Forward Projection Model Research Articles

Deformable motion compensation in interventional cone-beam CT with a context-aware learned autofocus metric.

Interventional Cone-Beam CT (CBCT) offers 3D visualization of soft-tissue and vascular anatomy, enabling 3D guidance of abdominal interventions. However, its long acquisition time makes CBCT susceptible to patient motion. Image-based autofocus offers a suitable platform for compensation of deformable motion in CBCT, but it relies on handcrafted motion metrics based on first-order image properties and that lack awareness of the underlying anatomy. This work proposes a data-driven approach to motion quantification via a learned, context-aware, deformable metric, , that quantifies the amount of motion degradation as well as the realism of the structural anatomical content in the image. The proposed was modeled as a deep convolutional neural network (CNN) trained to recreate a reference-based structural similarity metric-visual information fidelity (VIF). The deep CNN acted on motion-corrupted images, providing an estimation of the spatial VIF map that would be obtained against a motion-free reference, capturing motion distortion, and anatomic plausibility. The deep CNN featured a multi-branch architecture with a high-resolution branch for estimation of voxel-wise VIF on a small volume of interest. A second contextual, low-resolution branch provided features associated to anatomical context for disentanglement of motion effects and anatomical appearance. The deep CNN was trained on paired motion-free and motion-corrupted data obtained with a high-fidelity forward projection model for a protocol involving 120kV and 9.90mGy. The performance of was evaluated via metrics of correlation with ground truth and with the underlying deformable motion field in simulated data with deformable motion fields with amplitude ranging from 5 to 20mm and frequency from 2.4 up to 4 cycles/scan. Robustness to variation in tissue contrast and noise levels was assessed in simulation studies with varying beam energy (90-120kV) and dose (1.19-39.59mGy). Further validation was obtained on experimental studies with a deformable phantom. Final validation was obtained via integration of on an autofocus compensation framework, applied to motion compensation on experimental datasets and evaluated via metric of spatial resolution on soft-tissue boundaries and sharpness of contrast-enhanced vascularity. The magnitude and spatial map of showed consistent and high correlation levels with the ground truth in both simulation and real data, yielding average normalized cross correlation (NCC) values of 0.95 and 0.88, respectively. Similarly, achieved good correlation values with the underlying motion field, with average NCC of 0.90. In experimental phantom studies, properly reflects the change in motion amplitudes and frequencies: voxel-wise averaging of the local across the full reconstructed volume yielded an average value of 0.69 for the case with mild motion (2mm, 12 cycles/scan) and 0.29 for the case with severe motion (12mm, 6 cycles/scan). Autofocus motion compensation using resulted in noticeable mitigation of motion artifacts and improved spatial resolution of soft tissue and high-contrast structures, resulting in reduction of edge spread function width of 8.78% and 9.20%, respectively. Motion compensation also increased the conspicuity of contrast-enhanced vascularity, reflected in an increase of 9.64% in vessel sharpness. The proposed , featuring a novel context-aware architecture, demonstrated its capacity as a reference-free surrogate of structural similarity to quantify motion-induced degradation of image quality and anatomical plausibility of image content. The validation studies showed robust performance across motion patterns, x-ray techniques, and anatomical instances. The proposed anatomy- and context-aware metric poses a powerful alternative to conventional motion estimation metrics, and a step forward for application of deep autofocus motion compensation for guidance in clinical interventional procedures.

Direct voxel classification from x-ray projections for 3D pore detection applied to laser sintered parts

X-ray computed tomography (XCT) is a validated and frequently used tool to verify part geometry and to perform a non-destructive inspection of additive manufacturing parts. However, the acquisition of a large number of x-ray projections generates long inspection times. This conflicts with a high throughput of the production process and hinders the integration of XCT as an in-line quality control procedure for low-end parts. In this paper, we propose a method to obtain three-dimensional (3D) information of the internal pores from a limited view or limited angle scan. The method combines a forward projection model of a cone-beam x-ray system and a deep learning neural network to directly classify each individual voxel, based on the x-ray projections in order to avoid the reconstruction and segmentation step. Accompanying reconstruction artifacts for limited view and limited angle XCT scans are thereby reduced, while preserving 3D information of the pores, defects or inclusions inside the material. The method is validated on real x-ray projections of polymer laser sintered industrial parts and shows a significant reduction in the required x-ray projections, hence acquisition time.

Fully 3D implementation of the end-to-end deep image prior-based PET image reconstruction using block iterative algorithm

Objective. Deep image prior (DIP) has recently attracted attention owing to its unsupervised positron emission tomography (PET) image reconstruction method, which does not require any prior training dataset. In this paper, we present the first attempt to implement an end-to-end DIP-based fully 3D PET image reconstruction method that incorporates a forward-projection model into a loss function. Approach. A practical implementation of a fully 3D PET image reconstruction could not be performed at present because of a graphics processing unit memory limitation. Consequently, we modify the DIP optimization to a block iteration and sequential learning of an ordered sequence of block sinograms. Furthermore, the relative difference penalty (RDP) term is added to the loss function to enhance the quantitative accuracy of the PET image. Main results. We evaluated our proposed method using Monte Carlo simulation with [18F]FDG PET data of a human brain and a preclinical study on monkey-brain [18F]FDG PET data. The proposed method was compared with the maximum-likelihood expectation maximization (EM), maximum a posteriori EM with RDP, and hybrid DIP-based PET reconstruction methods. The simulation results showed that, compared with other algorithms, the proposed method improved the PET image quality by reducing statistical noise and better preserved the contrast of brain structures and inserted tumors. In the preclinical experiment, finer structures and better contrast recovery were obtained with the proposed method. Significance. The results indicated that the proposed method could produce high-quality images without a prior training dataset. Thus, the proposed method could be a key enabling technology for the straightforward and practical implementation of end-to-end DIP-based fully 3D PET image reconstruction.

A machine learning supported sinogram interpolation method for X-ray computed tomography

The time of an X-ray Computed Tomography (XCT) measurement is directly affected by the number of acquired X-ray projections. In general, a large number of X-ray projections, hence a large acquisition time is required to obtain a qualitative reconstruction and successive feature analysis. To expand the applicability of XCT towards low-end parts we propose a novel sinogram interpolation method that incorporates the object rotation. The method combines a forward projection model of the XCT system and a deep learning regression model to generate intermediate X-ray projections for XCT scans with a reduced number of projections. Thereby, the accompanying reconstruction artefacts can be reduced while preserving a lower acquisition time. The method is validated on simulated projections of the 3D Shepp-Logan phantom and simulated projections of real 3D printed components using the ASTRA-toolbox. Within the reconstructions, less streaking artefacts are observed and an increased contrast between different features is obtained without introducing rotational artefacts.

Multi-material blind beam hardening correction in near real-time based on non-linearity adjustment of projections

Beam hardening (BH) is one of the major artifacts that severely reduces the quality of computed tomography (CT) imaging. This BH artifact arises due to the polychromatic nature of the X-ray source and causes cupping and streak artifacts. This work aims to propose a fast and accurate BH correction method that requires no prior knowledge of the materials and corrects first and higher-order BH artifacts. This is achieved by performing a wide sweep of the material based on an experimentally measured look-up table to obtain the closest estimate of the material. Then, the non-linearity effect of the BH is corrected by adding the difference between the estimated monochromatic and the polychromatic simulated projections of the segmented image. The estimated polychromatic projection is accurately derived using the least square estimation (LSE) method by minimizing the difference between the experimental projection and the linear combination of simulated polychromatic projections. As a result, an accurate non-linearity correction term is derived that leads to an accurate BH correction result. The simulated projections in this work are performed using a multi-GPU-accelerated forward projection model which ensures a fast BH correction in near real-time. To evaluate the proposed BH correction method, we have conducted extensive experiments on real-world CT data. It is shown that the proposed method results in images with improved contrast-to-noise ratio (CNR) in comparison to the images corrected from only the scatter artifacts and the BH-corrected images using the state-of-the-art empirical BH correction method.

PET Image Reconstruction Incorporating Deep Image Prior and a Forward Projection Model

Convolutional neural networks (CNNs) have recently achieved remarkable performance in positron emission tomography (PET) image reconstruction. In particular, CNN-based direct PET image reconstruction, which directly generates the reconstructed image from the sinogram, has potential applicability to PET image enhancements because it does not require image reconstruction algorithms, which often produce some artifacts. However, these deep learning-based, direct PET image reconstruction algorithms have the disadvantage that they require a large number of high-quality training datasets. In this study, we propose an unsupervised direct PET image reconstruction method that incorporates a deep image prior framework. Our proposed method incorporates a forward projection model with a loss function to achieve unsupervised direct PET image reconstruction from sinograms. To compare our proposed direct reconstruction method with the filtered back projection (FBP) and maximum likelihood expectation maximization (ML-EM) algorithms, we evaluated using Monte Carlo simulation data of brain [$^{18}$F]FDG PET scans. The results demonstrate that our proposed direct reconstruction quantitatively and qualitatively outperforms the FBP and ML-EM algorithms with respect to peak signal-to-noise ratio and structural similarity index.

Evaluation of Wavelet Kernel-Based PET Image Reconstruction

Positron emission tomography (PET) imaging is used to track biochemical processes in the human body. PET image quality is limited by noise and several methods have been implemented to improve the quality. Kernel-based image reconstruction is among the methods implemented to increase PET image quality and commonly uses a Gaussian kernel to include spatial correlations from image priors into the forward projection model of PET. Unfortunately, the Gaussian kernel tends to smooth details in the reconstructed image. To reduce noise without losing contrast details, a different kernel is needed. Wavelet kernels can be more efficient than the Gaussian kernel in reducing noise while keeping contrast details by better separating signal from noise and thus, it does not over smooth peak values in the final reconstructed images. In this work, we evaluate a wavelet kernel for kernel-based PET image reconstruction. For this goal, a wavelet kernel approach has been tested using simulated brain data, physical phantom data, and patient data. Reconstruction results are presented and discussed in detail comparing the wavelet kernel method with the Gaussian kernel method. Our results suggest that a wavelet kernel performs better in contrast recovery for phantoms and also results in higher signal-to-noise ratio (SNR) for real patient data.

Scattering Correction of CBCT Projections for the Quality Enhanced CT Reconstruction Using an Efficient Monte Carlo Photon Transport Model

In industrial computed tomography, cone beam computed tomography (CBCT) setups are state-of-art because of its capabilities and speed. However, this technique highly suffers from the effect of scatter in comparison to fan beam computed tomography due to the large scanning 2D field of view. CBCT is more preferable to be used since it is considerably faster. In this work a fast Monte Carlo forward projection model based on photon transport has been developed to subtract the scatter from the measured X-ray projections. The ability of this forward model to compute any complex object from CAD models based on meshes polyhedron validate the proposed scatter subtraction algorithm. Depending on the number of photons used, the complexity and the size of the object each X-ray projection is obtained within two minute or less with this model. In addition to the use of the variance reduction techniques for a fast calculation of the scatter, the proposed scatter subtraction algorithm has been further reduced in computation time by the use of smoothing filters, mainly by the use of Savitzky-Golay filter which is a type of a squares polynomial approximation filter, this kind of smoothing plays significant role in the reduction of the computations time.

Impact of the non-negativity constraint in model-based iterative reconstruction from CT data.

Model-based iterative reconstruction is a promising approach to achieve dose reduction without affecting image quality in diagnostic x-ray computed tomography (CT). In the problem formulation, it is common to enforce non-negative values to accommodate the physical non-negativity of x-ray attenuation. Using this a priori information is believed to be beneficial in terms of image quality and convergence speed. However, enforcing non-negativity imposes limitations on the problem formulation and the choice of optimization algorithm. For these reasons, it is critical to understand the value of the non-negativity constraint. In this work, we present an investigation that sheds light on the impact of this constraint. We primarily focus our investigation on the examination of properties of the converged solution. To avoid any possibly confounding bias, the reconstructions are all performed using a provably converging algorithm started from a zero volume. To keep the computational cost manageable, an axial CT scanning geometry with narrow collimation is employed. The investigation is divided into five experimental studies that challenge the non-negativity constraint in various ways, including noise, beam hardening, parametric choices, truncation, and photon starvation. These studies are complemented by a sixth one that examines the effect of using ordered subsets to obtain a satisfactory approximate result within 50 iterations. All studies are based on real data, which come from three phantom scans and one clinical patient scan. The reconstructions with and without the non-negativity constraint are compared in terms of image similarity and convergence speed. In select cases, the image similarity evaluation is augmented with quantitative image quality metrics such as the noise power spectrum and closeness to a known ground truth. For cases with moderate inconsistencies in the data, associated with noise and bone-induced beam hardening, our results show that the non-negativity constraint offers little benefit. By varying the regularization parameters in one of the studies, we observed that sufficient edge-preserving regularization tends to dilute the value of the constraint. For cases with strong data inconsistencies, the results are mixed: the constraint can be both beneficial and deleterious; in either case, however, the difference between using the constraint or not is small relative to the overall level of error in the image. The results with ordered subsets are encouraging in that they show similar observations. In terms of convergence speed, we only observed one major effect, in the study with data truncation; this effect favored the use of the constraint, but had no impact on our ability to obtain the converged solution without constraint. Our results did not highlight the non-negativity constraint as being strongly beneficial for diagnostic CT imaging. Altogether, we thus conclude that in some imaging scenarios, the non-negativity constraint could be disregarded to simplify the optimization problem or to adopt other forward projection models that require complex optimization machinery to be used together with non-negativity.

An iterative reconstruction algorithm for pole figure inversion using total variation regularization

This paper describes a new discrete method for inverting X-ray pole figures to estimate the orientation distribution function (ODF). The method employs the equal-volume `cubochoric' representation for uniform discretization of orientation space, SO(3). The forward-projection model is combined with an anisotropic total variation term to iteratively determine the ODF. The efficacy of the new method is evaluated with both model and experimental data and compared with existing discrete and series expansion methods.

A 3-D Projection Model for X-ray Dark-field Imaging

The X-ray dark-field signal can be measured with a grating-based Talbot-Lau interferometer. It measures small angle scattering of micrometer-sized oriented structures. Interestingly, the signal is a function not only of the material, but also of the relative orientation of the sample, the X-ray beam direction, and the direction of the interferometer sensitivity. This property is very interesting for potential tomographically reconstructing structures below the imaging resolution. However, tomographic reconstruction itself is a substantial challenge. A key step of the reconstruction algorithm is the inversion of a forward projection model. In this work, we propose a very general 3-D projection model. We derive the projection model under the assumption that the observed scatter distribution has a Gaussian shape. We theoretically show the consistency of our model with existing, more constrained 2-D models. Furthermore, we experimentally show the compatibility of our model with simulations and real dark-field measurements. We believe that this 3-D projection model is an important step towards more flexible trajectories and, by extension, dark-field imaging protocols that are much better applicable in practice.

High Temporal-Resolution Dynamic PET Image Reconstruction Using a New Spatiotemporal Kernel Method

Current clinical dynamic PET has an effective temporal resolution of 5-10 seconds, which can be adequate for traditional compartmental modeling but is inadequate for exploiting the benefit of more advanced tracer kinetic modeling for characterization of diseases (e.g., cancer and heart disease). There is a need to improve dynamic PET to allow fine temporal sampling of 1-2 seconds. However, the reconstruction of these short-time frames from tomographic data is extremely challenging as the count level of each frame is very low and high noise presents in both spatial and temporal domains. Previously, the kernel framework has been developed and demonstrated as a statistically efficient approach to utilizing image prior for low-count PET image reconstruction. Nevertheless, the existing kernel methods mainly explore spatial correlations in the data and only have a limited ability in suppressing temporal noise. In this paper, we propose a new kernel method which extends the previous spatial kernel method to the general spatiotemporal domain. The new kernelized model encodes both spatial and temporal correlations obtained from image prior information and are incorporated into the PET forward projection model to improve themaximumlikelihood(ML) image reconstruction. Computer simulations and an application to real patient scan have shown that the proposed approach can achieve effective noise reduction in both spatial and temporal domains and outperform the spatial kernel method and conventional ML reconstruction method for improving the high temporal-resolution dynamic PET imaging.

Depth range accuracy for plenoptic cameras

Plenoptic cameras capture the directional information of the light distribution from a scene. This is accomplished by positioning a microlens array between the main lens and the sensor. This configuration obtains multiple projections for a point in the object space, which allows to retrieve the point’s depth on a single exposure. In recent years, several studies recover depth and shape from the lightfield data using several cues. Nonetheless, references regarding the depth capabilities of a standard plenoptic camera with different zoom and focus settings are scarce. In this work, we formalize a forward projection model and consider projection geometry cues to improve a metric reconstruction methodology for a calibrated standard plenoptic camera. The metric reconstruction methodology is used to evaluate the depth estimation accuracy under certain zoom and focus settings. The reconstruction is applied to new datasets captured for this purpose with objects placed at depths between 0.05 and 2.00 meters. The results indicate that these cameras are able to reconstruct accurately points within the depth range analyzed by appropriately choosing the zoom and focus depth settings. The zoom is a determinant factor on the reconstruction accuracy and the focus depth allows to determine the reconstruction depth range.

The role of off-focus radiation in scatter correction for dedicated cone beam breast CT.

Dedicated cone beam breast CT (CBBCT) suffers from x-ray scatter contamination. We aim to identify the source of the significant difference between the scatter distributions estimated by two recent methods proposed by our group and to investigate its effect on CBBCT image quality. We recently proposed two novel methods of scatter correction for CBBCT, using a library based (LB) technique and a forward projection (FP) model. Despite similar enhancement on CBBCT image qualities, these two methods obtain very different scatter distributions. We hypothesize that the off-focus radiation (OFR) is the contributor and results in nontrivial signals in x-ray projections, which is ignored in the scatter estimation via the LB method. Experiments using a thin wire test tool are designed to study the effect of OFR on CBBCT spatial resolution by measuring the point spread function (PSF) and the modulation transfer function (MTF). A narrow collimator setting is used to suppress the OFR-induced signals. In addition, "PSFs" and "MTFs" are measured on clinical CBBCT images obtained by the LB and FP methods using small calcifications as point sources. The improvement of spatial resolution achieved by suppressing OFR in the wire experiment as well as in the clinical study is quantified by the improvement ratios of PSFs and spatial frequencies at different MTF values. Our hypothesis that OFR causes the imaging difference between the FP and LB methods is verified if these ratios obtained from experimental and clinical data are consistent. In the wire experiment, the results show that suppression of OFR increases the maximum signal of the PSF by about 14% and reduces the full-width-at-half-maximum (FWHM) by about 12.0%. Similar improvement on spatial resolution is achieved by the FP method compared with the LB method in the patient study. The improvement ratios of spatial frequencies at different MTF values without OFR match very well in both studies at a level of around 16%, with an average root-mean-square difference of 0.47%. The results of the wire experiment and the clinical study indicate that the main difference between the LB and FP methods is whether the OFR-induced signals are included after scatter correction. Our study further shows that OFR significantly affects the image spatial resolution of CBBCT, indicating that the visualization of micro-calcifications is susceptible to OFR contamination. Our finding is therefore important in further improvement of diagnostic performance of CBBCT.

X-ray scatter correction for dedicated cone beam breast CT using a forward-projection model.

The quality of dedicated cone-beam breast CT (CBBCT) imaging is fundamentally limited by x-ray scatter contamination due to the large irradiation volume. In this paper, we propose a scatter correction method for CBBCT using a novel forward-projection model with high correction efficacy and reliability. We first coarsely segment the uncorrected, first-pass, reconstructed CBBCT images into binary-object maps and assign the segmented fibroglandular and adipose tissue with the correct attenuation coefficients based on the mean x-ray energy. The modified CBBCT are treated as the prior images toward scatter correction. Primary signals are first estimated via forward projection on the modified CBBCT. To avoid errors caused by inaccurate segmentation, only sparse samples of estimated primary are selected for scatter estimation. A Fourier-Transform based algorithm, herein referred to as local filtration hereafter, is developed to efficiently estimate the global scatter distribution on the detector. The scatter-corrected images are obtained by removing the estimated scatter distribution from measured projection data. We evaluate the method performance on six patients with different breast sizes and shapes representing the general population. The results show that the proposed method effectively reduces the image spatial non-uniformity from 8.27 to 1.91% for coronal views and from 6.50 to 3.00% for sagittal views. The contrast-to-deviation ratio is improved by an average factor of 1.41. Comparisons on the image details reveal that the proposed scatter correction successfully preserves fine structures of fibroglandular tissues that are lost in the segmentation process. We propose a highly practical and efficient scatter correction algorithm for CBBCT via a forward-projection model. The method is attractive in clinical CBBCT imaging as it is readily implementable on a clinical system without modifications in current imaging protocols or system hardware.

Inferential and forward projection modeling to evaluate options for controlling invasive mammals on islands.

Successful pest-mammal eradications from remote islands have resulted in important biodiversity benefits. Near-shore islands can also serve as refuges for native biota but require ongoing effort to maintain low-pest or pest-free status. Three management options are available in the presence of reinvasion risk: (1) control-to-zero density, in which immigration may occur but reinvaders are removed; (2) sustained population suppression (to relatively low numbers); or (3) no action. Biodiversity benefits can result from options one and two. The management challenge is to make evidence-based decisions on the selection of an appropriate objective and to identify a financially feasible control strategy that has a high probability of success. This requires understanding the pest species population dynamics and how it will respond to a range of potential management strategies, each with an associated financial cost. We developed a two-stage modeling approach that consisted of (1) Bayesian inferential modeling to estimate parameters for a model of pest population dynamics and control, and (2)a forward projection model to simulate a range of plausible management scenarios and quantify the probability of obtaining zero density within four years. We applied the model to an ongoing, six-year trapping program to control stoats (Mustela erminea) on Resolution Island, New Zealand. Zero density has not yet been achieved. Results demonstrate that management objectives were impeded by a combination of a highly fecund population, insufficient trap attractiveness, and a substantial proportion of the population that did not enter traps. Immigration is known to occur because the founding population arrived on the island by swimming from the mainland. However, immigration rate during this study was indistinguishable from zero. The forward projection modeling showed that control-to-zero density was feasible but required greater than a two-fold budget increase to intensify the trapping rate relative to population growth. The two-stage modeling provides the foundation for a management program in which broad-scale trials of additional trapping effort or improved trap lures would test model predictions and increase our understanding of system dynamics.

WE‐DE‐207B‐12: Scatter Correction for Dedicated Cone Beam Breast CT Based On a Forward Projection Model

Purpose:The image quality of dedicated cone‐beam breast CT (CBBCT) is fundamentally limited by substantial x‐ray scatter contamination, resulting in cupping artifacts and contrast‐loss in reconstructed images. Such effects obscure the visibility of soft‐tissue lesions and calcifications, which hinders breast cancer detection and diagnosis. In this work, we propose to suppress x‐ray scatter in CBBCT images using a deterministic forward projection model.Method:We first use the 1st‐pass FDK‐reconstructed CBBCT images to segment fibroglandular and adipose tissue. Attenuation coefficients are assigned to the two tissues based on the x‐ray spectrum used for imaging acquisition, and is forward projected to simulate scatter‐free primary projections. We estimate the scatter by subtracting the simulated primary projection from the measured projection, and then the resultant scatter map is further refined by a Fourier‐domain fitting algorithm after discarding untrusted scatter information. The final scatter estimate is subtracted from the measured projection for effective scatter correction. In our implementation, the proposed scatter correction takes 0.5 seconds for each projection. The method was evaluated using the overall image spatial non‐uniformity (SNU) metric and the contrast‐to‐noise ratio (CNR) with 5 clinical datasets of BI‐RADS 4/5 subjects.Results:For the 5 clinical datasets, our method reduced the SNU from 7.79% to 1.68% in coronal view and from 6.71% to 3.20% in sagittal view. The average CNR is improved by a factor of 1.38 in coronal view and 1.26 in sagittal view.Conclusion:The proposed scatter correction approach requires no additional scans or prior images and uses a deterministic model for efficient calculation. Evaluation with clinical datasets demonstrates the feasibility and stability of the method. These features are attractive for clinical CBBCT and make our method distinct from other approaches.Supported partly by NIH R21EB019597, R21CA134128 and R01CA195512.The content is solely the responsibility of the authors and does not necessarily represent the official views of the National Institutes of Health.

Forward projection model of non-central catadioptric cameras with spherical mirrors

SUMMARYNon-central catadioptric vision is widely used in robotics and vision but suffers from the lack of an explicit closed-form forward projection model (FPM) that relates a 3D point with its 2D image. The search for the reflection point where the scene ray is projected is extremely slow and unpractical for real-time applications. Almost all methods thus rely on the assumption of a central projection model, even at the cost of an exact projection.Two recent methods are able to solve this FPM, presenting a quasi-closed form FPM. However, in the special case of spherical mirrors, further enhancements can be made. We compare these two methods for the computation of the FPM and discuss both approaches in terms of practicality and performance. We also derive new expressions for the FPM on spherical mirrors (extremely useful to robotics and graphics) which speed up its computation.

Evaluating the effects of detector angular misalignments on simulated computed tomography data

The quality of dimensional measurements made by industrial X-ray computed tomography (CT) depends on a variety of influence factors in the measurement process. In this paper, the effects of angular misalignments of a flat-panel detector are investigated. First, a forward projection model is applied to evaluate distortions of the radiographic pixel coordinates assigned to X-ray intensities due to various detector rotation angles. Distortion maps are presented for a set of representative detector rotations and the sensitivity of image distortions to each rotation is discussed. It is shown from a simulation study that detector angular misalignments result in systematic errors of the reconstructed volume. The distortion model is inversely applied to generate correction maps that are used to correct the simulated radiographs from a misaligned detector. A new volume is reconstructed from the corrected radiographs and the new deviations are compared to the uncorrected results. The reduction of observed volumetric errors after radiographic correction validates the efficacy of the radiographic distortion model. Additionally, the output of this study can contribute to the development of a geometrical error model for volumetric measurements made by CT.

The effects of grey seal predation and commercial fishing on the recovery of a depleted cod stock

Cod (Gadus morhua) are preyed upon by grey seals (Halichoerus grypus), and there is debate over the impact this has had on the decline of stocks and their prospects for recovery. We analysed a depleted stock to the West of Scotland and show that seal predation rate is consistent with a type II functional response. Forward projections of a model including the functional response under varying levels of fishing and seal population size suggest that stock recovery is possible under current conditions, but there is a modest probability that the stock will decline further in both the short and long term. The potential recovery is fragile and sensitive to relatively small increases in either fishing or seal predation. Forward projection models that exclude the functional response estimate a lower probability of stock decline and may underestimate the risk to the stock. At low stock sizes and high fishing mortality rates, functional response models project slower recovery but the opposite is true at low fishing mortality.