Fast B-Spline 2D Curve Fitting for unorganized Noisy Datasets

In the context of coordinate metrology and reverse engineering, freeform curve reconstruction from unorganized data points still offers ways for improvement. Geometric convection is the process of fitting a closed shape, generally represented in the form of a periodic B-Spline model, to data points [WPL06]. This process should be robust to freeform shapes and convergence should be assured even in the presence of noise. The convection's starting point is a periodic B-Spline polygon defined by a finite number of control points that are distributed around the data points. The minimization of the sum of the squared distances separating the B-Spline curve and the points is done and translates into an adaptation of the shape of the curve, meaning that the control points are either inserted, removed or delocalized automatically depending on the accuracy of the fit. Computing distances is a computationally expensive step in which finding the projection of each of the data points requires the determination of location parameters along the curve. Zheng et al [ZBLW12] propose a minimization process in which location parameters and control points are calculated simultaneously. We propose a method in which we do not need to estimate location parameters, but rather compute topological distances that can be assimilated to the Hausdorff distances using a two-step association procedure. Instead of using the continuous representation of the B-Spline curve and having to solve for footpoints, we set the problem in discrete form by applying subdivision of the control polygon. This generates a discretization of the curve and establishes the link between the discrete point-to-curve distances and the position of the control points. The first step of the association process associates BSpline discrete points to data points and a segmentation of the cloud of points is done. The second step uses this segmentation to associate to each data point the nearest discrete BSpline segment. Results are presented for the fitting of turbine blades profiles and a thorough comparison between our approach and the existing methods is given [ZBLW12, WPL06, SKH98]

An Automated Algorithm for Approximation of Temporal Video Data Using Linear B'EZIER Fitting

This paper presents an efficient method for approximation of temporal video data using linear Bezier fitting. For a given sequence of frames, the proposed method estimates the intensity variations of each pixel in temporal dimension using linear Bezier fitting in Euclidean space. Fitting of each segment ensures upper bound of specified mean squared error. Break and fit criteria is employed to minimize the number of segments required to fit the data. The proposed method is well suitable for lossy compression of temporal video data and automates the fitting process of each pixel. Experimental results show that the proposed method yields good results both in terms of objective and subjective quality measurement parameters without causing any blocking artifacts.Comment: 14 Pages, IJMA 201

Knot Placement of B-spline Curves with Equally Spaced Geometric Information

受每个节点区间应该具有相同建模能力的启发,提出一种基于几何信息均分的B样条曲线节点设置算法.首先放置少量节点,以每个节点区间具有相等的几何信息量; 准则来确定节点的位置;为了提高样条的建模能力,根据上一次迭代中的拟合误差确定加细节点区间并使新节点均分该节点区间的几何信息.该算法可以快速有效地; 得到用户指定精度的逼近曲线.通过对一些具有不同几何复杂度的实例进行实验的结果表明,文中算法是有效的;与现有的2种算法相比,; 该算法在相同控制顶点的情况下能够得到更高精度的逼近结果.Motivated by the observation that each knot interval should be of the; same modeling ability, a knot placement algorithm based on equally; spaced geometric information for B-spline curves is proposed. In the; algorithm, a few of knots are determined according to the principle that; each knot interval is of the same amount of geometric information at the; initial iteration. In order to improve the modeling ability of the; B-splines, the knot interval needed to be refined is determined by the; last fitting errors and the new knot inserted is placed to equally space; the accumulated geometric information in the knot interval. Via the; adaptive knot placement algorithm, approximated curve with specified; tolerance can be produced rapidly and efficiently. Several models with; distinct geometric complexities are tested to demonstrate the efficacy; of our algorithm in fitting curves. Comparing to other two available; methods, more accurate results can be obtained by our method with the; same number of control points.国家自然科学基金; 福建省自然科学基金; 中央高校基本科研业务费专项资

Fast B-spline Curve Fitting by L-BFGS

We propose a novel method for fitting planar B-spline curves to unorganized data points. In traditional methods, optimization of control points and foot points are performed in two very time-consuming steps in each iteration: 1) control points are updated by setting up and solving a linear system of equations; and 2) foot points are computed by projecting each data point onto a B-spline curve. Our method uses the L-BFGS optimization method to optimize control points and foot points simultaneously and therefore it does not need to perform either matrix computation or foot point projection in every iteration. As a result, our method is much faster than existing methods

Geometric model for automated multi-objective optimization of foils

This paper describes a new generic parametric modeller integrated into an auto- mated optimization loop for shape optimization. The modeller enables the generation of shapes by selecting a set of design parameters that controls a twofold parameterization: geometrical - based on a skeleton approach - and architectural - based on the experience of practitioners - to impact the system performance. The resulting forms are relevant and effective, thanks to a smoothing procedure that ensures the consistency of the shapes produced. As an application, we propose to perform a multi-objective shape optimization of a AC45 foil. The modeller is linked to the fluid solver AVANTI, coupled with Xfoil, and to the optimization toolbox FAMOSA

MOZARD: Multi-Modal Localization for Autonomous Vehicles in Urban Outdoor Environments

Visually poor scenarios are one of the main sources of failure in visual localization systems in outdoor environments. To address this challenge, we present MOZARD, a multi-modal localization system for urban outdoor environments using vision and LiDAR. By extending our preexisting key-point based visual multi-session local localization approach with the use of semantic data, an improved localization recall can be achieved across vastly different appearance conditions. In particular we focus on the use of curbstone information because of their broad distribution and reliability within urban environments. We present thorough experimental evaluations on several driving kilometers in challenging urban outdoor environments, analyze the recall and accuracy of our localization system and demonstrate in a case study possible failure cases of each subsystem. We demonstrate that MOZARD is able to bridge scenarios where our previous work VIZARD fails, hence yielding an increased recall performance, while a similar localization accuracy of 0.2m is achieve