Active contours with normally generalized gradient vector flow external force

Gradient vector flow （GVF） is an effective external force for active contours, but its iso- tropic nature handicaps its performance. The recently proposed gradient vector flow in the normal direction （NGVF） is anisotropic since it only keeps the diffusion along the normal direction of the isophotes; however, it has difficulties forcing a snake into long, thin boundary indentations. In this paper, a novel external force for active contours called normally generalized gradient vector flow （NGGVF） is proposed, which generalizes the NGVF formulation to include two spatially varying weighting functions. Consequently, the proposed NGGVF snake is anisotropic and would improve ac- tive contour convergence into long, thin boundary indentations while maintaining other desirable properties of the NGVF snake, such as enlarged capture range, initialization insensitivity and good convergence at concavities. The advantages on synthetic and real images are demonstrated.

Existence for a Higher Order Coupled System of Korteweg-de Vries Equations

Consider the following system of coupled Korteweg-de Vries equations, where u, v ⊆ W2,2, 2≤N≤7 and λi,β > 0, β denotes a real coupling parameter. Firstly, we prove the existence of the solutions of a coupled system of Korteweg-de Vries equations using variation approach and minimization techniques on Nehari manifold. Then, we show the multiplicity of the equations by a bifurcation theory which is rare for studying higher order equations.

Road Surface Modeling and Representation from Point Cloud Based on Fuzzy Clustering

A scheme for an automatic road surface modeling from a noisy point cloud is presented. The normal vectors of the point cloud are estimated by distance-weighted fitting of local plane. Then, an automatic recognition of the road surface from noise is performed based on the fuzzy clustering of normal vectors, with which the mean value is calculated and the projecting plane of point cloud is created to obtain the geometric model accordingly. Based on fuzzy clustering of the intensity attributed to each point, different objects on the road surface are assigned different colors for representing abundant appearances. This unsupervised method is demonstrated in the experiment and shows great effectiveness in reconstructing and rendering better road surface.

Left-Invariant Minimal Unit Vector Fields on the Solvable Lie Group

Bozek(1980)has introduced a class of solvable Lie groups Gn with arbitrary odd dimension to construct irreducible generalized symmetric Riemannian space such that the identity component of its full isometry group is solvable.In this article,the authors provide the set of all left-invariant minimal unit vector fields on the solvable Lie group Gn,and give the relationships between the minimal unit vector fields and the geodesic vector fields,the strongly normal unit vectors respectively.

NORMAL VECTOR FIELDS OF IMMERSIONS OF n-MANIFOLDS IN (2n—1)-MANIFOLDS

This paper studies the nonzero normal vector fields of immersions homotopic to a map g: Mn→N2n-1. In the case of the stable normal bundle of g being orientable, rather complete results are obtained.

Auto-normalization algorithm for robotic precision drilling system in aircraft component assembly

A novel approach is proposed to detect the normal vector to product surface in real time for the robotic precision drilling system in aircraft component assembly, and the auto-normalization algorithm is presented based on the detection system. Firstly, the deviation between the normal vector and the spindle axis is measured by the four laser displacement sensors installed at the head of the multi-function end effector. Then, the robot target attitude is inversely solved according to the auto-normalization algorithm. Finally, adjust the robot to the target attitude via pitch and yaw rotations about the tool center point and the spindle axis is corrected in line with the normal vector simultaneously. To test and verify the auto-normalization algorithm, an experimental platform is established in which the laser tracker is introduced for accurate measurement. The results show that the deviations between the corrected spindle axis and the normal vector are all reduced to less than 0.5°, with the mean value 0.32°. It is demonstrated the detection method and the autonormalization algorithm are feasible and reliable.

A New Gradient Fidelity Term for Avoiding Staircasing Effect

Image denoising with some second order nonlinear PDEs often leads to a staircasing effect, which may produce undesirable blocky image. In this paper, we present a new gradient fidelity term and couple it with these PDEs to solve the problem. At first, we smooth the normal vector fields （i.e., the gradient fields） of the noisy image by total variation （TV） minimization and make the gradient of desirable image close to the smoothed normals, which is the idea of our gradient fidelity term. Then, we introduce the Euler-Lagrange equation of the gradient fidelity term into nonlinear diffusion PDEs for noise and staircasing removal. To speed up the computation of the vectorial TV minimization, the dual approach proposed by Bresson and Chan is employed. Some numerical experiments demonstrate that our gradient fidelity term can help to avoid the staircasing effect effectively, while preserving sharp discontinuities in images.

An orientation method and analysis of optical radiation sources based on polyhedron and parallel incident light

The spatial orientation of optical radiation sources has long been the hot topic in the aerospace and the military applications.Current researches mainly focus on the high precision orientation on the partial field of view.Thus,combination of several partial fields of view is required to achieve orientation when the field of view exceeds 180°,which results in the increase of size,weight,power consumption and the cost.By defining radiation energy and direction of the optical radiation source as a vector and applying the cosine law of radiation and vector theorem,it is shown that the vector can be obtained from unit normal vectors on the three un-coplanar surfaces and from the energy projected by the optical radiation source.Based on this,an orientation method with 360° full field of view by a polyhedron is suggested,the mathematical formula for anti-multipath interference is supposed and the error upper limit is derived.The feasibility and effectiveness of this method are validated by measurements and simulation.An accuracy better than 2.866° and 0.574° is achieved when the ratio of measurement error of energy on arbitrary surface and the true value are 5% and 1%,respectively,given the matrix composed of unit normal vectors on three measurement surfaces is orthogonal.

An Improved Algorithm for k-Nearest-Neighbor Finding and Surface Normals Estimation

This paper is to improve the speed of k-nearest-neighbor search and put forward algorithms related to tangent plane estimation based on existing methods. Starting from the points cloud, the algorithm segments the whole data into many different small cubes in space, and the size of cube is related to the density of the points cloud. Considering the position of the point in the cube, the algorithm enlarges the area around the given point step by step until the k-nearest-neighbor is accomplished. The neighbor’s least-squares tangent plane is estimated. In order to orient the planes, the k-nearest-neighbor is introduced into the problem of seeking the minimum spanning trees instead of searching the whole data. The research proved that the algorithms put forward in this paper were effective in processing data in short time and with high precision. The theory was useful for the practical application in reverse engineering and other areas related. Solution for finding k-nearest-neighbor problem, which still costs much time in present, was provided, and a propagation algorithm for orienting the planes was also discussed. The algorithm chose the orientation among the k-nearest-neighbor of the current point.

Atlas Compatibility Transformation:A Normal Manifold Learning Algorithm

Over the past few years,nonlinear manifold learning has been widely exploited in data analysis and machine learning.This paper presents a novel manifold learning algorithm,named atlas compatibility transformation(ACT),It solves two problems which correspond to two key points in the manifold definition:how to chart a given manifold and how to align the patches to a global coordinate space based on compatibility.For the first problem,we divide the manifold into maximal linear patch(MLP) based on normal vector field of the manifold.For the second problem,we align patches into an optimal global system by solving a generalized eigenvalue problem.Compared with the traditional method,the ACT could deal with noise datasets and fragment datasets.Moreover,the mappings between high dimensional space and low dimensional space are given.Experiments on both synthetic data and real-world data indicate the effection of the proposed algorithm.

Stroke-Based Surface Reconstruction

In this paper,we present a surface reconstruction via 2D strokes and a vector field on the strokes based on a two-step method.In the first step,from sparse strokes drawn by artists and a given vector field on the strokes,we propose a nonlinear vector interpolation combining total variation(TV)and H1 regularization with a curl-free constraint for obtaining a dense vector field.In the second step,a height map is obtained by integrating the dense vector field in the first step.Jump discontinuities in surface and discontinuities of surface gradients can be well reconstructed without any surface distortion.We also provide a fast and efficient algorithm for solving the proposed functionals.Since vectors on the strokes are interpreted as a projection of surface gradients onto the plane,different types of strokes are easily devised to generate geometrically crucial structures such as ridge,valley,jump,bump,and dip on the surface.The stroke types help users to create a surface which they intuitively imagine from 2D strokes.We compare our results with conventional methods via many examples.