Placement Of Control Points Research Articles

Splines on manifolds: A survey

Splines in the manifold setting have been defined as extensions from the standard Euclidean setting, but they are far more complicated. Alternative approaches, which are equivalent in the Euclidean case, lead to different results in the manifold case; the existence conditions are often quite restrictive; and the necessary computations are rather involved. All difficulties stem from the peculiar nature of the geodesic distance: in general, shortest geodesics may be not unique and the dependence on their endpoints may not be smooth; and distances cannot be computed in closed form. The former issue may impose strong limitations on the placement of control points. While the latter may greatly complicate the computations. Nevertheless, some recent results suggest that splines on surfaces may have practical impact on CAGD applications. We review the literature on this topic, accounting for both theoretical results and practical implementations.

Using existing infrastructure as ground control points to support citizen science coastal UAS monitoring programs

Recent publications have described the ability of citizen scientists to conduct unoccupied aerial system (UAS) flights to collect data for coastal management. Ground control points (GCPs) can be collected to georeference these data, however collecting ground control points require expensive surveying equipment not accessible to citizen scientists. Instead, existing infrastructure can be used as naturally occurring ground control points (NGCPs), although availably of naturally occurring ground control point placement on such infrastructure differs from published best practices of ground control point placement. This study therefore evaluates the achievable accuracy of sites georeferenced with naturally occurring ground control points through an analysis of 20 diverse coastal sites. At most sites naturally occurring ground control points produced horizontal and vertical root mean square errors (RMSE) less than 0.060 m which are similar to those obtained using traditional ground control points. To support future unoccupied aerial system citizen science coastal monitoring programs, an assessment to determine the optimal naturally occurring ground control point quantity and distribution was conducted for six coastal sites. Results revealed that generally at least seven naturally occurring ground control points collected in the broadest distribution across the site will result in a horizontal and vertical root mean square errors less than 0.030 m and 0.075 m respectively. However, the relationship between these placement characteristics and root mean square errors was poor, indicating that georeferencing accuracy using naturally occurring ground control points cannot be optimized solely through ideal quantity and distribution. The results of these studies highlight the value of naturally occurring ground control points to support unoccupied aerial system citizen science coastal monitoring programs, however they also indicate a need for an initial accuracy assessment of sites surveyed with naturally occurring ground control points at the onset of such programs.

Absolute IOP/EOP Estimation Models without Initial Information of Various Smart City Sensors

In smart cities, a large amount of optical camera equipment is deployed and used. Closed-circuit television (CCTV), unmanned aerial vehicles (UAVs), and smartphones are some examples of such equipment. However, additional information about these devices, such as 3D position, orientation information, and principal distance, is not provided. To solve this problem, the structured mobile mapping system point cloud was used in this study to investigate methods of estimating the principal point, position, and orientation of optical sensors without initial given values. The principal distance was calculated using two direct linear transformation (DLT) models and a perspective projection model. Methods for estimating position and orientation were discussed, and their stability was tested using real-world sensors. When the perspective projection model was used, the camera position and orientation were best estimated. The original DLT model had a significant error in the orientation estimation. The correlation between the DLT model parameters was thought to have influenced the estimation result. When the perspective projection model was used, the position and orientation errors were 0.80 m and 2.55°, respectively. However, when using a fixed-wing UAV, the estimated result was not properly produced owing to ground control point placement problems.

PLACEMENT OPTIMIZATION OF THE POINTS OF THE CONDITIONAL REPER NETWORK FOR RAILWAY CURVES

Railway facilities are responsible and complex structures related to the safety ofpassenger traffic and cargo transportation. To ensure the reliability of all systems, the railway trackneeds continual control of its geometric parameters. Railways require high accuracy of survey andmonitoring both at the construction stage and at the operation stage. Such control can be carried outusing control points of the geodetic benchmark network. These control points must be located nearthe railway track to provide it in the design position and in proper working condition. That is whythe development of "own" railways benchmark network is topical.The purpose of this article is to create a mathematical basis for calculating the locations ofown repers near the railway. These benchmarks will be control points that will be used by track-operation stations, track machine stations, engineering and geodetic departments, track-surveyingstations, services and departments, as well as project and construction organizations duringresearch, design, operation, repair, reconstruction, or new construction. This will keep the track ingood condition and be used for leveling the track during repair work. The paper considers thecalculation method for the placement of control points of the conditional benchmark network on thecurved section of the railway. The novelty is the usage of the mean-value theorem of integral calculusto calculate the coordinates of the curve independently of the national geodetic network. The creationof "own" conditional benchmark network allows railways to perform the pegging of lines and curvesregardless of the presence or remoteness of control points of the local or state geodetic network. Afterchoosing a conditional benchmark, the coordinates of the railway curve, which is divided into 5 parts,were calculated. It is shown that the number of points does not affect the accuracy of determining thecoordinates. Thus, fewer rappers can be dispensed, and the speed of the pegging will increase. Thepolar coordinates for the two polar distances from the conventional benchmark have been determined. It is established that the use of the mean-value theorem of the integral calculus to findthe coordinates of a point gives more accurate data, since this method does not involve replacing thearc with a chord. The described method of determining polar coordinates from any point of one'sown network of conditional benchmarks is of practical importance. After deviating the axis of thetrack from the movement of trains, maintenance workers can put it back without additionalcalculation.

A Class of C 2 Interpolating Splines

We present a class of non-polynomial parametric splines that interpolate the given control points and show that some curve types in this class have a set of highly desirable properties that were not previously demonstrated for interpolating curves before. In particular, the formulation of this class guarantees that the resulting curves have C 2 continuity everywhere and local support, such that only four control points define each curve segment between consecutive control points. These properties are achieved directly due to the mathematical formulation used for defining this class, without the need for a global numerical optimization step. We also provide four example spline types within this class. These examples show how guaranteed self-intersection-free curve segments can be achieved, regardless of the placement of control points, which has been a limitation of prior interpolating curve formulations. In addition, they present how perfect circular arcs and linear segments can be formed by splines within this class, which also have been challenging for prior methods of interpolating curves.

Mapping quality prediction for RTK/PPK-equipped micro-drones operating in complex natural environment

Drone mapping with GNSS-assisted photogrammetry is a highly efficient method for surveying small- or medium-sized areas. However, the mapping quality is not intuitively predictable, particularly in complex environments (with steep and cluttered terrain), in which the quality of the real-time kinematic (RTK) or post-processed kinematic (PPK) positioning varies. We present a method to predict the mapping quality from the information that is available prior to the flight, such as the flight plan, expected flight time, approximate digital terrain model, prevailing surface texture, and embedded sensor characteristics. After detailing the important considerations, we also present the concept of global precision within the context of minimal and efficient ground control point placement in a complex terrain. Finally, we validate the proposed methodology by means of rigorous statistical testing against numerous experiments conducted under different mapping conditions.

An Efficient B-Spline-Based Kinodynamic Replanning Framework for Quadrotors

Trajectory replanning for quadrotors is essential to enable fully autonomous flight in unknown environments. Hierarchical motion planning frameworks, which combine path planning with path parameterization, are popular due to their time efficiency. However, the path planning cannot properly deal with nonstatic initial states of the quadrotor, which may result in nonsmooth or even dynamically infeasible trajectories. In this article, we present an efficient kinodynamic replanning framework by exploiting the advantageous properties of the B-spline, which facilitates dealing with the nonstatic state and guarantees safety and dynamical feasibility. Our framework starts with an efficient B-spline-based kinodynamic (EBK) search algorithm, which finds a feasible trajectory with minimum control effort and time. To compensate for the discretization induced by the EBK search, an elastic optimization approach is proposed to refine the control point placement to the optimal location. Systematic comparisons against the state-of-the-art are conducted to validate the performance. Comprehensive onboard experiments using two different vision-based quadrotors are carried out showing the general applicability of the framework.

A new approach to vector scattering: the 3s boundary source method.

This paper describes a novel Boundary Source Method (BSM) applied to the vector calculation of electromagnetic fields from a surface defined by the interface between homogenous, isotropic media. In this way, the reflected and transmitted fields are represented as an expansion of the electric fields generated by a basis of orthogonal electric and magnetic dipole sources that are tangential to, and evenly distributed over the surface of interest. The dipole moments required to generate these fields are then calculated according to the extinction theorem of Ewald and Oseen applied at control points situated at either side of the boundary. It is shown that the sources are essentially vector-equivalent Huygens' wavelets applied at discrete points at the boundary and special attention is given to their placement and the corresponding placement of control points according to the Nyquist sampling criteria. The central result of this paper is that the extinction theorem should be applied at control points situated at a distance d = 3s (where s is the separation of the sources) and consequently we refer to the method as 3sBSM. The method is applied to reflection at a plane dielectric surface and a spherical dielectric sphere and good agreement is demonstrated in comparison with the Fresnel equations and Mie series expansion respectively (even at resonance). We conclude that 3sBSM provides an accurate solution to electromagnetic scattering from a bandlimited surface and efficiently avoids the singular surface integrals and special basis functions proposed by others.

Automated search of control points in surface-based morphometry

Cortical surface-based morphometry is based on a semi-automated analysis of structural MRI images. In FreeSurfer, a widespread tool for surface-based analyses, a visual check of gray-white matter borders is followed by the manual placement of control points to drive the topological correction (editing) of segmented data. A novel algorithm combining radial sampling and machine learning is presented for the automated control point search (ACPS).Four data sets with 3 T MRI structural images were used for ACPS validation, including raw data acquired twice in 36 healthy subjects and both raw and FreeSurfer preprocessed data of 125 healthy subjects from public databases. The unedited data from a subgroup of subjects were submitted to manual control point search and editing. The ACPS algorithm was trained on manual control points and tested on new (unseen) unedited data. Cortical thickness (CT) and fractal dimensionality (FD) were estimated in three data sets by reconstructing surfaces from both unedited and edited data, and the effects of editing were compared between manual and automated editing and versus no editing.The ACPS-based editing improved the surface reconstructions similarly to manual editing. Compared to no editing, ACPS-based and manual editing significantly reduced CT and FD in consistent regions across different data sets. Despite the extra processing of control point driven reconstructions, CT and FD estimates were highly reproducible in almost all cortical regions, albeit some problematic regions (e.g. entorhinal cortex) may benefit from different editing.The use of control points improves the surface reconstruction and the ACPS algorithm can automate their search reducing the burden of manual editing.

Simulation-Based Comparison of Holding Strategies for a Multibranch Light Rail Service

Light rail transit services face many operational challenges, such as capacity constraints, mixed-traffic interference, and branch junctions. The service plans developed for these lines typically specify a precise schedule for each vehicle. Running time and demand variability, special events, and incidents make it challenging to adhere to schedules. Operators can enact real-time control actions to mitigate delays. This research compared the effectiveness of schedule- and headway-based holding strategies applied en route and at terminals (i.e., dispatching) on a simulation model of the Massachusetts Bay Transportation Authority Green Line, a four-branch light rail line. The effects of control point placement at terminals, along branches, along a central trunk, and in combinations of these three were studied, as were the effects of limiting holding at midroute stations. Holding strategies were compared on the basis of service and passenger-oriented performance. Headway-based holding was found to be a more effective method for ensuring that passengers experienced reasonable wait times within scheduled headways. Holding at terminals appeared to be the most beneficial to passengers; additional holding along the branches and limited holding along the trunk were shown to enhance these benefits. Holding only within the trunk of a multibranch service worsened service because of blockages from held trains.

TU‐A‐9A‐01: A Precise Deformable Image Registration System Using Feature‐Based Irregular Meshes

Purpose:To develop a deformable image registration system using irregular meshes generated based on image features. Finer meshes are generated at organ or tissue boundaries so that higher deformation resolution is achieved with limited number of control points.Methods:This deformable image registration system consists of two parts: a finite element modeling system and a GPU‐based registration system. The finite element modeling system is used to generate irregular meshes for the entire body or region of interest without segmentation. This system uses a Laplacian of Gaussion operator to extract features such as boundaries between organs and tissues. The placement of control points (vertices) of meshes is optimized based on feature intensities. The registration framework uses elastic energy as regularity and guarantees the final deformation vector field to be diffeomorphic. This system has been compared with registration algorithms based on regular meshes or voxels (Demons). The comparison is performed on XCAT digital phantom data and patient data.Results:Both XCAT male phantom and female phantom were used. Two respiratory phases were treated as floating and fix images for every phantom. Similarity measures were performed for image intensity and displacement vector field (DVF) for four sets of testing data with three types of deformation algorithms (irregular mesh, regular grid, and voxel). It clearly shows that the voxel‐based Demons algorithm leads to slightly better images. However, the DVF results show that mesh‐based algorithms behave much better. Compared with regular meshes, the irregular mesh we proposed leads to much faster convergence and converge to better results. The calculation is accelerated by GPU cards and a typical registration of patient data could be completed in about 1 minute.Conclusion:The feature‐based irregular meshing method provides a fast and accurate deformable image registration.This research is supported by CPRIT individual investigator award RP110329 and Varian research grant.

Shape and tone depiction for implicit surfaces

We present techniques for rendering implicit surfaces in different pen-and-ink styles. The implicit models are rendered using point-based primitives to depict shape and tone using silhouettes with hidden-line attenuation, drawing directions, and stippling. We present sample renderings obtained for a variety of models. Furthermore, we describe simple and novel methods to control point placement and rendering style. Our approach is implemented using HRBF Implicits, a simple and compact representation, that has three fundamental qualities: a small number of point-normal samples as input for surface reconstruction, good projection of points near the surface, and smoothness of the gradient field. These qualities of HRBF Implicits are used to generate a robust distribution of points to position the drawing primitives.

Heuristic planning techniques applied to forest road profiles

Two heuristic techniques, the genetic algorithm (GA) and Tabu search (TS), both with an embedded linear programming routine for earthwork allocation, were compared to a manually designed forest road profile. The manually designed road length was 345.7m and its average gradient was 14.1%. The best costs of the profiles designed by GA and TS, without changing the placement of control points, were less than that designed manually. The best cost found by GA was almost the same as the global optimum solution. While TS could not find a better solution than GA, it usually found a good solution in less time. It was not possible to search all alternatives by changing the placement of control points and find the global optimum solution within a reasonable time. However, it can be concluded from the results that both GA and TS found good solutions within a reasonable time. Since it is not possible to manually evaluate many alternatives, road designers should find heuristic techniques helpful for design of the road profile. Moreover, the effect of the number of control points on construction costs was examined. The results indicated that increasing the number of control points reduces the construction costs. However, driving safety and comfort might be decreased.

Validation of contour-driven thin-plate splines for tracking fraction-to-fraction changes in anatomy and radiation therapy dose mapping

The goal of this study is to validate a deformable model using contour-driven thin-plate splines for application to radiation therapy dose mapping. Our testing includes a virtual spherical phantom as well as real computed tomography (CT) data from ten prostate cancer patients with radio-opaque markers surgically implanted into the prostate and seminal vesicles. In the spherical mathematical phantom, homologous control points generated automatically given input contour data in CT slice geometry were compared to homologous control point placement using analytical geometry as the ground truth. The dose delivered to specific voxels driven by both sets of homologous control points were compared to determine the accuracy of dose tracking via the deformable model. A 3D analytical spherically symmetric dose distribution with a dose gradient of ∼10% per mm was used for this phantom. This test showed that the uncertainty in calculating the delivered dose to a tissue element depends on slice thickness and the variation in defining homologous landmarks, where dose agreement of 3–4% in high dose gradient regions was achieved. In the patient data, radio-opaque marker positions driven by the thin-plate spline algorithm were compared to the actual marker positions as identified in the CT scans. It is demonstrated that the deformable model is accurate (∼2.5 mm) to within the intra-observer contouring variability. This work shows that the algorithm is appropriate for describing changes in pelvic anatomy and for the dose mapping application with dose gradients characteristic of conformal and intensity modulated radiation therapy.

Tracking the dose distribution in radiation therapy by accounting for variable anatomy

The goal of this research is to calculate the daily and cumulative dose distribution received by the radiotherapy patient while accounting for variable anatomy, by tracking the dose distribution delivered to tissue elements (voxels) that move within the patient. Non-linear image registration techniques (i.e., thin-plate splines) are used along with a conventional treatment planning system to combine the dose distributions computed for each 3D computed tomography (CT) study taken during treatment. For a clinical prostate case, we demonstrate that there are significant localized dose differences due to systematic voxel motion in a single fraction as well as in 15 cumulative fractions. The largest positive dose differences in rectum, bladder and seminal vesicles were 29%, 2% and 24%, respectively, after the first fraction of radiation treatment compared to the planned dose. After 15 cumulative fractions, the largest positive dose differences in rectum, bladder and seminal vesicles were 23%, 32% and 18%, respectively, compared to the planned dose. A sensitivity analysis of control point placement is also presented. This method provides an important understanding of actual delivered doses and has the potential to provide quantitative information to use as a guide for adaptive radiation treatments.

S-plane aerodynamics of nonplanar lifting surfaces

A compressible unsteady panel for predicting generalized force transfer functions for nonplanar lifting surfaces is described. The scheme is suitable for both subsonic and supersonic flow, and is valid everywhere in the complex Laplace s-plane. The effort of constructing the influence coefficient matrix is minimized by using the symmetry and scale properties of the kernel function. Results of steady and unsteady analyses for numerous configurations are compared with a lattice method, a point method, and a hybrid lattice-doublet point method, showing excellent agreement. With a view toward application to rotating ma- chinery, an analysis is given of a circular duct with guide vanes in both steady and unsteady flow. NSTEADY nonplanar lifting surface methods1'3 are routinely used in the aeroelastic analysis of aircraft to obtain the generalized aerodynamic forces resulting from vi- bration and gust loading. Although such methods have a long history, dating to the 1950s4-8 papers on the subject still ap- pear occasionally in literature.9-12 This article describes a scheme with several novel features that has been developed as part of an effort to integrate rotating blades with the rest of the aircraft. Only the nonrotating methodology will be described here; its integration with a rotor analysis will be discussed separately. The notable features are 1) both subsonic and supersonic flows are included; 2) the formulation is valid everywhere in the complex Laplace plane; and 3) the nu- merical overhead of constructing the influence coefficient ma- trix is minimized by taking advantage of the symmetries of the unsteady kernel function. The uniform validity in the s- plane has applications in aeroservoelas tic modeling, and to some extent removes the need for Fade (or other) curve-fitting techniques of analytic continuation from the imaginary axis (or at least allows the use of off-axis data in the curve fit). While both subsonic and supersonic flows are dealt with, any strong nonlinearities, whether of transonic, hypersonic, or high incidence origin, invalidate the model. In the interest of brevity, only subsonic results are presented here. For steady flow, the discretization used reduces to a piece- wise constant load, collocated panel method. This gives rea- sonable smoothness at supersonic speeds and considerable insensitivity to control point placement. However, nonsteady effects are included by a point approximation, thereby re- ducing the computational cost. In this latter aspect, the scheme resembles the doublet point method of Ueda and Dowell.2 However, since the point approximation is applied only to nonsingular quantities, no special care need be exercised near singularities. The basic structure is such that practically any steady panel code could easily be modified for unsteady ef- fects, simply by multiplying the influence coefficients by ap- propriate phase factors. Formulation