The document discusses surface reconstruction from point cloud data. It describes how laser scanners are used to capture point clouds, which are then processed using software to reconstruct the surface. The key techniques for surface reconstruction include interpolation methods like weighted average, polynomials and splines, as well as regularization which formulates the problem variably to minimize an energy function.

1. SURFACE RECONSTRUCTION BY
POINT CLOUD DATA

2. SURFACE RECONSTRUCTION BY
POINT CLOUD DATA
BY
ISHAN KOSAMBE

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

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

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

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

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

8. Laser scanners

10. • 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

11. Reverse
Engineering
Laser Scanners
Point Cloud
Data
Surface
Reconstruction

12. 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)

13. 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

14. 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

15. 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

16. 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

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

18. 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

19. 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

20. 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

21. 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

22. 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

23. 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

24. Phases in Reconstruction