Minimum Number Of Control Points Research Articles

Improvement of FFD parametric approach in the application of a lifting body

AbstractFFD (free-form deformation method) is one of the most commonly used parameterisation methods at present. It places the parameterised objects inside the control volume through coordinate system transformation, and controls the control volume through control points, thus realising the deformation control of its internal objects. Firstly, this paper systematically analyses and compares the characteristics and technical requirements of Bernstein, B-spline and NURBS (non-uniform rational b-splines) basic functions that can be adopted by FFD, and uses the minimum number of control points required to achieve the specified control effect threshold to express the control capability. Aiming at the problem of discontinuity at the right end in the actual calculation of B-spline basis function, a method of adding a small epsilon is proposed to solve it. Then, three basic functions are applied to the FFD parameterisation method, respectively, and the differences are compared from two aspects of the accurate expression of the model and the ability of deformation control. It is found that the BFFD (b-spline free-form deformation) approach owns better comprehensive performance when the control points are distributed correctly. In this paper, the BFFD method is improved, and a p-BFFD (reverse solution points based BFFD) method based on inverse solution is proposed to realise the free distribution of control points under the specified topology. Further, for the lifting body configuration, the control points of the p-BFFD method are brought closer to the airframe forming the EDGE-p-BFFD (edge constraints based p-BFFD) method. For the case in this paper, the proposed EDGE-p-BFFD method not only has fairly high parameterisation accuracy, but also reduces the expression error from 1.01E-3 to 1.25E-4, which is nearly ten times. It can also achieve effective lifting body guideline constraints, and has the ability of local deformation adapting to the configuration characteristics. In terms of the proportion of effective control points, the EDGE-p-BFFD method increases the proportion of effective control points from 36.7% to 50%, and the more control points, the more obvious the proportion increase effect. The new method also has better effect on the continuity of geometric deformation. At the same time, this paper introduces the independent deformation method of the upper and lower surfaces based on the double control body frames, which effectively avoids the deformation coupling problem of the simultaneous change of the upper and lower surfaces caused by the movement of control points in the traditional single control framework.

THE STUDY OF MOBILE LASER SCANNING DATA ADJUSTMENT RESULTS FOR LARGE SCALE TOPOGRAPHIC MAPPING

Abstract. Mobile laser scanning (MLS) data are widely used for solving various tasks. To be sure that these data are appropriate for a specific task it is necessary to adjust data with a certain accuracy. Large scale topographic mapping is one from the tasks often solved by MLS data. Necessary accuracy of creating topographic plans is determined with a requirements document. Topographic plans are always created in a certain coordinate system. For this reason, MLS data should be previously transformed in the required one. For transformation control points measured with other more accurate methods should be applied. The quantity of necessary control points depends on a surveying area. For urban areas a lot of control points are required due to bad quality of GNSS signal. Much research has been conducted for these areas. For areas with open view of the sky it is required significantly fewer control points. Moreover, there are not so many vertical objects in areas with open view of the sky. Large errors can take place in the result of automatic adjustment of point cloud’s multi-passes. The results of both relative and absolute MLS data adjustment are given for the area with a good GNSS signal. The paper presents the results of accuracy estimation with different quantity of control points. The main goal of the paper is to determine the minimum number of control points for MLS data to be appropriate for creating topographic plans at a scale of 1:500 with a contour interval of 0.25 m.

Optimal Excitation Matching Strategy for Sub-Arrayed Phased Linear Arrays Generating Arbitrary-Shaped Beams

The design of phased arrays able to generate arbitrary-shaped beams through a sub-arrayed architecture is addressed here. The synthesis problem is cast in the excitation matching framework, so as to yield clustered phased arrays providing optimal trade-offs between the complexity of the array architecture (i.e., the minimum number of control points at the sub-array level) and the matching of a reference pattern. A synthesis tool based on the k-means algorithm is proposed for jointly optimizing the sub-array configuration and the complex sub-array coefficients. Selected numerical results, including pencil beams with sidelobe notches and asymmetric lobes as well as shaped main lobes, are reported and discussed to highlight the peculiarities of the proposed approach also in comparison with some extensions to complex excitations of state-of-the-art sub-array design methods.

APPROXIMATION ORDER OF C3QUARTIC B-SPLINE APPROXIMATION OF CIRCULAR ARC

In this paper, we present a <TEX>$C^3$</TEX> quartic B-spline approximation of circular arcs. The Hausdorff distance between the <TEX>$C^3$</TEX> quartic B-spline curve and the circular arc is obtained in closed form. Using this error analysis, we show that the approximation order of our approximation method is six. For a given circular arc and error tolerance we find the <TEX>$C^3$</TEX> quartic B-spline curve having the minimum number of control points within the tolerance. The algorithm yielding the <TEX>$C^3$</TEX> quartic B-spline approximation of a circular arc is also presented.

A method for inversion of periodic open boundary conditions in two-dimensional tidal models

For parameter estimation problems, it is of great importance to reduce the number of spatially varying control variables because of the ill-posedness of inverse problem. A new method for the inversion of periodic open boundary conditions in two-dimensional tidal models is developed in this work. In this method, the open boundary curves are generated by linearly interpolating the values at feature points (FPs). The FPs are selected by calculating the second-order derivatives of discrete curves. The advantage is that most of the variations of the curves can be reproduced by the minimum number of control points. The adjoint-based 4DVAR data assimilation method is then applied to simulate the tides in the Bohai, Yellow and East China Seas by optimizing the Fourier coefficients at FPs. The model and the method are calibrated in twin experiments where the prescribed distributions along open boundaries are successfully inverted. The results of twin experiments demonstrate that the effect of inversion is in inverse proportion with the number of FPs which characterizes the complexity of open boundary curves. In order to test the method in practical application, real experiments are performed and the FPs are selected by analyzing the background information from a global tidal model DTU10. During the assimilation, both the data misfit between observations and modeling results and L2 norm of gradients of cost function with respect to control variables have decreased significantly. The relation between the number of control variables and parameter inversion is discussed. It is concluded the method developed in this work will be especially useful and effective when dealing with complex open boundary forcing or applying in highly refined models.

Mapping with MAV: Experimental Study on the Contribution of Absolute and Relative Aerial Position Control

Abstract. This study highlights the benefit of precise aerial position control in the context of mapping using frame-based imagery taken by small UAVs. We execute several flights with a custom Micro Aerial Vehicle (MAV) octocopter over a small calibration field equipped with 90 signalized targets and 25 ground control points. The octocopter carries a consumer grade RGB camera, modified to insure precise GPS time stamping of each exposure, as well as a multi-frequency/constellation GNSS receiver. The GNSS antenna and camera are rigidly mounted together on a one-axis gimbal that allows control of the obliquity of the captured imagery. The presented experiments focus on including absolute and relative aerial control. We confirm practically that both approaches are very effective: the absolute control allows omission of ground control points while the relative requires only a minimum number of control points. Indeed, the latter method represents an attractive alternative in the context of MAVs for two reasons. First, the procedure is somewhat simplified (e.g. the lever-arm between the camera perspective and antenna phase centers does not need to be determined) and, second, its principle allows employing a single-frequency antenna and carrier-phase GNSS receiver. This reduces the cost of the system as well as the payload, which in turn increases the flying time.

Assessment of cartographic potential of EgyptSat-1 satellite image (case study in flat areas)

Egypt has launched its first Earth remote sensing satellite EgyptSat-1 in 2007. A series of evaluations of the usefulness and limitations of EgyptSat-1 images for different applications are required. This research is concerned with the investigation of the geometric and cartographic potential of EgyptSat-1 image in order to know to what scale EgyptSat-1 image is suitable for map production and map updating. The geometrical accuracy of rectification of EgyptSat-1 based on non-parametric rectification (polynomial approach and rubber sheeting) has been evaluated. Four methods of rectification have been compared: different orders of 2D polynomials (first-order polynomial, second-order polynomial, third-order polynomial) and rubber sheeting method. Different sets of ground control points (observed with differential global positioning system) have been tested. Several experiments were performed to rectify EgyptSat-1 image using the four rectification methods. For each method, different numbers of ground control points (GCPs) were used starting at 15 points, and then the number was reduced each time till the minimum number of GCPs for each method is reached and with three different GCP distributions. Various issues such as the solutions, feasibility, accuracy, and requirements for control information are addressed. The results show that rubber sheeting followed by third-order polynomial then second-order polynomial then first-order polynomial gives the best root mean square error. Actually, a serious mapping should be based on a satisfying by the theory justified mathematical model so that rubber sheeting should not be used for a serious mapping even it shows smaller discrepancies, but for the flat test area, an approximate 2D transformation can be accepted. Also although third-order polynomial is accurate in the proximity of GCPs and shows smaller discrepancies compared to the first- and the second-order polynomials, they can lead to significant errors for regions outside the GCP range and should not be used for a serious mapping. One can be considered the best resulted rectified image that obtained from second-order polynomial followed by the first-order polynomial. It was found in our study area that the minimum number of control points for each method gives accuracy better than a pixel. The first-order polynomial and rubber sheeting are good from the economical cost that they use minimum number of control points (three). It was found that the planimetric accuracy of rectified EgyptSat image met the 1:25,000 mapping standard (National Map Accuracy Standards). Also from the assessment of the information content of the EgyptSat image, it was found that it is consistent with the map scale of 1:25,000. In conclusion by analysis of the results, it is obvious that EgyptSat images are able to produce and update map of scale 1:25,000.

NURBS skinning surface for ship hull design based on new parameterization method

Surface reconstruction from sets of cross-sectional data is important in a variety of applications. The problem of generating a ship hull surface from non-regular cross-sectional curves is addressed. Generating non-uniform rational B-splines (NURBS) surfaces that represent cross-sectional curves is a challenge, since the number of control points is growing due to the non-avoidable process of having compatible cross-sectional curves. A new NURBS parameterization method that yields a minimum number of control points, and is adequate in generating a smooth and fair NURBS surface for ship hulls is proposed. This method allows for multiple knots and close domain knots. The results of applying different parameterization methods on the forward perpendicular (FP) region of a ship hull (organized in eight sections) shows that the proposed method reduces the number of control points and generates a smooth and fair NURBS surface, without sacrificing the original object shape of the FP region.

Optimal Geometric Representation of Turbomachinery Cascades Using Nurbs

Simulation-based shape optimization is getting a lot of attention at present. The geometric representation of the shape plays an important role in the optimization process; it affects the number of design variables as well as the smoothness of the final profile. This work is on finding an optimum representation of gas turbine blade profiles in two-dimensions using nonuniform rational B-splines (NURBS). This parameterization involves the solution of an inverse problem for the control points and weights, where the error in the representation is minimized using Simulated Annealing (SA), the latter gives the control points and weights that would approximate a given blade shape with minimum error, yet without loosing its smoothness. The optimum parameterization involves the minimum number of control points, their position and weight for a given error tolerance, and is identified for generic as well as real compressor and turbine blade cascades. The effect of this parameterization on the blades' aerodynamic performance is then discussed.

Camera calibration with genetic algorithms

We present an approach based on genetic algorithms for performing camera calibration. Contrary to the classical nonlinear photogrammetric approach, the proposed technique can correctly find the near-optimal solution without the need of initial guesses (with only very loose parameter bounds) and with a minimum number of control points (7 points). Results from our extensive study using both synthetic and real image data as well as performance comparison with Tsai's procedure (1987) demonstrate the excellent performance of the proposed technique in terms of convergence, accuracy, and robustness.

Registration of physical space to laparoscopic image space for use in minimally invasive hepatic surgery.

While laparoscopes are used for numerous minimally invasive (MI) procedures, MI liver resection and ablative surgery is infrequently performed. The paucity of cases is due to the restriction of the field of view by the laparoscope and the difficulty in determining tumor location and margins under video guidance. By merging MI surgery with interactive, image-guided surgery (IIGS), we hope to overcome localization difficulties present in laparoscopic liver procedures. One key component of any IIGS system is the development of accurate registration techniques to map image space to physical or patient space. This manuscript focuses on the accuracy and analysis of the direct linear transformation (DLT) method to register physical space with laparoscopic image space on both distorted and distortion-corrected video images. Experiments were conducted on a liver-sized plastic phantom affixed with 20 markers at various depths. After localizing the points in both physical and laparoscopic image space, registration accuracy was assessed for different combinations and numbers of control points (n) to determine the quantity necessary to develop a robust registration matrix. For n = 11, average target registration error (TRE) was 0.70 +/- 0.20 mm. We also studied the effects of distortion correction on registration accuracy. For the particular distortion correction method and laparoscope used in our experiments, there was no statistical significance between physical to image registration error for distorted and corrected images. In cases where a minimum number of control points (n = 6) are acquired, the DLT is often not stable and the mathematical process can lead to high TRE values. Mathematical filters developed through the analysis of the DLT were used to prospectively eliminate outlier cases where the TRE was high. For n = 6, prefilter average TRE was 17.4 +/- 153 mm for all trials; when the filters were applied, average TRE decreased to 1.64 +/- 1.10 mm for the remaining trials.

Short antenna spaceborne SAR concepts

This analysis concludes that, for a “swath/azimuth resolution” (SAR) ratio not exceeding 10 4 (as is the case for the missions designed and imagined up until now), it is possible, thanks to new imaging modes based on timing diagram saturation, to reduce the length of the antenna by two (defined along the speed vector) under equivalent performance, antenna area, onboard energy and spectral occupancy conditions. One of the advantages is that the Spotlight mode is not needed except if one wishes to exceed the ratio of 10 4, which gives, in addition to the elimination of the operational limitations of this mode, high cost reduction possibilities with very simplified antenna architectures. These principles are applicable to all types of satellite architectures provided that the rejection of the nadir echo is done other than in the temporal domain, here too saturated. They are especially interesting for the RADAR SAIL case, lowering the costs of the RADAR satellite concept invented by CNES, based on the use of a vertical antenna placed in the orbit plane. On the one hand, they get round the length limitation related to this concept and generalise its utilisation range. On the other hand, the absence of the nadir echo (physically rejected on account of the SAIL concept geometry) enables antenna simplification to be pushed as far as possible without having to preserve a minimum number of control points required for beam nulling toward nadir and, in addition, a single diagram, that of the pencil beam, enables all incidences and modes to be covered, which simplifies the characterisation, calibration and operation of the Radar.

Results from a Precise Photogrammetric Densification of Urban Control Network

Adjustment of a photogrammetric block located in the city of Sudbury, Ontario, demonstrates that an accuracy of 2 cm in planimetric coordinates can be achieved using a minimum number of control points if additional constraints in the form of observed spatial distances are combined with the photogrammetric mathematical model to reduce the control point requirement. This accuracy has been estimated by error ellipsoids of the adjusted ground coordinates, and by independent field checking. The data have also been used to compare different mathematical functions for the compensation of systematic errors in the method of bundle adjustment with self-calibration.