Point Constraints Research Articles

Research on global measurement method based on multi-cameras

The 3D reconstruction based on multi-cameras has been widely used and studied in the field of advanced manufacturing. Many 3D reconstruction methods have been proposed, but the limitation of high-accuracy, large-scale measurement always exists. The construction and calibration of multi-cameras system are the fundamental task as well as the key for the accurate measurement. In this paper, a high-precision camera calibration method for existing multi-cameras system is put forward. The transparent glass checkerboard and the principle of least time is applied in the method. The application of the transparent glass checkerboard leads to refraction phenomenon, which will generate calibration error. The refractive projection model is proposed to eliminate the error. Then the Scale-invariant feature transform (SIFT) algorithm is used to extract the feature point and epipolar geometry constraint is used to match the feature points. Finally, the 3D points can be obtained based on the principle of the triangle. The experimental results show the ability and robustness of the proposed approach.

Mixed mode embedded circular delamination propagation in spar wingskin joint made with curved FRP composite laminates

This paper presents the mixed mode propagation of circular delamination pre-embedded at the interface of 1st and 2nd plies of wingskin adherend of the Spar Wingskin Joint made with curved fibre reinforced plastic composite panels. Three dimensional finite element analyses of these joints under uniformly applied out of plane transverse load have been carried out using contact and multi point constraint elements. The growth of embedded delamination is simulated by sequential release of the constraints of these elements ahead of the delamination front. The inter-laminar stresses and strain energy release rate values being indicative parameters in delamination growth studies are computed in the vicinity of the curved delamination fronts. These values are evaluated using virtual crack closure technique. It has been observed that the circular delamination size significantly influences the magnitudes of inter-laminar stresses and the three components of SERR values in the vicinity of delamination front. Maximum values of peel stress and mode I SERR occur at orthogonal locations to the loading direction i.e. at θ = 90° and 270° measured counter clockwise from positive X-axis along the periphery of the delamination fronts. The variations of inter-laminar stresses and the values of SERR are non-uniform along the circular delamination front indicating variable rates of propagation. This simulation procedure will be used for the assessment of loss of structural integrity of the SWJs having circular delamination when the embedded delamination undergoes propagation upon increase of loading.

Relative enumerative invariants of real nodal del Pezzo surfaces

The surfaces considered are real, rational and have a unique smooth real $$(-2)$$ -curve. Their canonical class K is strictly negative on any other irreducible curve in the surface and $$K^2>0$$ . For surfaces satisfying these assumptions, we suggest a certain signed count of real rational curves that belong to a given divisor class and are simply tangent to the $$(-2)$$ -curve at each intersection point. We prove that this count provides a number which depends neither on the point constraints nor on deformation of the surface preserving the real structure and the $$(-2)$$ -curve.

TOP-SIFT: the selected SIFT descriptor based on dictionary learning

The large amount of SIFT descriptors in an image and the high dimensionality of SIFT descriptor have made problems for the large-scale image database in terms of speed and scalability. In this paper, we present a descriptor selection algorithm based on dictionary learning to remove the redundant features and reserve only a small set of features, which we refer to as TOP-SIFTs. During the experiment, we discovered the inner relativity between the problem of descriptor selection and dictionary learning in sparse representation, and then turned our problem into dictionary learning. We designed a new dictionary learning method to adapt our problem and employed the simulated annealing algorithm to obtain the optimal solution. During the process of learning, we added the sparsity constraint and spatial distribution characteristic of SIFT points. And lastly selected the small representative feature set with good spatial distribution. Compared with the earlier methods, our method is neither relying on the database nor losing important information, and the experiments have shown that our algorithm can save memory space a lot and increase time efficiency while maintaining the accuracy as well.

Optimization of Mayer Problem with Sturm–Liouville-Type Differential Inclusions

The present paper studies a new class of problems of optimal control theory with Sturm–Liouville-type differential inclusions involving second-order linear self-adjoint differential operators. Our main goal is to derive the optimality conditions of Mayer problem for differential inclusions with initial point constraints. By using the discretization method guaranteeing transition to continuous problem, the discrete and discrete-approximation inclusions are investigated. Necessary and sufficient conditions, containing both the Euler–Lagrange and Hamiltonian-type inclusions and “transversality” conditions are derived. The idea for obtaining optimality conditions of Mayer problem is based on applying locally adjoint mappings. This approach provides several important equivalence results concerning locally adjoint mappings to Sturm–Liouville-type set-valued mappings. The result strengthens and generalizes to the problem with a second-order non-self-adjoint differential operator; a suitable choice of coefficients then transforms this operator to the desired Sturm–Liouville-type problem. In particular, if a positive-valued, scalar function specific to Sturm–Liouville differential inclusions is identically equal to one, we have immediately the optimality conditions for the second-order discrete and differential inclusions. Furthermore, practical applications of these results are demonstrated by optimization of some “linear” optimal control problems for which the Weierstrass–Pontryagin maximum condition is obtained.

Determination of optimal measurement configurations for self-calibrating a robotic visual inspection system with multiple point constraints

In this paper, we propose an algorithm to determine optimal measurement configurations for self-calibrating a robotic visual inspection system with multiple point constraints. The algorithm aims to improve the robotic visual inspection system’s calibration accuracy. To do so, a pre-calibration of the robotic visual inspection system is needed to obtain the hand-eye and robot exterior relationship to implement the inverse kinematic algorithm. The candidate measurement configurations with one point constraint can be obtained using the inverse kinematic algorithm for the robotic visual inspection system, so DETMAX is implemented to determine a given number of optimal measurement configurations from the candidate measurement configurations. Particle swarm optimization is used to optimize the positions of the multiple points one by one. To verify the efficiency of the proposed approach, experiment evaluation is conducted on a robotic visual inspection system.

Vibroacoustic study of a point-constrained plate mounted in a duct

The vibroacoustic study of the interaction of sound with a point-constrained, simply-supported square plate is considered in this paper. The plate is mounted flush on one of the walls of an infinite duct of rectangular cross section and is backed by a cavity. The plate response and the acoustic field is predicted by solving the coupled governing equations using modal expansion with the relevant eigenmodes of the plate dynamics and acoustic fields in the duct and cavity. By varying the location of the point constraint, the frequency characteristics of the transmission loss in the duct can be tuned. The point constraint can also alter the amplitude and spectral characteristics of the plate's response. Interestingly, some new peaks are observed in the response because of the excitation of unsymmetric modes which are otherwise dormant. Mode-localization phenomenon, which is the localization of vibration in specific regions of the plate, is observed for selected constrained points.

Two stochastic optimization algorithms for convex optimization with fixed point constraints

Two optimization algorithms are proposed for solving a stochastic programming problem for which the objective function is given in the form of the expectation of convex functions and the constraint set is defined by the intersection of fixed point sets of nonexpansive mappings in a real Hilbert space. This setting of fixed point constraints enables consideration of the case in which the projection onto each of the constraint sets cannot be computed efficiently. Both algorithms use a convex function and a nonexpansive mapping determined by a certain probabilistic process at each iteration. One algorithm blends a stochastic gradient method with the Halpern fixed point algorithm. The other is based on a stochastic proximal point algorithm and the Halpern fixed point algorithm; it can be applied to nonsmooth convex optimization. Convergence analysis showed that, under certain assumptions, any weak sequential cluster point of the sequence generated by either algorithm almost surely belongs to the solution set of the problem. Convergence rate analysis illustrated their efficiency, and the numerical results of convex optimization over fixed point sets demonstrated their effectiveness.

Estimating Ideal Points from Roll-Call Data: Explore Principal Components Analysis, Especially for More Than One Dimension?

For two or more dimensions, the two main approaches to estimating legislators’ ideal points from roll-call data entail arbitrary, yet consequential, identification and modeling assumptions that bring about both indeterminateness and undue constraints for the ideal points. This paper presents a simple and fast approach to estimating ideal points in multiple dimensions that is not marred by those issues. The leading approach at present is that of Poole and Rosenthal. Also prominent currently is one that uses Bayesian techniques. However, in more than one dimension, they both have several problems, of which nonidentifiability of ideal points is the most precarious. The approach that we offer uses a particular mode of principal components analysis to estimate ideal points. It applies logistic regression to estimate roll-call parameters. It has a special feature that provides some guidance for deciding how many dimensions to use. Although its relative simplicity makes it useful even in just one dimension, its main advantages are for more than one.

Analysis and approximation of one-dimensional scalar conservation laws with general point constraints on the flux

We introduce and analyze a class of models with nonlocal point constraints for traffic flow through bottlenecks, such as exit doors in the context of pedestrians traffic and toll gates in vehicular traffic. Constraints are defined based on data collected from non-local in space and/or in time observations of the flow. We propose a theoretical analysis and discretization framework that permits to include different data acquisition strategies; a numerical comparison is provided. Nonlocal constraint allows to model, e.g., the irrational behavior (“panic”) near the exit observed in dense crowds and the capacity drop at tollbooth in vehicular traffic.Existence and uniqueness of solutions are shown under suitable and “easy to check” assumptions on the constraint operator. A numerical scheme for the problem, based on finite volume methods, is designed, its convergence is proved and its validation is done with an explicit solution. Numerical examples show that nonlocally constrained models are able to reproduce important features in traffic flow such as self-organization.

Method of Camera Calibration Using Concentric Circles and Lines through Their Centres

A novel method for camera calibration is proposed based on an analysis of lens distortion in camera imaging. In the method, a line through the centre of concentric circles is used as a template in which orthogonal directions can be determined from an angle of circumference that corresponds to a diameter. By using three lines through the centre of concentric circles, based on the invariance of the cross-ratio, an image at the centre of the concentric circles can be used to obtain the vanishing point. The intrinsic parameters of the camera can be computed based on the constraints of the orthogonal vanishing points and the imaged absolute conic. The lens distortion causes points in the template to have a position offset. In the proposed method, we optimize the positions of the distortion points such that they gradually approach those of the ideal points. The simulated and real-world experiments demonstrate that the proposed method is efficient and feasible.

Remote Sensing Image Registration Based on Phase Congruency Feature Detection and Spatial Constraint Matching

In this paper, a novel remote sensing image registration method based on phase congruency (PC) and spatial constraint is proposed. PC can provide intrinsic and meaningful image features, even when there are complex intensity changes or noise. Image features will be well detected from the corresponding PC images by the SAR-SIFT operator. It means that the feature detection methods in the frequency domain (PC) and the spatial domain (SAR-SIFT operator) are combined. To further improve the result of registration, spatial constraints, including point and line constraint, are established by utilizing the position and orientation information. Then, one to more matches can be removed and the influence of adjacent point can be greatly eliminated. The experimental results demonstrate that our method can obtain a better registration performance with higher accuracy and more correct correspondences than the state-of-the-art methods, such as SIFT, SAR-SIFT, SURF, PSO-SIFT, RIFT, and GLPM.

Improvement of Gaofen-3 Absolute Positioning Accuracy Based on Cross-Calibration.

The Chinese Gaofen-3 (GF-3) mission was launched in August 2016, equipped with a full polarimetric synthetic aperture radar (SAR) sensor in the C-band, with a resolution of up to 1 m. The absolute positioning accuracy of GF-3 is of great importance, and in-orbit geometric calibration is a key technology for improving absolute positioning accuracy. Conventional geometric calibration is used to accurately calibrate the geometric calibration parameters of the image (internal delay and azimuth shifts) using high-precision ground control data, which are highly dependent on the control data of the calibration field, but it remains costly and labor-intensive to monitor changes in GF-3’s geometric calibration parameters. Based on the positioning consistency constraint of the conjugate points, this study presents a geometric cross-calibration method for the rapid and accurate calibration of GF-3. The proposed method can accurately calibrate geometric calibration parameters without using corner reflectors and high-precision digital elevation models, thus improving absolute positioning accuracy of the GF-3 image. GF-3 images from multiple regions were collected to verify the absolute positioning accuracy after cross-calibration. The results show that this method can achieve a calibration accuracy as high as that achieved by the conventional field calibration method.

Multi-stage global trajectory optimization for the overlapping shift of a seamless two-speed transmission using Legendre pseudo-spectral method

For a seamless two-speed transmission specially equipped in electric vehicles, the global trajectory optimization problem of the overlapping shift process with multiple stages and complex path/point constraints is investigated in this article. The overlapping shift principle and the dynamic models in each phase are also demonstrated in detail. The parameters to evaluate the shift quality are analyzed and then introduced into the objective function and constraints, respectively. The jerks in process and at the key moments have been distinguished and selected as the path and point constraints, respectively. Moreover, considering the joint characteristics of the torque phase and the inertia phase, the trajectory optimization problems in the above two phases are summarized as a multi-stage global trajectory optimization problem. Then, Legendre pseudo-spectral method is used to transfer the multi-stage global trajectory optimization problem into a nonlinear programming problem for numerical solutions. Finally, the effectiveness and feasibility of the multi-stage global trajectory optimization method have been verified through the comparison of the optimal shift trajectories under different conditions with that obtained by the piecewise trajectory optimization method.

Characterizing the nonlinear response of elastomeric material systems under critical point constraints

Engineered materials that dissipate large shock and vibration through tailoring microscopic properties are of growing interest. To this end, reversible buckling of slender, elastomeric beams serving as microscopic constituents of engineered material systems is shown to be effective to tune the mechanical properties. Yet, the viscoelasticity and nonlinear deformations inherent in an engineered, elastomeric material system having critically constrained internal constituents challenge the understanding of the macroscopic dynamic properties borne out of such intersection of complex characteristics. This research undertakes analytical and experimental efforts considering a model specimen to illuminate how criticality, viscoelasticity, and nonlinearity interact to yield the macroscopic dynamic behavior of engineered, elastomeric material systems subjected to harmonic forcing. The analysis reveals that large strain of the internal beam constituents is a predominant mode of harmonic energy dissipation for more elastically dominated material characteristics. In contrast, a more equitable balance of viscous and elastic phenomena results in dissipation properties that involve history dependent reactions in tandem with the instantaneous strain on the constituents. Nonlinear deformations induced by critical constraints on the internal viscoelastic beams are discovered to strongly govern the relative amplitude of force transmission and significance of frequency tuning observed macroscopically. Experiments validate the findings and emphasize the non-intuitive character of elastomeric material system behaviors by virtue of the intersection of viscoelasticity, nonlinearity, and critical point constraints.

Enumeration of real curves in CP2n−1 and a Witten–Dijkgraaf–Verlinde–Verlinde relation for real Gromov–Witten invariants

We establish a homology relation for the Deligne-Mumford moduli spaces of real curves which lifts to a WDVV-type relation for real Gromov-Witten invariants of real symplectic manifolds; we also obtain a vanishing theorem for these invariants. For many real symplectic manifolds, these results reduce all genus 0 real invariants with conjugate pairs of constraints to genus 0 invariants with a single conjugate pair of constraints. In particular, we give a complete recursion for counts of real rational curves in odd-dimensional projective spaces with conjugate pairs of constraints and specify all cases when they are nonzero and thus provide non-trivial lower bounds in high-dimensional real algebraic geometry. We also show that the real invariants of the three-dimensional projective space with conjugate point constraints are congruent to their complex analogues modulo 4.

Precise iterative closest point algorithm with corner point constraint for isotropic scaling registration

The traditional iterative closest point (ICP) algorithm could register two point sets well, but it is easily affected by local dissimilarity. To deal with this problem, this paper proposes an isotropic scaling ICP algorithm with corner point constraint. First of all, because the corner points can preserve the similarity of the whole shapes, an objective function based on least square error is proposed under the guidance of the corner points. Second, a new ICP algorithm is proposed to complete the isotropic scaling registration. At each iterative step of this new algorithm, the correspondence is built based on the closest point searching, and then a closed-form solution of the transformation is computed. This new algorithm converges monotonically to a local minimum from any given initial scaling transformation. To obtain the expected minimum, the traditional scaling ICP algorithm is applied to compute the initial transformation. The experimental results demonstrate that our algorithm can prevent the influence of the local dissimilarity and improve the registration precision compared with the traditional ICP algorithm.

Simplified Model and Response Analysis for Crankshaft of Air Compressor

The original model of crankshaft is simplified to the appropriateness to balance the calculation precision and calculation speed, and then the finite element method is used to analyse the vibration response of the structure. In order to study the simplification and stress concentration for crankshaft of air compressor, this paper compares calculative mode frequency and experimental mode frequency of the air compressor crankshaft before and after the simplification, the vibration response of reference point constraint conditions is calculated by using the simplified model, and the stress distribution of the original model is calculated. The results show that the error between calculative mode frequency and experimental mode frequency is controlled in less than 7%, the constraint will change the model density of the system, the position between the crank arm and the shaft appeared stress concentration, so the part of the crankshaft should be treated in the process of manufacture.

Globally Consistent Indoor Mapping via a Decoupling Rotation and Translation Algorithm Applied to RGB-D Camera Output

This paper presents a novel RGB-D 3D reconstruction algorithm for the indoor environment. The method can produce globally-consistent 3D maps for potential GIS applications. As the consumer RGB-D camera provides a noisy depth image, the proposed algorithm decouples the rotation and translation for a more robust camera pose estimation, which makes full use of the information, but also prevents inaccuracies caused by noisy depth measurements. The uncertainty in the image depth is not only related to the camera device, but also the environment; hence, a novel uncertainty model for depth measurements was developed using Gaussian mixture applied to multi-windows. The plane features in the indoor environment contain valuable information about the global structure, which can guide the convergence of camera pose solutions, and plane and feature point constraints are incorporated in the proposed optimization framework. The proposed method was validated using publicly-available RGB-D benchmarks and obtained good quality trajectory and 3D models, which are difficult for traditional 3D reconstruction algorithms.

A camera calibration method based on plane mirror and vanishing point constraint

In order to avoid a cumbersome calibration of camera parameters, a method of self-calibration using the imaging features of a plane mirror and the vanishing point pair constraint is proposed. A plane mirror and calibration template were placed at a certain angle and non-vertical geometric constraints were obtained from the calibration template, as well as from the virtual image of the calibration template. So all the internal parameters were calibrated at once. In order to reduce the influence on the calibration parameters of the vanishing point position, the least squares algorithm and the LM algorithm were used to optimize the parameters. Simulations and real experimental results show that the method has a high accuracy and robustness.