Geometric Projection Research Articles

Blind carrier phase estimation based on geometric projection for the multi-band VLC system

The carrier phase offset induced by the mismatch between the signal subcarrier frequency and arbitrary waveform generator (AWG) reference clock is a key problem for high-speed multi-band visible light communication (VLC) system. In this paper, we propose a blind carrier phase estimation (CPE) algorithm based on geometric projection for multi-band Nyquist pulse amplitude modulation (PAM) system. Compared with traditional CPE algorithms, the proposed method does not contain any feedback loop and the Mth power operation. Therefore, the lower computational complexity and simpler system structure are both achieved. Furthermore, we experimentally validate the proposed CPE algorithm in a three-band PAM-8 VLC system. The measured results show the system performance can be greatly improved. And compared with the Viterbi and Viterbi (V&V) algorithm using training symbols (20% of the total symbol length), the proposed CPE algorithm can slightly outperform. However, the scheme is a blind estimation without any assistant training sequences. Thus higher bandwidth efficiency is achieved.

Modular preprocessing pipelines can reintroduce artifacts into fMRI data.

The preprocessing pipelines typically used in both task and resting-state functional magnetic resonance imaging (rs-fMRI) analysis are modular in nature: They are composed of a number of separate filtering/regression steps, including removal of head motion covariates and band-pass filtering, performed sequentially and in a flexible order. In this article, we illustrate the shortcomings of this approach, as we show how later preprocessing steps can reintroduce artifacts previously removed from the data in prior preprocessing steps. We show that each regression step is a geometric projection of data onto a subspace, and that performing a sequence of projections can move the data into subspaces no longer orthogonal to those previously removed, reintroducing signal related to nuisance covariates. Thus, linear filtering operations are not commutative, and the order in which the preprocessing steps are performed is critical. These issues can arise in practice when any combination of standard preprocessing steps including motion regression, scrubbing, component-based correction, physiological correction, global signal regression, and temporal filtering are performed sequentially. In this work, we focus primarily on rs-fMRI. We illustrate the problem both theoretically and empirically through application to a test-retest rs-fMRI data set, and suggest remedies. These include (a) combining all steps into a single linear filter, or (b) sequential orthogonalization of covariates/linear filters performed in series.

As-Aligned-As-Possible Image Stitching Based on Deviation-Corrected Warping With Global Similarity Constraints

Handling local misalignment caused by the local warp remains a common and challenging task for image stitching. Moreover, the stitched image is prone to appearing ghosting due to the variations of the image viewpoint between images. To solve the problem of local misalignment, we propose a projection deviation-corrected local warping method with a global similarity constraint for image stitching. Recent warps prove that the warp of the local mesh guide image effectively improves the accuracy of image alignment. Geometric projection deviation is well used to accurately correct pixel offsets in image warping. To correct pixel offsets, we first remove the outliers from matching points by using the normal distribution model. The retained matches are more precise and can improve the accuracy of image alignment. Next, we use the local warping model combining local homography and global similarity for image warping. To further address the misalignment problem caused by local warping, we describe the local projection deviation of the local warping model by adopting a three-dimensional mesh interpolation model. Finally, the warped images are blended by a linear smoothing model. Experimental results show that our method outperforms the state-of-the-arts in alignment accuracy, and also provides better visual effects on challenging images.

X-ray three-dimensional imaging based on light field imaging technology

X-ray three-dimensional (3D) imaging technology is a research hotspot in the field of X-ray imaging. However, for some special imaging targets, the imaging mode of the traditional computer tomography (CT) circular trajectory is prone to lack of projection information, and thus affects the quality of CT reconstruction images, which limites the application of CT imaging. Light field imaging technology, in which a microlens array is inserted between the sensor and main lens in a traditional camera, achieves four-dimensional (4D) light field data with sensor during imaging including both the two-dimensional (2D) directional information of the radiance propagation and 2D spatial distribution information of object radiation. Through computer calculation imaging, 3D imaging such as digital refocusing, slice in the depth direction, stereo imaging, and depth estimation is realized. This article focuses on the 3D X-ray imaging based on the theory of light field imaging in visible light. Based on the model of parallel X-ray of synchrotron radiation source, the data of the X-ray light field with many projection views are acquired by rotating the image sample. Then, the light passing through any voxel in the imaging target is acquired by a geometric projection method, and based on integral imaging theory of light field imaging, the gray value of the slice in depth dimension is reconstructed and the depth information of reconstructed target is acquired. The reconstruction results show that this method can be used to reconstruct the internal slices at any depth in any viewing direction of the imaging target. In the optical imaging, the scene beyond the depth of field is blurred, making the scene more prominent and the imaging effect better. However, for the X-ray imaging, the imaging mode that is completely transmissive, and the light passing through the foreground carry the information about the background. In the refocusing process, the object at the refocusing depth is focused, and other background information is defocused. Excessive background information overwhelms the real useful information, and makes the slice, especially the edge of the image, blurred. Consequently more severe background noise is introduced due to the defocusing phenomenon in the optical refocusing process. Referring to the reconstruction method of the X-ray 3D imaging and light field imaging, the S-L filter is applied to the original data in the article. After filtering the original data, the X-ray "light field refocusing" is processed. The reconstruction results shown that the method can effectively eliminate reconstruction artifacts and improve image reconstruction quality in the reconstruction depth slice. And in this paper, the light field data are collected by rotating the sample with low time resolution. For the fast imaging, according to the digital refocusing theory of the light field imaging, the array X-ray source and detector can be used. After being calibrated, the system can realize the 3D reconstruction of the light field of the target field with high time resolution. This research has not only the theoretical significance in algorithm, but also great application value in the rapid detection of more complicated targets such as industry and medical treatment.

Mapping of local lattice parameter ratios by projective Kikuchi pattern matching

We describe a lattice-based crystallographic approximation for the analysis of distorted crystal structures via Electron Backscatter Diffraction (EBSD) in the scanning electron microscope. EBSD patterns are closely linked to local lattice parameter ratios via Kikuchi bands that indicate geometrical lattice plane projections. Based on the transformation properties of points and lines in the real projective plane, we can obtain continuous estimations of the local lattice distortion based on projectively transformed Kikuchi diffraction simulations for a reference structure. By quantitative image matching to a projective transformation model of the lattice distortion in the full solid angle of possible scattering directions, we enforce a crystallographically consistent approximation in the fitting procedure of distorted simulations to the experimentally observed diffraction patterns. As an application example, we map the locally varying tetragonality in martensite grains of steel.

Heat flux analysis of Type-I ELM impact on a sloped, protruding surface in the JET bulk tungsten divertor

Tungsten (W) melting due to transient power loads, for example those delivered by edge localised modes (ELMs), is a major concern for next step fusion devices. A series of experiments has been performed on JET to investigate the dynamics of Type-I ELM-induced transient melting. Following initial exposures in 2013 of a W-lamella with sharp leading edge in the bulk W outer divertor, new experiments have been performed in 2016–2017 on a protruding W-lamella with a 15° slope, allowing direct and spatially resolved (0.85 mm/pixel) observation of the top surface using the IR thermography system viewing from the top of the poloidal cross-section. Thermal and IR analysis have already been conducted assuming the geometrical projection of the parallel heat flux on the W-lamellas, thus ignoring the gyro-radius orbit of plasma particles. Although it is well justified during L-mode or inter-ELM period, the hypothesis becomes questionable during ELM when the ion Larmor radius is larger. The goal of this paper is to extend the previous analysis based on the forward approach to the H-mode discharges and investigate in particular the gyro-radius effect during the Type-I ELMs, those used to achieve transient melting on the slope of the protruding W-lamella. Surface temperatures measured by the IR camera are compared with reconstructed synthetic data from 3D thermal modelling using heat loads derived from optical projection of the parallel heat flux (ignoring the gyro-radius orbit), 2D gyro-radius orbit and particle-in-cell (PIC) simulations describing the influence of finite Larmor-radius effects and electrical potential on the deposited power flux. Results show that the ELM power deposition behaves differently than the optical projection of the parallel heat flux, contrary to the L-mode observations, and may thus be due to the much larger gyro-orbits of the energetic ELM ions in comparison to L-mode or inter-ELM conditions.

Auto-calibration by locally consistent contours for dental CBCT

The image quality of dental cone-beam computed tomography (CBCT) is limited by the accuracy of device calibration. Inaccurate calibration introduces errors in the reconstruction process, which may lead to severe artifacts in the reconstructed volume. Patient motion during scan acquisition induces similar effects. This paper introduces a novel auto-calibration approach calculating geometrical projection parameters from unknown patient geometry. We formulate consistency conditions linking the information of consecutive projection images and a regularization technique to prevent overall distortions. Implemented as a global optimization problem we present an efficient greedy optimizer as well. Our strategy turns out to be robust towards inaccurate initialization. As our method does not rely on consistency between projection data and tomography reconstruction it is robust towards reconstruction artifacts such as e.g. truncation. Applying our approach for auto-calibration shows a relative improvement of sharpness up to of in a standard dental CBCT setup. Evaluation is performed on digital reconstructed radiographs (DRRs) of a CT head-scan. In particular different motion types are considered and the number of anatomical structures used for calibration is varied to achieve an understanding of the behavior of the approach.

Modeling and Simulation of Coordinated Motion of Dual-arm Industrial Robot

Dual-arm industrial robot, Geometric project method, Coordinated movement, Pole-inhole insertion.

On the normalized FRB luminosity function

Thirty-three fast radio bursts (FRBs) had been detected by March 2018. Although the sample size is still limited, meaningful statistical studies can already be carried out. The normalised luminosity function places important constraints on the intrinsic power output, sheds light on the origin(s) of FRBs, and can guide future observations. In this paper, we measure the normalised luminosity function of FRBs. Using Bayesian statistics, we can naturally account for a variety of factors such as receiver noise temperature, bandwidth, and source selection criteria. We can also include astronomical systematics, such as host galaxy dispersion measure, FRB local dispersion measure, galaxy evolution, geometric projection effects, and Galactic halo contribution. Assuming a Schechter luminosity function, we show that the isotropic luminosities of FRBs have a power-law distribution that covers approximately three orders of magnitude, with a power-law index ranging from $-1.8$ to $-1.2$ and a cut off $\sim 2\times 10^{44}\,\rm erg\,s^{-1}$. By using different galaxy models and well-established Bayesian marginalisation techniques, we show that our conclusions are robust against unknowns, such as the electron densities in the Milky Way halo and the FRB environment, host galaxy morphology, and telescope beam response.

A Weak Formulation for Isogeometric Analysis of Vibro-Acoustic Systems with Non-Conforming Interfaces

This paper develops a weak formulation for steady-state dynamic analysis of vibro-acoustic systems in the isogeometric framework. The Non-Uniform Rational B-Splines (NURBS) polynomials are used as basis functions for both geometrical transformation and numerical approximation. Starting from a NURBS-based geometrical projection that transforms a general, complex domain to a regular, spectral domain, an energy-based numerical model is then built, in which NURBS are again used as wholly admissible functions to approximate the structural displacement and the acoustic sound pressure. This process eventually leads to a set of discretized equations, based on which the system’s dynamic properties can be obtained. Besides better accuracy and excellent geometrical adaptivity, the main merit of the proposed method lies in its element-free feature of system modeling, which provides a natural solution for structural-acoustic coupling with non-conforming interfaces. This non-conformity results from either non-matching control points along the boundary or distinct polynomial orders used by adjacent patches, which is inevitable for a vibro-acoustic system given its multi-physics nature. The reliability of the proposed method is validated by a benchmark example. Its accuracy and efficiency are further investigated through a more general, car-like vibro-acoustic system.

Geometric feature descriptor and dissimilarity-based registration of remotely sensed imagery.

Image registration of remotely sensed imagery is challenging, as complex deformations are common. Different deformations, such as affine and homogenous transformation, combined with multimodal data capturing can emerge in the data acquisition process. These effects, when combined, tend to compromise the performance of the currently available registration methods. A new image transform, known as geometric mean projection transform, is introduced in this work. As it is deformation invariant, it can be employed as a feature descriptor, whereby it analyzes the functions of all vertical and horizontal signals in local areas of the image. Moreover, an invariant feature correspondence method is proposed as a point matching algorithm, which incorporates new descriptor’s dissimilarity metric. Considering the image as a signal, the proposed approach utilizes a square Eigenvector correlation (SEC) based on the Eigenvector properties. In our experiments on standard test images sourced from “Featurespace” and “IKONOS” datasets, the proposed method achieved higher average accuracy relative to that obtained from other state of the art image registration techniques. The accuracy of the proposed method was assessed using six standard evaluation metrics. Furthermore, statistical analyses, including t-test and Friedman test, demonstrate that the method developed as a part of this study is superior to the existing methods.

Unsupervised Nonlinear Hyperspectral Unmixing Based on Bilinear Mixture Models via Geometric Projection and Constrained Nonnegative Matrix Factorization

Bilinear mixture model-based methods have recently shown promising capability in nonlinear spectral unmixing. However, relying on the endmembers extracted in advance, their unmixing accuracies decrease, especially when the data is highly mixed. In this paper, a strategy of geometric projection has been provided and combined with constrained nonnegative matrix factorization for unsupervised nonlinear spectral unmixing. According to the characteristics of bilinear mixture models, a set of facets are determined, each of which represents the partial nonlinearity neglecting one endmember. Then, pixels’ barycentric coordinates with respect to every endmember are calculated in several newly constructed simplices using a distance measure. In this way, pixels can be projected into their approximate linear mixture components, which reduces greatly the impact of collinearity. Different from relevant nonlinear unmixing methods in the literature, this procedure effectively facilitates a more accurate estimation of endmembers and abundances in constrained nonnegative matrix factorization. The updated endmembers are further used to reconstruct the facets and get pixels’ new projections. Finally, endmembers, abundances, and pixels’ projections are updated alternately until a satisfactory result is obtained. The superior performance of the proposed algorithm in nonlinear spectral unmixing has been validated through experiments with both synthetic and real hyperspectral data, where traditional and state-of-the-art algorithms are compared.

Vector Representation of Triadic Transformations

This article introduces two vectors intended to formalize some triadic transformations, considering specially the Chromatic Transformational System by David KOPP (2002). The numeric content of vector K describes concisely the processes associated to a given operation that must be applied for transforming a referential perfect triad onto a derived one. Vector G informs the spatial position of an operation considering its geometric projection on a referential two-dimensional plan (a Tonnetz). A practical application concerning analysis by computational means is presented in the last section of the study.

Unsteady aerodynamics of a pitching-flapping-perturbed revolving wing at low Reynolds number

Due to adverse viscous effects, revolving wings suffer universally from low efficiency at low Reynolds number (Re). By reciprocating wing revolving motion, natural flyers flying at low Re successfully exploit unsteady effects to augment force production and efficiency. Here we investigate the aerodynamics of an alternative, i.e., a revolving wing with concomitant unsteady pitching and vertical flapping perturbations (a pitching-flapping-perturbed revolving wing). The current work builds upon a previous study on flapping-perturbed revolving wings (FP-RWs) and focuses on combined effects of pitching-flapping perturbation on force generation and vortex behaviors. The results show that, compared with a FR-RW, pitching motion further (1) reduces the external driving torque for rotating at 0° angle of attack (α0) and (2) enhances lift and leads to a self-rotating equilibrium at α0 = 20°. The power loading of a revolving wing at α0 = 20° can be improved using pitching-flapping perturbations with large pitching amplitude but small Strouhal number. Additionally, an advanced pitching improves the reduction of external driving torque, whereas a delayed pitching weakens both the lift enhancement and the reduction of external driving torque. Further analysis shows that pitching effects can be mainly decomposed into the Leading-Edge-Vortex (LEV)-mediated pressure component and geometric projection component, together they determine the force performance. LEV circulation is found to be determined by the instantaneous effective angle of attack but could be affected asymmetrically between upstroke and downstroke depending on the nominal angle of attack. Pitching-flapping perturbation thus can potentially inspire novel mechanisms to improve the aerodynamic performance of rotary wing micro air vehicles.

RESEARCH ON COORDINATE TRANSFORMATION METHOD OF GB-SAR IMAGE SUPPORTED BY 3D LASER SCANNING TECHNOLOGY

Abstract. In the image plane of GB-SAR, identification of deformation distribution is usually carried out by artificial interpretation. This method requires analysts to have adequate experience of radar imaging and target recognition, otherwise it can easily cause false recognition of deformation target or region. Therefore, it is very meaningful to connect two-dimensional (2D) plane coordinate system with the common three-dimensional (3D) terrain coordinate system. To improve the global accuracy and reliability of the transformation from 2D coordinates of GB-SAR images to local 3D coordinates, and overcome the limitation of traditional similarity transformation parameter estimation method, 3D laser scanning data is used to assist the transformation of GB-SAR image coordinates. A straight line fitting method for calculating horizontal angle was proposed in this paper. After projection into a consistent imaging plane, we can calculate horizontal rotation angle by using the linear characteristics of the structure in radar image and the 3D coordinate system. Aided by external elevation information by 3D laser scanning technology, we completed the matching of point clouds and pixels on the projection plane according to the geometric projection principle of GB-SAR imaging realizing the transformation calculation of GB-SAR image coordinates to local 3D coordinates. Finally, the effectiveness of the method is verified by the GB-SAR deformation monitoring experiment on the high slope of Geheyan dam.

An Image Registration Approach Based on 3D Geometric Projection Similarity of the Human Head

This study aims to develop a novel brain image registration algorithm, the geometry projection similarity (GPS) algorithm, which utilizes the anatomical feature of human head and simplifies the objective function for optimization and search for registration parameters in a step-by-step fashion, largely reducing the solution space and improving the efficiency. The algorithm was tested and compared with existing algorithms in simulation environment and tested on computed tomography/magnetic resonance imaging (CT/MRI) clinical datasets pre- and post-craniotomy surgery. Compared with the maximal mutual information algorithm, the GPS algorithm showed significantly smaller errors (1.2 ± 1.1 vs. 4.5 ± 3.5, 1.0 ± 1.0 vs. 3.5 ± 2.5, 0.8 ± 1.1 vs. 2.8 ± 2.4 pixels, at cluster size of 100, 150 and 200, respectively) and shorter computational durations. Compared with the iterative closest point algorithm, the GPS algorithm showed a greater robustness to the perturbed initial mismatch between registering images (registration failure rate 0 vs. 29 out of 200 trials), while keeping a satisfactorily low registration error (0.71 ± 0.83 pixels). Overall results demonstrated that registration accuracy, efficiency, and robustness of this new algorithm surpass those of existing methods. Pilot test on CT/MRI clinical datasets also showed a satisfactory outcome, demonstrating great potentials for future applications of registration of brain images across modalities.

Possible Photometric Signatures of Moderately Advanced Civilizations: The Clarke Exobelt

Abstract This paper puts forward a possible new indicator of the presence of moderately advanced civilizations on transiting exoplanets. The idea is to examine the region of space around a planet where potential geostationary or geosynchronous satellites would orbit (hereafter, the Clarke exobelt). Civilizations with a high density of devices and/or space junk in that region, but otherwise similar to ours in terms of space technology (our working definition of “moderately advanced”), may leave a noticeable imprint on the light curve of the parent star. The main contribution to such a signature comes from the exobelt edge, where its opacity is maximum due to geometrical projection. Numerical simulations have been conducted for a variety of possible scenarios. In some cases, a Clarke exobelt with a fractional face-on opacity of ∼10−4 would be easily observable with existing instrumentation. Simulations of Clarke exobelts and natural rings are used to quantify how they can be distinguished by their light curves.

A geometric projection method for designing three‐dimensional open lattices with inverse homogenization

The article from this special issue was previously published in International Journal for Numerical Methods in Engineering, Volume 112, Issue 11, 2017. For completeness we are including the title page of the article. The full text of the article can be read in Issue 112:11 on Wiley Online Library: http://onlinelibrary.wiley.com/doi/10.1002/nme.5569/full

Impact of roadway geometric features on crash severity on rural two-lane highways

This study examines the impact of a wide range of roadway geometric features on the severity outcomes of crashes occurred on rural two-lane highways. We argue that crash data have a hierarchical structure which needs to be addressed in modeling procedure. Moreover, most of previous studies ignored the impact of geometric features on crash types when developing crash severity models. We hypothesis that geometric features are more likely to determine crash type, and crash type together with other occupant, environmental and vehicle characteristics determine crash severity outcome. This paper presents an application of multilevel models to successfully capture both hierarchical structure of crash data and indirect impact of geometric features on crash severity. Using data collected in Illinois from 2007 to 2009, multilevel ordered logit model is developed to quantify the impact of geometric features and environmental conditions on crash severity outcome. Analysis results revealed that there is a significant variation in severity outcomes of crashes occurred across segments which verifies the presence of hierarchical structure. Lower risk of severe crashes is found to be associated with the presence of 10-ft lane and/or narrow shoulders, lower roadside hazard rate, higher driveway density, longer barrier length, and shorter barrier offset. The developed multilevel model offers greater consistency with data generating mechanism and can be utilized to evaluate safety effects of geometric design improvement projects.

Pose determination of a blade implant in threedimensions from a single two-dimensional radiograph.

The aim of the study was to introduce a mathematical method to estimate the correct pose of a blade by evaluating the radiographic features obtained from a single two-dimensional image.Blade-form implant bed preparation was performed using the piezosurgery device, and placement was attained with the use of magnetic mallet. The pose determination of the blade was described by means of three consecutive rotations defined by three angles of orientation (triplet φ, θ and ψ). Retrospective analysis on periapical radiographs was performed. This method was used to compare implant (axial length along the marker, i.e. the implant structure) vs angular correction factor (a trigonometric function of the triplet). The accuracy of the method was tested by generating two-dimensional radiographic simulations of the blades, which were then compared with the images of the implants as appearing on the real radiographs. Two patients had to be excluded from further evaluation because the values of the estimated pose angles showed a too-wide range to be effective for a good standardization of serial radiographs: intrapatient range from baseline to 1-year survey was > of a threshold determined by the clinicians (30°). The linear dependence between implant (CF°) and angular correction factor (CF^) was estimated by a robust linear regression, yielding the following coefficients: slope, 0.908; intercept, -0.092; and coefficient of determination, 0.924. The absolute error in accuracy was -0.29 ± 4.35, 0.23 ± 3.81 and 0.64 ± 1.18°, respectively, for the angles φ, θ and ψ. The present theoretical and experimental study established the possibility of determining, a posteriori, a unique triplet of angles (φ, θ and ψ) which described the pose of a blade upon a single two-dimensional radiograph, and of suggesting a method to detect cases in which the standardized geometric projection failed. The angular correction of the bone level yielded results very close to those obtained with an internal marker related to the implant length.