SURFACE RECONSTRUCTION BY POINT CLOUD DATA

SURFACE RECONSTRUCTION BY POINT CLOUD DATA

BYISHAN KOSAMBE

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. Featuresiii. 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 ModelII. Metrology/Quality InspectionIII. Medical ImagingIV. Geographic Information SystemV. Data Compression

Point Cloud Data

Reverse Engineering

Laser Scanners

Point Cloud Data

Surface Reconstruction

POINT CLOUD PROCESSING SOFTWARE

• Cyclone and Cyclone Cloudworx (Leica, www.leica-geosystems.com)

• Polyworks (Innovmetric, www.innovmetric.com)• Riscan Pro (Riegl, www.riegl.com)• Isite Studio (Isite, www.isite3d.com)• LFM Software (Zoller+Fröhlich, www.zofre.de )• Split FX (Split Engineering, www.spliteng.com )• RealWorks Survey (Trimble, www.trimble.com)

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 coefficients2. 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