Set Of Control Points Research Articles

Robust Registration of Multispectral Satellite Images Based on Structural and Geometrical Similarity

Accurate registration of multispectral satellite images is a challenging task due to the significant and nonlinear radiometric differences between these data. To address this problem, this letter explores the strategy of geometrical similarity between triplets of feature points, and it is combined with the structural similarity between images in a feature-based image registration framework. The underlying principle is that the structural and geometrical similarities generally preserve across the images being registered. In this feature-based image registration framework, a set of control points (CPs) are first detected. Then, the geometric similarity between triplets of CPs is defined, followed by a ranking operation of these triplets of CPs. The highly ranked triplets are used to estimate a spatial transformation between images. Finally, initial matches obtained by a benchmark registration technique are refined by the estimated transformation. The experimental results demonstrate the great effectiveness of the proposed technique for registering multispectral satellite images.

On the parametrisation of motion kinematics for experimental aerodynamic optimisation

The levels of agility and flight or swimming performance demonstrated by insects, birds, fish, and even some aquatic invertebrates, are often vastly superior to what even the most advanced human-engineered vehicles operating in the same regimes are capable of. Key to this superior locomotion is the animal's manipulation of the generation and shedding of vortices through optimal control of their motion kinematics. Many research efforts related to biological and bio-inspired propulsion focus on understanding the influence of the motion kinematics on the propulsion performance and on optimising the kinematics to improve efficiency or manoeuvrability. One of the first challenges to tackle when conducting a numerical or experimental optimisation of motion kinematics of objects moving through a fluid is the parameterisation of the motion kinematics. In this paper, we present three different approaches to parameterise kinematics, using a set of control points that are connected by a spline interpolation, a finite Fourier series, and a reduced order modal reconstruction based on a proper orthogonal decomposition of a set of random walk trajectories. We compare the results and performance of the different parameterisations for the example of an experimental multi-objective optimisation of the pitching kinematics of a robotic flapping wing device. The optimisation was conducted using a genetic algorithm with the objective to maximise stroke average lift and efficiency. The performance is evaluated with regard to the diversity of the randomly created initial populations, the convergence behaviour of the optimisation, and the final Pareto fronts with their corresponding fitness values.

A parameter identification scheme for the orthotropic Poly6 yield function satisfying the convexity condition

The yield surface is the boundary of the elastic domain of a material and determines, via the normality rule, the direction of plastic deformation. Therefore, an accurate model of the yield surface of a material is crucial for the numerical simulation of its deformation processes. In addition, the yield surface must be convex in order to ensure a one-to-one relationship between the plastic strain rate and a corresponding stress state. In this context, homogeneous polynomial functions, in their most general form, have been shown to have a wide modeling range. However, it is also well known that these functions are not convex by default and hence the material parameters (the polynomial coefficients) must be subject to additional convexity constraints. Here we show that Poly6, the sixth order polynomial, features complete decoupling between pure shear and uniaxial traction. This allows us to devise a simple least squares optimization scheme based on biaxial and uniaxial test data, and an additional set of convexity control points which leads to a fast and explicit identification algorithm (Supporting code at https://github.com/stefanSCS/Poly6).

Adjoint Optimization Method for Head Shape of High- ‎Speed Maglev Train

The head shape of a high-speed maglev train was optimized in this study, based on the adjoint method, ‎and the aerodynamic drag of four optimized train models were simulated and compared using different ‎control point generation methods. The effectiveness of using the adjoint method to develop a ‎compressible model for a maglev train was verified. The results show that the adjoint matrix optimization ‎method can quickly and effectively capture the shape characteristics of the train head that are sensitive to ‎aerodynamic resistance. When the design variables of the head are not defined separately, the grid control ‎point set and surface control point set can be used to carry out the adjoint closed-loop optimization of the ‎train head shape, and the exchange control point generation method can be used to perform closed-loop ‎optimization. The results of a numerical simulation show that the optimized train model reduces ‎aerodynamic resistance by approximately 4.8%‎‎.

Comprehensive vertical accuracy analysis of freely available DEMs for different landscape types of the Rur catchment, Germany

This study evaluates the vertical accuracy of nine freely available digital elevation models (DEMs) with a medium spatial resolution for a typical mid-latitude flat to hilly landscape in the Rur catchment in Germany. All datasets were evaluated with two reference datasets, a 1 m DEM and a highly precise set of elevation control points. The accuracy was evaluated with regard to different slopes, landforms and land use. The results reveal in flat areas an average error of 2–4 m which increases about two to three times in undulated terrain. Areas with dense tree cover show a mean error of 6–10 m. The highest accuracies were achieved by the SRTM DEM, followed by other DEMs that mainly implemented SRTM data. TanDEM-X and Copernicus DEM showed ambivalent results showing a higher ratio of existing errors in the elevation product for vegetation and water areas that prevent a higher overall accuracy of these DEMs.

Silhouette Vectorization by Affine Scale-Space

Silhouettes are building elements of logos, graphic symbols and fonts. These shapes can be designed and exchanged in vector form, but more often they are drawn, printed, scanned, or directly found in digital images. Such raster forms require vectorization to get scale-invariant exchangeable formats. There is a need for a mathematically well-defined and justified shape vectorization process, which also provides a minimal set of control points with geometric meaning. In this paper, we propose a new silhouette vectorization paradigm. It extracts the outline of a 2D shape from a raster binary image and converts it to a combination of cubic Bézier polygons and perfect circles. The proposed method uses the sub-pixel curvature extrema and affine scale-space for silhouette vectorization. By construction, our control points are geometrically stable under affine transformations. The proposed method can also be used as a reliable feature point detector for silhouettes. Compared to state-of-the-art image vectorization software, our algorithm demonstrates a superior reduction in the number of control points while maintaining high accuracy.

Degree Reduction of Q-Bézier Curves via Squirrel Search Algorithm

Q-Bézier curves find extensive applications in shape design owing to their excellent geometric properties and good shape adjustability. In this article, a new method for the multiple-degree reduction of Q-Bézier curves by incorporating the swarm intelligence-based squirrel search algorithm (SSA) is proposed. We formulate the degree reduction as an optimization problem, in which the objective function is defined as the distance between the original curve and the approximate curve. By using the squirrel search algorithm, we search within a reasonable range for the optimal set of control points of the approximate curve to minimize the objective function. As a result, the optimal approximating Q-Bézier curve of lower degree can be found. The feasibility of the method is verified by several examples, which show that the method is easy to implement, and good degree reduction effect can be achieved using it.

Conversion Between Cubic Bezier Curves and Catmull\u2013Rom Splines

Splines are one of the main methods of mathematically representing complicated shapes, which have become the primary technique in the fields of Computer Graphics (CG) and Computer-Aided Geometric Design (CAGD) for modeling complex surfaces. Among all, Bézier and Catmull–Rom splines are the most common in the sub-fields of engineering. In this paper, we focus on conversion between cubic Bézier and Catmull–Rom curve segments, rather than going through their properties. By deriving the conversion equations, we aim at converting the original set of the control points of either of the Catmull–Rom or Bézier cubic curves to a new set of control points, which corresponds to approximately the same shape as the original curve, when considered as the set of the control points of the other curve. Due to providing simple linear transformations of control points, the method is very simple, efficient, and easy to implement, which is further validated in this paper using some numerical and visual examples.

Optimizing the placement of piezoelectric wafers on closed sections using a genetic algorithm – Towards application in structural health monitoring

Sensor network design is essential to efficiently integrate Structural Health Monitoring (SHM) systems in aerospace, automotive, and civil structures. This study describes an optimization model for piezoelectric (PZT) wafer placement on curved structures and closed sections.The proposed approach relied on the transformation of any complex/closed surface regardless of the shape of its cross-section into a flat plate and imposed a set of boundary conditions to account for the wave propagation characteristics. Because the structure was continuous and the wave could propagate in every direction, for simplicity and without sacrificing accuracy, our model assumed that a pair of PZT elements communicated information in the two shortest directions. Thus, the concept of having two paths for each PZT couple was introduced to tackle this multidirectional behavior. The plate was then discretized into a set of control points that represented the structure geometry. The PZT couples covered the control points along the line of sight and in the neighborhood of their direct and indirect paths. The objective function was to maximize the number of covered points while minimizing the number of PZT wafers.The proposed model was solved using a genetic algorithm and was validated on circular and square sections. Sensors were spread on the circumference of the structure rather than mounting them in the form of rings or axial lines. The optimized PZT networks had high coverage that reached 99% in simulations. Notably, the optimized model improved the preliminary solution coverage by 14%. Experimental validation was performed on the circular section (pipe). The results demonstrated the proficiency of the developed model in distributing the PZT wafers on closed sections. The coverage was further evaluated by assessing if damaged areas on the pipe surface could be identified. Artificial damage was accurately located within 18 mm from the actual location. These results demonstrate that our model efficiently distributes PZT wafers on closed structures.

PHOTOGRAMMETRY AND COMPUTED TOMOGRAPHY POINT CLOUD REGISTRATION USING VIRTUAL CONTROL POINTS

Abstract. In this paper we propose a virtual control point based method for the registration of photogrammetry and computed tomography (CT) data. Because of the fundamentally different two data sources, conventional registration methods, such as manual control points registration or 3D local feature-based registration, are not suitable. The registration objective of our application is about 3D reconstructions of gyroscopes, which contain abundant geometric primitives to be fitted in the point clouds. In the first place, photogrammetry and CT scanning are applied, respectively, for 3D reconstructions. Secondly, our workflow implements a segmentation after obtaining the surface point cloud from the complete CT volumetric data. Then geometric primitives are fitted in this point cloud benefitting from the less complex cluster segments. In the next step, intersection operations of the parametrized primitives generates virtual points, which are utilized as control points for the transformation parameters estimation. A random sample consensus (RANSAC) method is applied to find the correspondences of both virtual control point sets using corresponding descriptors and calculates the transformation matrix as an initial alignment for further refining the registration. The workflow is invariant to pose, resolution, completeness and noise within our validation process.

Optimization of placement of piezoelectric wafers based on a hybrid model using pitch-catch and pulse-echo configurations

The development of Structural Health Monitoring (SHM) systems and integration in our structures is a necessity. It has proven to provide a robust and low-cost solution for monitoring structural integrity and can predict the remaining life of our structures. One of the most important aspects of SHM systems is the design and implementation of sensor networks. This study proposes a new hybrid model for optimizing sensor placement on convex and non-convex structures. We propose a novel framework in which two detection mechanisms are considered: pitch-catch and pulse-echo to provide coverage for a given surface. These two mechanisms will complement each other to minimize the number of sensors used while maintaining a high coverage. This combination also allows for better coverage of the corners and regions in the proximity of geometrical discontinuity (such as holes and openings). The monitored area is discretized into a set of control points. For a control point to be covered, it should satisfy the user-defined coverage level which is the number of sensing paths crossing that point. These sensing paths are provided by two modes of communications (pitch-catch and pulse-echo) between the actuator-sensor pairs. The model, which is solved using a genetic algorithm (GA), provides flexibility by allowing the user to input different parameters such as the attenuation distance of the propagating waves and the sensing path limits of both coverage configurations that can be determined through experimentation. The efficiency of the proposed model is then demonstrated by simulating different geometrical shapes. Significant improvement in the coverage of the monitored area, reaching 34.6%, was achieved when compared to the coverage provided by some preliminary solutions such as uniformly placing the sensors on the plate under study. Also, the advantage of combining both configurations (pitch-catch and pulse-echo) in the same model was investigated. It was shown that the latter highly impacted the coverage in the blind zones (corners and edges) where a single configuration is not effective. Afterward, experimental validation was carried out to evaluate the model’s accuracy in damage localization within the optimized sensor networks. The results demonstrated the proficiency of the model developed in distributing the sensors on the tested specimens.

Sensitivity Analysis of Quality of B-spline Parameterization on Isogeometric Analysis

Isogeometric analysis (IGA) is a mesh free technique which make use of B-spline basis functions for geometry and field variable representation. Parameterization of B-spline for IGA is the counterpart of meshing as in finite element method (FEM). The objective of parameterization is to find the optimum set of control points for B-spline modelling. The position of control points of a B-spline model has huge effect on IGA results. In this work, the effect of B-spline parameterization on IGA result is presented. One dimensional case of bar with self-weight is solved and compared with exact analytical solution. First fundamental matrix is used as evaluation metric to check the quality of parameterization for 2-D domains. A heat conduction problem of a square domain is presented to study the parameterization effect for 2-D case.

Conditions for injectivity of toric volumes with arbitrary positive weights

Parameterizations, which map parametric domains into certain domains, are widely used in computer aided design, computer aided geometric design, computer graphics, isogeometric analysis, and related fields. The parameterizations of curves, surfaces, and volumes are injective means that they do not have self-intersections. A 3D toric volume is defined via a set of 3D control points with weights that correspond to a set of finite 3D lattice points. Rational tensor product or tetrahedral Bézier volumes are special cases of toric volumes. In this paper, we proved that a toric volume is injective for any positive weights if and only if the lattice points set and control points set are compatible. An algorithm is also presented for checking the compatibility of the two sets by the mixed product of three vectors. Some examples illustrate the effectiveness of the proposed method. Moreover, we improve the algorithm based on the properties and results of clean and empty tetrahedrons in combinatorics.

A Multilane Tracking Algorithm Using IPDA with Intensity Feature.

Detection of multiple lane markings on road surfaces is an important aspect of autonomous vehicles. Although a number of approaches have been proposed to detect lanes, detecting multiple lane markings, particularly across a large number of frames and under varying lighting conditions, in a consistent manner is still a challenging problem. In this paper, we propose a novel approach for detecting multiple lanes across a large number of frames and under various lighting conditions. Instead of resorting to the conventional approach of processing each frame to detect lanes, we treat the overall problem as a multitarget tracking problem across space and time using the integrated probabilistic data association filter (IPDAF) as our basis filter. We use the intensity of the pixels as an augmented feature to correctly group multiple lane markings using the Hough transform. By representing these extracted lane markings as splines, we then identify a set of control points, which becomes a set of targets to be tracked over a period of time, and thus across a large number of frames. We evaluate our approach on two different fronts, covering both model- and machine-learning-based approaches, using two different datasets, namely the Caltech and TuSimple lane detection datasets, respectively. When tested against model-based approach, the proposed approach can offer as much as , , and improvements on the true positive, false positive, and false positives per frame rates compared to the best alternative approach, respectively. When compared against a state-of-the-art machine learning technique, particularly against a supervised learning method, the proposed approach offers , , , and improvements on the false positive, false negative, accuracy, and frame rates. Furthemore, the proposed approach retains the explainability, or in other words, the cause of actions of the proposed approach can easily be understood or explained.

A Bio-inspired trajectory planning method for robotic manipulators based on improved bacteria foraging optimization algorithm and tau theory.

In this paper, a novel bio-inspired trajectory planning method is proposed for robotic systems based on an improved bacteria foraging optimization algorithm (IBFOA) and an improved intrinsic Tau jerk (named Tau-J*) guidance strategy. Besides, the adaptive factor and elite-preservation strategy are employed to facilitate the IBFOA, and an improved Tau-J* with higher-order of intrinsic guidance movement is used to avoid the nonzero initial and final jerk, so as to overcome the computational burden and unsmooth trajectory problems existing in the optimization algorithm and traditional interpolation algorithm. The IBFOA is utilized to determine a small set of optimal control points, and Tau-J* is then invoked to generate smooth trajectories between the control points. Finally, the results of simulation tests demonstrate the eminent stability, optimality, and rapidity capability of the proposed bio-inspired trajectory planning method.

Active Subdivision Surfaces for the Semiautomatic Segmentation of Biomedical Volumes.

We present a new family of active surfaces for the semiautomatic segmentation of volumetric objects in 3D biomedical images. We represent our deformable model by a subdivision surface encoded by a small set of control points and generated through a geometric refinement process. The subdivision operator confers important properties to the surface such as smoothness, reproduction of desirable shapes and interpolation of the control points. We deform the subdivision surface through the minimization of suitable gradient-based and region-based energy terms that we have designed for that purpose. In addition, we provide an easy way to combine these energies with convolutional neural networks. Our active subdivision surface satisfies the property of multiresolution, which allows us to adopt a coarse-to-fine optimization strategy. This speeds up the computations and decreases its dependence on initialization compared to singleresolution active surfaces. Performance evaluations on both synthetic and real biomedical data show that our active subdivision surface is robust in the presence of noise and outperforms current state-of-the-art methods. In addition, we provide a software that gives full control over the active subdivision surface via an intuitive manipulation of the control points.

ГЕОДЕЗІЯ, КАРТОГРАФІЯ І АЕРОФОТОЗНІМАННЯ

Aim. Determination of the elements of external spatial orientation of the surveying systems at the moment of image acquisition is the fundamental task in photogrammetry. Principally, this problem is solving in two ways. The first way is direct positioning and measuring of directions of camera optical axis in the geodetic space with the help of GNSS/INS equipment. The second way is the analytical solution of the problem using a set of reference information (often such information is a set of ground control points whose geodetic positions are known with sufficient accuracy and which are reliably recognised on aerial images of the photogrammetric block). The authors consider the task of providing reference and control information using the second approach, which has a number of advantages in terms of reliability and accuracy of determining the unknown image exterior orientation parameters. It is proposed to obtain additional images of ground control points by the method of their auxiliary aerial photography using an unmanned aerial vehicle (UAV) on a larger scale compared to the scale of the images of the photogrammetric block. The aim of the presented work is the implementation of the method of creating reference points and experimental confirmation of its effectiveness for photogrammetric processing. Methods and results. For the entire realization of the potential of the analytical way to determine the elements of external orientation of images, it is necessary to have a certain number of ground control points (GCP) and to keep the defined scheme of their location on the photogrammetric block. As the main source of input data authors use UAV aerial images of the terrain, which are obtained separately from the block of aerial survey, and have a better geometric resolution and which clearly depict the control reference points. Application of such auxiliary images gives the possibility of automated transferring of the position of ground control point into images of the main photogrammetric block. In our interpretation, these images of ground control points and their surroundings on the ground are called "control reference images". The basis of the work is to develop a method for obtaining the auxiliary control reference images and transferring of position of GCP depicted on them into aerial or space images of terrain by means of computer stereo matching. To achieve this goal, we have developed a processing method for the creation of control reference images of aerial image or a series of auxiliary multi-scale aerial images obtained by a drone from different heights above the reference point. The operator identifies and measures the GCP once on the auxiliary aerial image of the highest resolution. Then there is an automatic stereo matching of the control reference image in the whole series of auxiliary images in succession with a decrease in the resolution and, ultimately, directly with the aerial images of photogrammetric block. On this stage there are no recognition/cursor targeting by the human operator, and therefore there are no discrepancies, errors or mistakes related to it. In addition, if to apply fairly large size of control reference images, the proposed method can be used on a low-texture terrain, and therefore deal in many cases without the physical marking of points measured by GNSS method. And this is a way to simplify and reduce the cost of photogrammetric technology. The action of the developed method has been verified experimentally to provide the control reference information of the block of archival aerial images of the low-texture terrain. The results of the experimental approbation of the proposed method give grounds to assert that the method makes it possible to perform geodetic reference of photogrammetric projects more efficiently due to the refusal of the physical marking of the area before aerial survey. The proposed method can also be used to obtain the information for checking the quality of photogrammetric survey for provision of check points. The authors argue that the use of additional equipment - UAV of semi-professional class to obtain control reference images is economically feasible. Scientific novelty and practical relevance. The results of approbation of the "control reference image" method with obtaining stereo pairs of aerial images with vertical placement of the base are presented for the first time. There was implemented the study of the properties of such stereo pairs of aerial images to obtain images of reference points. The effectiveness of including reference images in the main block of the digital aerial triangulation network created on UAV’s images is shown.

A Method to Use Kriging With Large Sets of Control Points to Morph Finite Element Models of the Human Body.

As developing finite element (FE) human body models for automotive impact is a time-consuming process, morphing using interpolation methods such as kriging has often been used to rapidly generate models of different shapes and sizes. Kriging can be computationally expensive when many control points (CPs) are used, i.e., for very detailed target geometry (e.g., shape of bones and skin). It can also lead to element quality issues (up to inverted elements) preventing the use of the morphed models for finite element simulation. This paper presents a workflow combining iterative subsampling and spatial subdivision methodology that effectively reduces the computational costs and allows for the generation of usable models through kriging with hundreds of thousands of control points. As subdivision introduces discontinuities in the interpolation function that can cause distortion of elements on the boundaries of individual subdivision areas, algorithms for smoothing the interpolation over those boundaries are proposed and compared. Those techniques and their combinations were tested and evaluated in a scenario of mass change on the detailed 50th percentile male model of the global human body models consortium (GHBMC): the model, which has body mass index (BMI) 25.34, was morphed toward a statistical surface model of a person with body mass index 20, 22.7 and 35. 234 777 control points were used to successfully morph the model in less than 15 min on an office PC. Open source implementation is provided.

A Phase-Congruency-Based Scene Abstraction Approach for 2D-3D Registration of Aerial Optical and LiDAR Images

Registration of aerial images to enrich 3-D light detection and ranging (LiDAR) points with radiometric information can enhance the capability of object detection, scene classification, and semantic segmentation. However, airborne LiDAR data may not always come with on-board optical images collected during the same flight mission. Indirect georeferencing can be adopted, if ancillary imagery data are found available. Nevertheless, automatic recognition of control primitives in LiDAR and imagery datasets becomes challenging, especially when they are collected on different dates. This article proposes a generic registration mechanism based on using the phase congruency (PC) model and scene abstraction to overcome the stated challenges. The approach relies on the use of a PC measure to compute the image moments that determine the study scene's edges. Potential candidate points can be identified based on thresholding the image moments' values. A shape context descriptor is adopted to automatically pair symmetric candidate points to produce a final set of control points. Coordinate transformation parameters between the two datasets were estimated using a least squares adjustment for four registration models: first- (affine), second-, third-order polynomials, and direct linear transform models. Datasets covering different urban landscapes were used to examine the proposed workflow. The root-mean-square error of the registration is between one and two pixels. The proposed workflow is found to be computationally efficient especially with small-sized datasets, and generic enough to be applied in registering various imagery data and LiDAR point clouds.

Memory‐Efficient Bijective Parameterizations of Very‐Large‐Scale Models

AbstractAs high‐precision 3D scanners become more and more widespread, it is easy to obtain very‐large‐scale meshes containing at least millions of vertices. However, processing these very‐large‐scale meshes is still a very challenging task due to memory limitations. This paper focuses on a fundamental geometric processing task, i.e., bijective parameterization construction. To this end, we present a spline‐enhanced method to compute bijective and low distortion parameterizations for very‐large‐scale disk topology meshes. Instead of computing descent directions using the mesh vertices as variables, we estimate descent directions for each vertex by optimizing a proxy energy defined in spline spaces. Since the spline functions contain a small set of control points, it significantly decreases memory requirement. Besides, a divide‐and‐conquer method is proposed to obtain bijective initializations, and a submesh‐based optimization strategy is developed to reduce distortion further. The capability and feasibility of our method are demonstrated over various complex models. Compared to the existing methods for bijective parameterizations of very‐large‐scale meshes, our method exhibits better scalability and requires much less memory.