Surface reconstruction using point cloud

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Surface reconstruction using point cloud

  1. 1. SURFACE RECONSTRUCTION BY POINT CLOUD DATA
  2. 2. SURFACE RECONSTRUCTION BY POINT CLOUD DATA BY ISHAN KOSAMBE
  3. 3. Contents • Reverse Engineering • Laser Scanners • Point Cloud Data • Surface Reconstruction • Various Techniques • Algorithm • Data Simplification
  4. 4. • Original Manufacturer • Inadequate Documentation • Improve the product performance • Competition • Low cost production Reverse Engineering • Need • Process • Application
  5. 5. • Need • Process • Application • Duplication of existing part • By capturing the components i. Dimensions ii. Features iii. Material properties Reverse Engineering
  6. 6. Manufacturing Drawing Inspection Create 3D Model Obtaining Dimensional Details Physical Product • Need • Process • Application
  7. 7. • Need • Process • Application • Entertainment • Automotive • Consumer Products • Mechanical designs • Rapid product development • Software Engineering Reverse Engineering
  8. 8. Laser scanners
  9. 9. • 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
  10. 10. Reverse Engineering Laser Scanners Point Cloud Data Surface Reconstruction
  11. 11. 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)
  12. 12. 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
  13. 13. 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
  14. 14. 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
  15. 15. 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
  16. 16. Surface Interpolation Methods • Weighted average methods • Interpolation by polynomials • Interpolation by splines • Surface interpolation by regularization
  17. 17. 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
  18. 18. 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
  19. 19. 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
  20. 20. 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
  21. 21. 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
  22. 22. 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
  23. 23. Phases in Reconstruction
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