Clustering for Different Scales of Measurement - the Gap-Ratio Weighted K-means Algorithm

This paper describes a method for clustering data that are spread out over large regions and which dimensions are on different scales of measurement. Such an algorithm was developed to implement a robotics application consisting in sorting and storing objects in an unsupervised way. The toy dataset used to validate such application consists of Lego bricks of different shapes and colors. The uncontrolled lighting conditions together with the use of RGB color features, respectively involve data with a large spread and different levels of measurement between data dimensions. To overcome the combination of these two characteristics in the data, we have developed a new weighted K-means algorithm, called gap-ratio K-means, which consists in weighting each dimension of the feature space before running the K-means algorithm. The weight associated with a feature is proportional to the ratio of the biggest gap between two consecutive data points, and the average of all the other gaps. This method is compared with two other variants of K-means on the Lego bricks clustering problem as well as two other common classification datasets.Comment: 13 pages, 6 figures, 2 tables. This paper is under the review process for AIAP 201

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]

Path planning with PH G2 splines in R2

International audienceIn this article, we justify the use of parametric planar Pythagorean Hodograph spline curves in path planning. The elegant properties of such splines enable us to design an efficient interpolator algorithm, more precise than the classical Taylor interpolators and faster than an interpolator based on arc length computations

A simple and generic CAD/CAM approach for AFM probe-based machining

Atomic Force Microscopy (AFM) probe-based machining allows surface structuring at the nano-scale via the mechanical modification of material. This results from the direct contact between the tip of an AFM probe and the surface of a sample. Given that AFM instruments are primarily developed for obtaining high-resolution topography information of inspected specimen, raster scanning typically defines the trajectory followed by the tip of an AFM probe. Although most AFM manufacturers provide software modules to perform user-defined tip displacement operations, such additional solutions can be limited with respect to 1) the range of tip motions that can be designed, 2) the level of automation when defining tip displacement strategies and 3) the portability for easily transferring trajectories data between different AFM instruments. In this context, this research presents a feasibility study, which aims to demonstrate the applicability of a simple and generic CAD/CAM approach when implementing AFM probe-based nano-machining for producing two-dimensional (2D) features with a commercial AFM instrument