonance (MR) images is the reconstruction method that is employed, and specifically, the type of prior knowledge that is exploited during reconstruction. In this work, we introduce a new type of prior knowledge, partial discreteness (PD), where a small number of regions in the image are assumed to be homogeneous and can be well represented by a constant magnitude. In particular, we mathematically formalize the partial discreteness property based on a Gaussian Mixture Model (GMM) and derive a partial discreteness image representation that characterizes the salient features of partially discrete images: a constant intensity in homogeneous areas and texture in heterogeneous areas. The partial discreteness representation is then used to construct a novel prior dedicated to the reconstruction of partially discrete MR images. The strength of the proposed prior is demonstrated on various simulated and real k-space data-based experiments with partially discrete images. Results demonstrate that the PD algorithm performs competitively with state-of-the-art reconstruction methods, being flexible and easy to implement.

X-ray computed tomography (CT) is a powerful tool for non-invasive cardiac imaging. However, radiation dose is a major issue. In this paper, we propose an iterative reconstruction method that reduces the radiation dose without compromising image quality. This is achieved by exploiting prior knowledge in two ways: the reconstructed object is assumed to consist of both stationary and dynamic regions over time and the dynamic region is assumed to have sparse structures after a proper sparsifying space-time transform. Experiments on simulation data and a real μCT cardiac mouse dataset show that, with comparable image quality, the radiation dose can be substantially reduced compared to conventional acquisition/reconstruction protocols.

The throughput of an inline computed tomography (CT) based inspection system depends on the speed of its image reconstruction algorithm. Filtered back projection (FBP) provides fast reconstructions, but requires many high quality radiographs from all angles to obtain accurate reconstructions. This is not achievable in an inline environment. Iterative reconstruction methods yield adequate reconstructions from limited, but they are slow. Recently a new reconstruction algorithm was introduced [1] that can handle limited data and is very fast: the neural network FBP (NN-FBP). In this work, we introduce a neural network (NN) based Hilbert transform FBP (NN-hFBP) for inline inspection. This method reconstructs images with a filter-based Hilbert transform FBP method. The filters are application specific and trained by a neural network. Comparison of the NN-hFBP and conventional reconstruction methods applied to inline fan-beam X-ray data of apples shows that the NN-hFBP yields high quality images in a short reconstruction time.

In magnetic resonance imaging the spin-lattice relaxation time (T1) of tissues is estimated from a set of T1-weighted images. As the T1estimation is a voxel-wise estimation, correct alignment of the T1-weighted images is crucial for T1mapping. Therefore, to correct for motion, the T1-weighted images are often registered prior to the T1estimation. This two-step approach, however, does not provide an accurate motion detection due to the high dynamic contrast changes in the series of images. Moreover, interpolation effects during registration, propagate to the T1estimation. In this work, we propose a unified approach, where the motion estimation is integrated into the T1estimation procedure. The motion model parameters and T1parameters are jointly estimated using a Maximum Likelihood (ML) approach. Results on simulation and real data experiments show a substantial improvement in the precision and accuracy of the estimated T1map compared to the conventional two-step approach.

In Magnetic Resonance (MR) image reconstruction, under-sampled data sets lead to ill-posed reconstruction problems. To regularize these problems, prior knowledge is commonly exploited. In this work, we introduce a new type of prior knowledge, partial discreteness, where part of the image is assumed to be homogeneous and can be well represented by a constant magnitude. We propose a novel reconstruction algorithm that incorporates this prior knowledge by iteratively enforcing discreteness through Bayesian segmentation regularization. Results on simulated MR images of breast implants and MR angiography images evidence the benefits of the partial discreteness prior when compared to state-of-the-art reconstruction methods.

The study of fluid flow through solid matter by computed tomography (CT) imaging has many applications, ranging from petroleum and aquifer engineering to biomedical, manufacturing, and environmental research. To avoid motion artifacts, current experiments are often limited to slow fluid flow dynamics. This severely limits the applicability of the technique. In this paper, a new iterative CT reconstruction algorithm for improved a temporal/spatial resolution in the imaging of fluid flow through solid matter is introduced. The proposed algorithm exploits prior knowledge in two ways. First, the time-varying object is assumed to consist of stationary (the solid matter) and dynamic regions (the fluid flow). Second, the attenuation curve of a particular voxel in the dynamic region is modeled by a piecewise constant function over time, which is in accordance with the actual advancing fluid/air boundary. Quantitative and qualitative results on different simulation experiments and a real neutron tomography data set show that, in comparison with the state-of-the-art algorithms, the proposed algorithm allows reconstruction from substantially fewer projections per rotation without image quality loss. Therefore, the temporal resolution can be substantially increased, and thus fluid flow experiments with faster dynamics can be performed.

The proposed Fractional Eigenfaces method is a feature extraction technique for high dimensional data. It is related to Fractional PCA (FPCA), which is based on the theory of fractional covariance matrix, and it is an extension of the classical Eigenfaces. Like FPCA, it computes projections for a low dimensional space from the fractional covariance matrix and similar to the Eigenfaces, it is suited for high dimensional data. Moreover, the proposed technique extends the fractional transformation of the data for more stages of the feature extractions than FPCA. The Fractional Eigenfaces is evaluated in three different face databases. Results show that it achieves a higher accuracy rate than FPCA and Eigenfaces according to the Wilcoxon hypothesis test.

In this paper, we describe a framework for surface registration. The framework consists of a combination of rigid registration, elasticity modulated registration and the use of a shape model prior. The main goal in this paper is to minimize the geometric surface registration error while maintaining correspondences. Experiments show improved geometric fit, correspondence, and timing compared to the current state of the art. Possible applications of the framework are construction of correspondences for shape models, reconstruction of missing parts, and artifact reduction.

This paper proposes the use of the type-2 fuzzy GMM (T2FGMM) framework in order to improve the verification rates of the standard GMM-UBM text-independent speaker verification system in noisy environments. Based on type-2 fuzzy sets, the T2FGMM framework describes GMMs with uncertain parameters and provides likelihood intervals for them. The proposed method (T2F-GMM-UBM) estimates the parameter intervals using the noisy speeches from the speakers and the Bayesian estimation used in the standard GMM-UBM system. The proposed method was evaluated using the MIT Device Speaker Verification Corpus (MITDSVC) which contains speeches from 48 speakers recorded in three different locations: a quiet office, a mildly noisy lobby, and a busy street intersection. The Equal Error Rate (EER) was computed for each speaker and the mean and standard deviation were analyzed. Although the proposed method did not achieve better performance in the office location, significant improvements were achieved in both lobby and street intersection locations. The improvement in the lobby was 14.21% while in the street intersection location was 10.47%. The left tailed paired Rank Sign Wilcox on Test was also performed in both locations and the p-values found were 0.0127 and 0.0230, respectively. The proposed method proved to have better performance in noisy environments compared to the standard GMM-UBM system.

In tomography, slight differences between the geometry of the scanner hardware and the geometric model used in the reconstruction lead to alignment artifacts. To exploit high-resolution detectors used in many applications of tomography, alignment of

In computed tomography (CT), partial volume effects impede accurate segmentation of structures that are small with respect to the pixel size. In this paper, it is shown that for objects consisting of a small number of homogeneous materials, the reconstruction resolution can be substantially increased without altering the acquisition process. A super-resolution reconstruction approach is introduced that is based on discrete tomography, in which prior knowledge about the materials in the object is assumed. Discrete tomography has already been used to create reconstructions from a low number of projection angles, but in this paper, it is demonstrated that it can also be applied to increase the reconstruction resolution. Experiments on simulated and real μCT data of bone and foam structures show that the proposed method indeed leads to significantly improved structure segmentation and quantification compared with what can be achieved from conventional reconstructions.

X-ray computed tomography (CT) is a powerful tool for noninvasive imaging of time-varying objects. In the past, methods have been proposed to reconstruct images from continuously changing objects. For discretely or structurally changing objects, however, such methods fail to reconstruct high quality images, mainly because assumptions about continuity are no longer valid. In this paper, we propose a method to reconstruct structurally changing objects. Starting from the observation that there exist regions within the scanned object that remain unchanged over time, we introduce an iterative optimization routine that can automatically determine these regions and incorporate this knowledge in an algebraic reconstruction method. The proposed algorithm was validated on simulation data and experimental μCT data, illustrating its capability to reconstruct structurally changing objects more accurately in comparison to current techniques.

We present a combined features approach for speaker segmentation task. This approach utilizes different acoustic features extracted from audio stream. The Bayesian Information Criterion (BIC) is used for each acoustic feature as a distance measure to verify the merging of two audio segments. An Artificial Neural Network (ANN) combines the time index from each ?BIC with the highest value, and estimates the change point. In the experiments, a data set containing examples with several speakers is used to compare our approach with the Chen and Gopalakrishnan's window-growing-based approach, using different acoustic features sets. The results show an improvement in both the Miss Detection Rate (MDR) and the False Alarm Rate (FAR) compared to the window-growing-based approach.

This paper proposes the use of a type-2 fuzzy framework in the standard GMM-UBM based text-independent speaker verification systems. Based on type-2 fuzzy sets, the framework provides pertinence intervals for the models. The decision process is obtained using a Support Vectors Machine (SVM) that processes the interval likelihoods. A Voice Activity Detection (VAD) algorithm was also used to discard the parts of the speech signal without voice. The proposed method was tested on the MIT Device Speaker Verification Corpus which contains several different mobile devices used in different environments. The result shows the robustness of the system and the improvements in the verification ratios of the T2F-GMM-UBM compared to the classical GMM-UBM based systems.

This paper presents a motion compensation technique applied in the permutation-based digital video encryption and compression method introduced by Socek et al. The encryption method is based in permutations that can improve the spatial correlation on each video frame, making them more compressible by a spatial encoder. However, the compression performance of this method depends on the temporal correlation between consecutive frames and the algorithm does not provide a way to explore non-trivial temporal correlation properly. Consequently, the compression ratio of an encrypted video is very sensitive to the motion in the scene. Here, we propose a motion compensation method to be applied in both encryption and decryption process. Experiments using the H.264 codec show a significant improvement of the compression performance in high motion video sequences.

Pedestrian detection is a very promising area in computer vision, since it enables interesting and a variety of applications such as car assistance, surveillance systems and robot vision. During the last years, a variety of new techniques were proposed which greatly improved the detection rates. However, the performance of such systems rapidly deteriorates when pedestrians are under occlusion. This paper analyze how the detection rates of HOG, HOG-LBP, and two new combinations, HOG-LTP and HOG-LMEBP, are affected when occlusion area are progressively added to pedestrian images. Using the INRIA dataset, occlusions were synthetically generated by merging different sizes of non-pedestrian images from different directions. We show that detection of pedestrian under occlusion can be improved by simply combining features.

Discrete tomography (DT) is concerned with the tomographic reconstruction of images that consist of only a small number of grey levels. Recently, DART, a practical algorithm was introduced for discrete tomography, which was validated in the domain of X-ray computed and electron tomography. In this paper, DART is introduced for magnetic resonance imaging. Using simulation experiments, it is shown that the proposed MRI-DART algorithm is capable of computing high quality reconstructions from substantially fewer data compared to state-of-the-art MRI reconstruction methods.

Computed tomography (CT) is a technique for noninvasive imaging of physical objects. In the discrete algebraic reconstruction technique (DART), prior knowledge about the material's densities is exploited to obtain high quality reconstructed images from a limited number of its projections. In practice, this prior knowledge is typically not readily available. Here, a fully automatic method, called projection distance minimization DART (PDM-DART), is proposed in which the optimal grey level parameters are adaptively estimated during the reconstruction process. To apply PDM-DART, only the number of different grey levels should be known in advance. Simulation as well as real μCT experiments show that PDM-DART is capable of computing reconstructed images of which the quality is similar to reconstructions computed by conventional DART based on exact prior knowledge, thereby eliminating the need for tedious and error-prone user interaction.

This paper describes a framework for establishing a reference airway tree segmentation, which was used to quantitatively evaluate fifteen different airway tree extraction algorithms in a standardized manner. Because of the sheer difficulty involved in manually constructing a complete reference standard from scratch, we propose to construct the reference using results from all algorithms that are to be evaluated. We start by subdividing each segmented airway tree into its individual branch segments. Each branch segment is then visually scored by trained observers to determine whether or not it is a correctly segmented part of the airway tree. Finally, the reference airway trees are constructed by taking the union of all correctly extracted branch segments. Fifteen airway tree extraction algorithms from different research groups are evaluated on a diverse set of twenty chest computed tomography (CT) scans of subjects ranging from healthy volunteers to patients with severe pathologies, scanned at different sites, with different CT scanner brands, models, and scanning protocols. Three performance measures covering different aspects of segmentation quality were computed for all participating algorithms. Results from the evaluation showed that no single algorithm could extract more than an average of 74% of the total length of all branches in the reference standard, indicating substantial differences between the algorithms. A fusion scheme that obtained superior results is presented, demonstrating that there is complementary information provided by the different algorithms and there is still room for further improvements in airway segmentation algorithms.

In this paper, we present an iterative reconstruction algorithm for discrete tomography, called discrete algebraic reconstruction technique (DART). DART can be applied if the scanned object is known to consist of only a few different compositions, each corresponding to a constant gray value in the reconstruction. Prior knowledge of the gray values for each of the compositions is exploited to steer the current reconstruction towards a reconstruction that contains only these gray values. Based on experiments with both simulated CT data and experimental μCT data, it is shown that DART is capable of computing more accurate reconstructions from a small number of projection images, or from a small angular range, than alternative methods. It is also shown that DART can deal effectively with noisy projection data and that the algorithm is robust with respect to errors in the estimation of the gray values.

In this paper, we present a novel approach to segment dense, homogeneous objects in a tomographic reconstruction (or tomogram). A popular method to extract such objects from a tomogram is global thresholding, in which the threshold value is determined from the image histogram. However, accurate threshold selection is not straightforward, since, due to noise or artefacts in the reconstruction, the histogram does not always contain a clear, separate peak for the dense object. We propose a new threshold estimation approach, segmentation inconsistency minimization, that exploits the available projection data to determine the optimal global threshold. The proposed algorithm was tested on simulation data and on experimental μCT data. The results show that this method results in more accurate segmentations, compared to alternative threshold selection methods.

Statistical shape modeling is an established technique and is used for a variety of tasks in medical image processing, such as image segmentation and analysis. A challenging task in the construction of a shape model is establishing a good correspondence across the set of training shapes. Especially for shapes of cylindrical topology, very little work has been done. This paper describes an automatic method to obtain a correspondence for a set of cylindrical shapes. The method starts from an initial correspondence which is provided by cylindrical parameterization. The quality of the obtained correspondence, measured in terms of the description length, is then improved by deforming the parameterizations using cylindrical b-spline deformations and by optimization of the spatial alignment of the shapes. In order to allow efficient gradient-guided optimization, an analytic expression is provided for the gradient of this quality measure with respect to the parameters of the parameterization deformation and the spatial alignment. A comparison is made between models obtained from the correspondences before and after the optimization. The results show that, in comparison with parameterization-based correspondences, this new method establishes correspondences that generate models with significantly increased performance in terms of reconstruction error, generalization ability, and specificity.

Diffusion kurtosis imaging (DKI) is a new magnetic resonance imaging (MRI) model that describes the non-Gaussian diffusion behavior in tissues. It has recently been shown that DKI parameters, such as the radial or axial kurtosis, are more sensitive to brain physiology changes than the well-known diffusion tensor imaging (DTI) parameters in several white and gray matter structures. In order to estimate either DTI or DKI parameters with maximum precision, the diffusion weighting gradient settings that are applied during the acquisition need to be optimized. Indeed, it has been shown previously that optimizing the set of diffusion weighting gradient settings can have a significant effect on the precision with which DTI parameters can be estimated. In this paper, we focus on the optimization of DKI gradients settings. Commonly, DKI data are acquired using a standard set of diffusion weighting gradients with fixed directions and with regularly spaced gradient strengths. In this paper, we show that such gradient settings are suboptimal with respect to the precision with which DKI parameters can be estimated. Furthermore, the gradient directions and the strengths of the diffusion-weighted MR images are optimized by minimizing the Cramér-Rao lower bound of DKI parameters. The impact of the optimized gradient settings is evaluated, both on simulated as well as experimentally recorded datasets. It is shown that the precision with which the kurtosis parameters can be estimated, increases substantially by optimizing the gradient settings.

Grey value thresholding is a segmentation technique commonly applied to tomographic image reconstructions. Many procedures have been proposed to optimally select the grey value thresholds based on the tomogram data only (e.g., using the image histogram). In this paper, a projection distance minimization (PDM) method is presented that uses the tomographic projection data to determine optimal thresholds. These thresholds are computed by minimizing the distance between the forward projection of the segmented image and the measured projection data. An important contribution of the current paper is the efficient implementation of the forward projection method, which makes the use of the original projection data as a segmentation criterion feasible. Simulation experiments applied to various phantom images show that our proposed method obtains superior results compared to established histogram-based methods.

Functional magnetic resonance imaging (fMRI) data that are corrupted by temporally colored noise are generally preprocessed (i.e., prewhitened or precolored) prior to functional activation detection. In this paper, we propose likelihood-based hypothesis tests that account for colored noise directly within the framework of functional activation detection. Three likelihood-based tests are proposed: the generalized likelihood ratio (GLR) test, the Wald test, and the Rao test. The fMRI time series is modeled as a linear regression model, where one regressor describes the task-related hemodynamic response, one regressor accounts for a constant baseline and one regressor describes potential drift. The temporal correlation structure of the noise is modeled as an autoregressive (AR) model. The order of the AR model is determined from practical null data sets using Akaike's information criterion (with penalty factor 3) as order selection criterion. The tests proposed are based on exact expressions for the likelihood function of the data. Using Monte Carlo simulation experiments, the performance of the proposed tests is evaluated in terms of detection rate and false alarm rate properties and compared to the current general linear model (GLM) test, which estimates the coloring of the noise in a separate step. Results show that theoretical asymptotic distributions of the GLM, GLR, and Wald test statistics cannot be reliably used for computing thresholds for activation detection from finite length time series. Furthermore, it is shown that, for a fixed false alarm rate, the detection rate of the proposed GLR test statistic is slightly, but (statistically) significantly improved compared to that of the common GLM-based tests. Finally, simulations results reveal that all tests considered show seriously inferior performance if the order of the AR model is not chosen sufficiently high to give an adequate description of the correlation structure of the noise, whereas the effects of (slightly) overmodeling are observed to be less harmful.

Discrete tomography (DT) is concerned with the tomographic reconstruction of images that consist of only a small number of gray levels. DT reconstruction problems are usually underdetermined. Therefore, incorporation of heuristic rules to guide the reconstruction algorithm towards an optimal as well as intuitive solution would be valuable. In this paper, we introduce DART: a new, heuristic DT algorithm that is based on an iterative algebraic reconstruction method. Starting from a continuous reconstruction, a discrete image is reconstructed by consistent updating of border pixels. Using simulation experiments, it is shown that the DART algorithm is capable of computing high quality reconstructions from substantially fewer projections than required for conventional continuous tomography.

In this paper, a nonrigid coregistration algorithm based on a viscous fluid model is proposed that has been optimized for diffusion tensor images (DTI), in which image correspondence is measured by the mutual information criterion. Several coregistration strategies are introduced and evaluated both on simulated data and on brain intersubject DTI data. Two tensor reorientation methods have been incorporated and quantitatively evaluated. Simulation as well as experimental results show that the proposed viscous fluid model can provide a high coregistration accuracy, although the tensor reorientation was observed to be highly sensitive to the local deformation field. Nevertheless, this coregistration method has demonstrated to significantly improve spatial alignment compared to affine image matching.

Statistical tests developed for the analysis of (intrinsically complex valued) functional magnetic resonance time series, are generally applied to the data's magnitude components. However, during the past five years, new tests were developed that incorporate the complex nature of fMRI data. In particular, a generalized likelihood ratio test (GLRT) was proposed based on a constant phase model. In this work, we evaluate the sensitivity of GLRTs for complex data to small misspecifications of the phase model by means of simulation experiments. It is argued that, in practical situations, GLRTs based on magnitude data are likely to perform better compared to GLRTs based on complex data in terms of detection rate and constant false alarm rate properties.

A new anisotropic diffusion noise filtering technique is proposed. The technique has two specific features: it is designed for vector-valued images in general and for color images in particular, and it is a multiresolution technique, using wavelet transforms. The vector-valued feature is based on the first fundamental form, which reflects the edge information of a vector-valued image. The multiresolution feature is based on an extension of the first fundamental form towards multiscale fundamental forms. In an experimental section, the proposed technique is evaluated and compared to the single-valued and single-scale versions.

The problem of parameter estimation from Rician distributed data (e.g., magnitude magnetic resonance images) is addressed. The properties of conventional estimation methods are discussed and compared to maximum-likelihood (ML) estimation which is known to yield optimal results asymptotically. In contrast to previously proposed methods, ML estimation is demonstrated to be unbiased for high signal-to-noise ratio (SNR) and to yield physical relevant results for low SNR.

An important issue in the analysis of two-dimensional electrophoresis images is the detection and quantification of protein spots. In this paper we describe a new robust technique to segment and model the different spots present in the gels. For the segmentation a watershed technique is applied. For the quantification of the spots, a new spot model is constructed, based on diffusion principles. Besides the advantage of having a physical interpretation, the model is demonstrated to be superior to the commonly used Gaussian models.