Surface reconstruction using point cloud

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Information about Surface reconstruction using point cloud

Published on March 11, 2014

Author: IshanKossambe




Contents • Reverse Engineering • Laser Scanners • Point Cloud Data • Surface Reconstruction • Various Techniques • Algorithm • Data Simplification

• Original Manufacturer • Inadequate Documentation • Improve the product performance • Competition • Low cost production Reverse Engineering • Need • Process • Application

• Need • Process • Application • Duplication of existing part • By capturing the components i. Dimensions ii. Features iii. Material properties Reverse Engineering

Manufacturing Drawing Inspection Create 3D Model Obtaining Dimensional Details Physical Product • Need • Process • Application

• Need • Process • Application • Entertainment • Automotive • Consumer Products • Mechanical designs • Rapid product development • Software Engineering Reverse Engineering

Laser scanners

• A point cloud is a set of data points in some coordinate system • Intended to represent the external surface of an object • Find Application in I. 3D CAD Model II. Metrology/Quality Inspection III. Medical Imaging IV. Geographic Information System V. Data Compression Point Cloud Data

Reverse Engineering Laser Scanners Point Cloud Data Surface Reconstruction

POINT CLOUD PROCESSING SOFTWARE • Cyclone and Cyclone Cloudworx (Leica, • Polyworks (Innovmetric, • Riscan Pro (Riegl, • Isite Studio (Isite, • LFM Software (Zoller+Fröhlich, ) • Split FX (Split Engineering, ) • RealWorks Survey (Trimble,

Surface Reconstruction • Objective is to find a function that agrees with all the data points • Accuracy of finding this function depends upon 1. Density and the distribution of the reference points 2. Method

Classifying Surface Fitting Methods • Closeness of fit of the resulting representation to the original data • Extent of support of the surface fitting method • Mathematical models

Closeness of Fit • Fitting method can be either an interpolation or an approximation • Interpolation methods fit a surface that passes through all data points • Approximation methods construct a surface that passes near data points

Extent of Support of the Surface Fitting Method • Method is classified as global or local • In the global approach, the resulting surface representation incorporates all data points to derive the unknown coefficients of the function • With local methods, the value of the constructed surface at a point considers only data at relatively nearby points

Surface Interpolation Methods • Weighted average methods • Interpolation by polynomials • Interpolation by splines • Surface interpolation by regularization

Weighted average methods • Direct summation of the data at each interpolation point • The weight is inversely proportional to the distance ri • Suitable for interpolating a surface from arbitrarily distributed data • Drawback is the large amount of calculations • To overcome this problem, the method is modified into a local version

Interpolation by polynomials • p is a function defined in one dimension for all real numbers x by p(x) = ao + alx + ... + aN_lxN-1 + aNxN • Fitting a surface by polynomials proceeds in two steps 1. Determination of the coefficients 2. Evaluates the polynomial

The general procedure for surface fitting with piecewise polynomials • Partitioning the surface into patches of triangular or rectangular shape • Fitting locally a leveled, tilted, or second- degree plane at each patch • Solving the unknown parameters of the polynomial

Disadvantages of interpolation by polynomial 1. Singular system of equations 2. Tendency to oscillate, resulting in a considerably undulating surface 3. Interpolation by polynomials with scattered data causes serious difficulties

Interpolation by splines • A spline is a piecewise polynomial function • In defining a spline function, the continuity and smoothness between two segments are constrained • Bicubic splines, which have continuous second derivatives are commonly used for surface fitting

Surface Interpolation by Regularization • A problem is either well-posed or ill posed • Regularization is the frame within which an ill- posed problem is changed into a well-posed one • The problem is then reformulated, based on the variational principle, so as to minimize an energy function E • It has two functionals S & D • The variable λ is the controls the influence of the two functionals

Phases in Reconstruction

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