Surface reconstruction using point cloud
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SURFACE RECONSTRUCTION BY POINT CLOUD DATA
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SURFACE RECONSTRUCTION BY POINT CLOUD DATA
BYISHAN KOSAMBE
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Contents
• Reverse Engineering
• Laser Scanners
• Point Cloud Data
• Surface Reconstruction
• Various Techniques
• Algorithm
• Data Simplification
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• Original Manufacturer • Inadequate Documentation
• Improve the product performance
• Competition
• Low cost production
Reverse Engineering
• Need
• Process
• Application
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• Need
• Process
• Application
• Duplication of existing part• By capturing the components i. Dimensions ii. Featuresiii. Material properties
Reverse Engineering
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Manufacturing
Drawing
Inspection
Create 3D Model
Obtaining Dimensional Details
Physical Product
• Need
• Process
• Application
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• Need
• Process
• Application
• Entertainment
• Automotive
• Consumer Products
• Mechanical designs
• Rapid product development
• Software Engineering
Reverse Engineering
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Laser scanners
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• 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
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Reverse Engineering
Laser Scanners
Point Cloud Data
Surface Reconstruction
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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)
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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
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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
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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
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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
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Surface Interpolation Methods
• Weighted average methods• Interpolation by polynomials• Interpolation by splines• Surface interpolation by regularization
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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
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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
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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
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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
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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
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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
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Phases in Reconstruction
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