Geodesic Method Research Articles

Groundwater overexploitation and soil subsidence monitoring on Recife plain (Brazil)

The city of Recife, in the northeast of Brazil, is formed by a coastal plain, which is surrounded by several hills, the Atlantic ocean and a number of rivers that cross the city. The plain was formed by fluviomarine sediment, which was produced by marine transgressions and regressions. Its hydrogeological characteristics and geographical position, located slightly above sea level, lead to water-related problems, such as coastal erosion and frequent flooding. In the last 50 years, an increase in the exploitation of groundwater has caused a lowering of the piezometric surface (up to 100 m at certain points). In porous sedimentary aquifers, pumping fluid decreases pore pressure and reduces the support provided by the overlying layers of soil. This reduction in pressure is caused by the lowering of the piezometric surface and leads to soil deformation, usually called subsidence. As a result of the excessive exploitation of groundwater in Recife, and the consequent decrease in groundwater levels, soil subsidence has become a great concern and requires careful investigation. Geodesic methods of monitoring and quantifying the vertical deformation of soil, caused by the removal of groundwater, have been used around the world. The present study describes a method of assessing the occurrence of soil subsidence in an area where excessive exploitation of groundwater has taken place. High-precision geometric leveling was used to quantify the phenomenon and to perform comparative analysis of altitude values from the year 1958 with more recent altitude values (from 2012 and 2015). The experiments confirmed a difference of 3.86 cm for one of the reference levels, located within the subsidence monitoring area. Thus, the leveling analysis provided estimates of a vertical displacement of approximately 0.68 mm/year in this area.

The Tool Path Planning of Composed Surface of Big-twisted Blisk

To solve the problem of the difficulty in tool path planning of big-twisted blisk in five-axis CNC machining, a composed surface processing method was proposed in this paper, taking the blade and flow channel as a whole composed surface to plan the tool path. At first, the tool was feed from the edge of air intake and exhaust respectively, processing along the blade from top to the root, and transiting to flow channel, then to the root of the adjacent blade and coming out from the top in the end, which avoids the problem of tool deformation caused by using long tool in the traditional helix method. The tool path of the composed surface was planned by adopting partition method, which is to divide the composed surface into the blade area and the flow channel area, and planned the tool path respectively. For the blade area, it is divided into the blade body area and the blade edge area. The blade body area adopted iso-parametric method; and since the edge of the blade is thin and the curvature of which changes dramatically, a geodesic distance method was proposed in tool path planning to avoid the abrupt change of tool direction. For the flow channel area, a cross-section method was proposed to connect the tool path of the adjacent blade, ensuring the smooth transition of the tool path and avoiding the problem of the machining area which cannot be completely covered by using geodesic distance method. Finally, based on Rhino software platform a corresponding CNC module was developed in the way of secondary development, and a continuous tool path was generated.

Fast Geodesic Regression for Population-Based Image Analysis.

Geodesic regression on images enables studies of brain development and degeneration, disease progression, and tumor growth. The high-dimensional nature of image data presents significant computational challenges for the current regression approaches and prohibits large scale studies. In this paper, we present a fast geodesic regression method that dramatically decreases the computational cost of the inference procedure while maintaining prediction accuracy. We employ an efficient low dimensional representation of diffeomorphic transformations derived from the image data and characterize the regressed trajectory in the space of diffeomorphisms by its initial conditions, i.e., an initial image template and an initial velocity field computed as a weighted average of pairwise diffeomorphic image registration results. This construction is achieved by using a first-order approximation of pairwise distances between images. We demonstrate the efficiency of our model on a set of 3D brain MRI scans from the OASIS dataset and show that it is dramatically faster than the state-of-the-art regression methods while producing equally good regression results on the large subject cohort.

Haustral loop extraction for CT colonography using geodesics

PurposeThe human colon has complex geometric structures because of its haustral folds, which are thin flat protrusions on the colon wall. The haustral loop is the curve (approximately triangular in shape) that encircles the highly convex region of the haustral fold, and is regarded as the natural landmark of the colon, intersecting the longitude of the colon in the middle. Haustral loop extraction can assist in reducing the structural complexity of the colon, and the loops can also serve as anatomic markers for computed tomographic colonography (CTC). Moreover, haustral loop sectioning of the colon can help with the performance of precise prone–supine registration.MethodsWe propose an accurate approach of extracting haustral loops for CT virtual colonoscopy based on geodesics. First, the longitudinal geodesic (LG) connecting the start and end points is tracked by the geodesic method and the colon is cut along the LG. Second, key points are extracted from the LG, after which paired points that are used for seeking the potential haustral loops are calculated according to the key points. Next, for each paired point, the shortest distance (geodesic line) between the paired points twice is calculated, namely one on the original surface and the other on the cut surface. Then, the two geodesics are combined to form a potential haustral loop. Finally, erroneous and nonstandard potential loops are removed.ResultsTo evaluate the haustral loop extraction algorithm, we first utilized the algorithm to extract the haustral loops. Then, we let the clinicians determine whether the haustral loops were correct and then identify the missing haustral loops. The extraction algorithm successfully detected 91.87% of all of the haustral loops with a very low false positive rate.ConclusionsWe believe that haustral loop extraction may benefit many post-procedures in CTC, such as supine–prone registration, computer-aided diagnosis, and taenia coli extraction.

A minimal-variable symplectic integrator on spheres

We construct a symplectic, globally defined, minimal-coordinate, equivariant integrator on products of 2-spheres. Examples of corresponding Hamiltonian systems, called spin systems, include the reduced free rigid body, the motion of point vortices on a sphere, and the classical Heisenberg spin chain, a spatial discretisation of the Landau-Lifschitz equation. The existence of such an integrator is remarkable, as the sphere is neither a vector space, nor a cotangent bundle, has no global coordinate chart, and its symplectic form is not even exact. Moreover, the formulation of the integrator is very simple, and resembles the geodesic midpoint method, although the latter is not symplectic.

Manifold differential evolution (MDE)

Computing centroidal Voronoi tessellations (CVT) has many applications in computer graphics. The existing methods, such as the Lloyd algorithm and the quasi-Newton solver, are efficient and easy to implement; however, they compute only the local optimal solutions due to the highly non-linear nature of the CVT energy. This paper presents a novel method, called manifold differential evolution (MDE), for computing globally optimal geodesic CVT energy on triangle meshes. Formulating the mutation operator using discrete geodesics, MDE naturally extends the powerful differential evolution framework from Euclidean spaces to manifold domains. Under mild assumptions, we show that MDE has a provable probabilistic convergence to the global optimum. Experiments on a wide range of 3D models show that MDE consistently out-performs the existing methods by producing results with lower energy. Thanks to its intrinsic and global nature, MDE is insensitive to initialization and mesh tessellation. Moreover, it is able to handle multiply-connected Voronoi cells, which are challenging to the existing geodesic CVT methods.

Improved image method for a holographic description of conical defects

The geodesics prescription in holographic approach in Lorentzian signature is valid only for geodesics which connect spacelike-separated points at the boundary, since there are no timelike geodesics which reach the boundary. There is also no straightforward analytic Euclidean continuation for a general background, such as e. g. moving particle in AdS. We propose an improved geodesic image method for two-point Lorentzian correlators which is valid for arbitrary time intervals in case of the bulk spacetime deformed by point particles. We illustrate that our prescription is consistent with the case when the analytic continuation exists and with the quasigeodesics prescription used in previous work. We also discuss some other applications of the improved image method, such as holographic entanglement entropy and multiple particles in AdS3.

Optimal Trajectory Planning of Industrial Robots using Geodesic

<p>This paper intends to propose an optimal trajectory planning technique using geodesic to achieve smooth and accurate trajectory for industrial robots. Geodesic is a distance minimizing curve between any two points on a Riemannian manifold. A Riemannian metric has been assigned to the workspace by combining its position and orientation space together in order to attain geodesic conditions for desired motion of the end-effector. Previously, trajectory has been planned by considering position and orientation separately. However, practically we cannot plan separately because the manipulator joints are interlinked. Here, trajectory is planned by combining position and orientation together. Cartesian trajectories are shown by joint trajectories in which joint variables are treated as local coordinates of position space and orientation space. Then, the obtained geodesic equations for the workspace are evaluated for initial conditions of trajectory and results are plotted. The effectiveness of the geodesic method validated through numerical computations considering a Kawasaki RS06L robot model. The simulation results confirm the accuracy, smoothness and the optimality of the end-effector motion. </p>

Optimization of Zero Forcing Beamformer for the Full Duplex Relay System

In full-duplex (FD) relay networks, the self-interference from its transmit antennas dominates over the signal received from remote sites, and hence, the suppression of self-interference at the relay is crucial in FD relaying operation. Digital domain approaches to the self-interference suppression helps the analog domain ones to achieve a sufficient removal of the interference. In multi-antenna relays, zero-forcing beamformer (ZFBF)-based digital domain approaches are known to be effective for this purpose. Exploiting the geometric geodesic beamforming method, we, in this letter, further improve the ZFBF in FD relay networks. Our proposed method is shown to find an optimal beamformer within the ZFBF class. Simulation results identify conditions in which the proposed optimization scheme add about 1-dB gain over the conventional ZFBF schemes.

Vessel tree extraction using radius-lifted keypoints searching scheme and anisotropic fast marching method

Geodesic methods have been widely applied to image analysis. They are particularly efficient to extract a tubular structure, such as a blood vessel, given its two endpoints in a 2D or 3D medical image. We address here a more difficult problem: the extraction of a full vessel tree structure given a single initial root point, by growing a collection of keypoints or new initial source points, connected by minimal geodesic paths. In this article, those keypoints are iteratively added, using a new detection criteria, which utilize the weighted geodesic distances with respect to a radius-lifted Riemannian metric, the standard Euclidean curve length and a path score. Two main weaknesses of classical keypoints searching approach are that the weighted geodesic distance and the Euclidean path length do not take into account the orientation of the tubular structure or object boundaries, due to the use of an isotropic geodesic Riemannian metric, and suffer from a leakage problem. In contrast, we use an anisotropic geodesic Riemannian metric, and develop new criteria for selecting keypoints based on the path score and automatically stopping the tree growth. Experimental results demonstrate that our method can obtain the expected results, which can extract vessel structures at a finer scale, with increased accuracy.

Supersonic intensity and non-negative intensity for prediction of radiated sound.

Two numerical methods to identify the surface areas of a vibrating structure that radiate sound are presented. The supersonic intensity identifies only the supersonic wave components of the sound field contributing to far-field radiated sound. The supersonic intensity is calculated using a two-dimensional convolution between a spatial radiation filter and the sound field. To compute the spatial radiation filter, the shortest surface distance between two points on the structure is calculated using the geodesic distance method. The non-negative intensity is based on acoustic radiation modes and identifies the radiated sound power from a vibrating structure. Numerical models of a baffled plate, a cylinder and an engine crankcase are presented. The supersonic intensity is shown to be difficult to implement at low frequencies due to the size of the spatial radiation filter and accuracy of the surface distances. A cut-off coefficient associated with the acoustic wavenumber of the spatial radiation filter is used to reduce the aperture error. A comparison of the two intensity-based techniques both in terms of a sound power ratio and the modal assurance criterion is introduced to identify the optimal values of the cut-off coefficients that result in better convergence between the intensity techniques.

Efficient molecular dynamics using geodesic integration and solvent-solute splitting.

We present an approach to Langevin dynamics in the presence of holonomic constraints based on decomposition of the system into components representing geodesic flow, constrained impulse and constrained diffusion. We show that a particular ordering of the components results in an integrator that is an order of magnitude more accurate for configurational averages than existing alternatives. Moreover, by combining the geodesic integration method with a solvent–solute force splitting, we demonstrate that stepsizes of at least 8 fs can be used for solvated biomolecules with high sampling accuracy and without substantially altering diffusion rates, approximately increasing by a factor of two the efficiency of molecular dynamics sampling for such systems. The methods described in this article are easily implemented using the standard apparatus of modern simulation codes.

Comparison of segmentation using fast marching and geodesic active contours methods for bone

Image processing is important in diagnosing diseases or damages of human organs. One of the important stages of image processing is segmentation process. Segmentation is a separation process of the image into regions of certain similar characteristics. It is used to simplify the image to make an analysis easier. The case raised in this study is image segmentation of bones. Bone's image segmentation is a way to get bone dimensions, which is needed in order to make prosthesis that is used to treat broken or cracked bones. Segmentation methods chosen in this study are fast marching and geodesic active contours. This study uses ITK (Insight Segmentation and Registration Toolkit) software. The success of the segmentation was then determined by calculating its accuracy, sensitivity, and specificity. Based on the results, the Active Contours method has slightly higher accuracy and sensitivity values than the fast marching method. As for the value of specificity, fast marching has produced three image results that have higher specificity values compared to those of geodesic active contour's. The result also indicates that both methods have succeeded in performing bone's image segmentation. Overall, geodesic active contours method is quite better than fast marching in segmenting bone images.

Peak‐to‐average power ratio reduction in multiple‐input multiple‐output orthogonal frequency‐division multiple access systems using geodesic descent method

In this study, the authors consider a peak-to-average power ratio (PAPR) reduction for orthogonal frequency-division multiplexing systems based on the decomposition of the set of subcarriers in subsets of subcarriers, denoted resource blocks, each one weighted by a different complex factor. They present a new iterative sphere-geodesic descent method for obtaining these weighting factors so as to minimise the PAPR of the transmitted signals. This method, which they term geodesic descent method, efficiently makes use of the Riemannian structure of the power constraint. The authors’ performance results show that the proposed technique provides good trade-off between the PAPR reduction and the bit error rate performance, for both uncoded and coded scenarios.

Adaptive Complex-Valued Independent Component Analysis Based on Second-Order Statistics

This paper proposes a two-stage fast convergence adaptive complex-valued independent component analysis based on second-order statistics of complex-valued source signals. The first stage constructs a cost function by extending the real-valued whiten cost function to a complex-valued domain and optimizes the cost function using a complex-valued gradient. The second stage uses the restriction that the pseudocovariance matrix of the separated signal is a diagonal matrix to construct the cost function and the geodesic method is used to optimize the cost function. Compared with other adaptive complex-valued independent component analysis, the proposed method shows a faster convergence rate and smaller error. Computer simulations were performed on synthesized signals and communications signals. The simulation results demonstrate the validity of the proposed algorithm.

Localized quench in 1+1 conformal field theory

We study the boundary dual of AdS3 spacetime with a point particle. Particles in AdS3 generate topological defects, which allows to formulate the geodesic image method for boundary correlators. We propose the generalization of the geodesic recipe to arbitrary time intervals in case of the bulk spacetime deformed by a point particle.

A finite dimensional approach to Bramham’s approximation theorem

Using pseudoholomorphic curve techniques from symplectic geometry, Barney Bramham proved recently that every smooth irrational pseudo-rotation of the unit disk is the limit, for the C 0 topology, of a sequence of smooth periodic diffeomorphisms. We give here a finite dimensional proof of this result that works in the case where the pseudo-rotation is smoothly conjugate to a rotation on the boundary circle. The proof extends to C 1 pseudo rotations and is based on the dynamical study of the gradient flow associated to a generating family of functions given by Chaperon’s broken geodesics method.

Single-satellite global positioning system

A new concept of a global positioning support system, based on only one satellite, was offered. Unlike all other GPS and GLONASS satellite systems that are in use, within the offered modification, all metrological support is provided by on-board measurements, which means, that it does not need any ground support of coordinate measurements or orbital characteristics of the satellite system. The cosmic-based angle-measuring instrument measures the arcs lengths between the measured ground-points, that are marked with light beacons, and navigation stars. Each measurement takes approximately 0.04s, with the precision of 1mm in recalculation to ground-relations. Long series of arc measurements between different objects on the ground and in the sky enable the solution of both determination of geodesic coordinates of the measured points and position of the spacecraft during the measuring process by using geodesic equation methods. In addition, it enables the qualification of the geopotential guaranties. The offered scheme will be used for the determination of the frame of selenocentric coordinates during the “Luna-Globe” and “Luna-Resource” missions for precise navigation of landing modules and maybe will be used for precise gridding of the Martian surface.

Extremely low‐frequency surface response caused by underground resource

Electromagnetic (EM) surface responses in the extremely low-frequency (ELF) band caused by possible underground resources are studied. Unlike traditional solutions, the authors apply the geodesic finite-difference time domain method to simulate ELF EM wave propagation in the whole Earth (including the crust)-ionosphere (E-I) system to study these responses. In this way, more rigorous analysis can be achieved by simulating the complex E-I environments, including the inhomogeneous crust and part of the ionosphere. Based on this method, they established a hypothetical model to study the effects of underground objects on received artificial signals. Through simulations, local surface responses and response perturbations caused by underground objects are studied and approximate formulas are obtained for predicting the behaviour of these responses. Finally, potential applications of the method and the results of this work are discussed.

Automated Segmentation and Analysis of Corpus Callosum in Autistic MR Brain Images Using Fuzzy-c-Means-Based Level Set Method

In this work, the segmentation and analysis of the corpus callosum (CC) in autistic MR brain images is carried out using a fuzzy c-means (FCM)-based level set method. Initially, the images are skull-stripped using the geodesic active contour method. The CC is extracted from the skull-stripped images using the FCM-based level set method. FCM clustering forms the initial contour. The evolution of the curve is then regularized using a distance function in the level sets. The segmented CC is divided into five segments, whose areas are measured. The subjective results show that the proposed method is able to extract the CC from skull-stripped images. It is demonstrated that the level set with the FCM as the initial contour gives better results than those obtained with a manual initial contour. It is found that the autistic subjects have a reduced CC area compared to that of control subjects. The total CC area of autistic subjects gives a correlation of R = 0.39 with the verbal intelligence quotient (IQ) values. Further analysis shows that the anterior third region of the CC gives significant discrimination of the control and autistic subjects compared to the other segments. Its correlation (R) with verbal IQ is found to be 0.27 in autistic subjects. The feature area extracted from the CC and its segments are significant, hence the results may be clinically helpful in the mass screening of autistic subjects.