## SURFACE RECONSTRUCTION IN COMPUTER VISION.This thesis concentrates on a two-stage algorithm for surface reconstruction from sparse data. We present methods to handle noise, outliers and discontinuities in a common framework. The basic paradigm is to clean and grid (the first stage), and then to fit the data with a discontinuity preserving spline (the second stage). The first stage consists of a robust local approximation algorithm to both remove outliers in the data and create a grid from the original scattered data points which preserves |

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### Contents

BACKGROUND | 18 |

THEORY AND ALGORITHMS FOR SURFACE RECONSTRUC | 43 |

EXPERIMENTS | 63 |

Copyright | |

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### Common terms and phrases

algorithm presented approximation problem B-spline basis functions Besl bicubic spline approximation breakdown point computer vision create cubic spline data points data values dense depth data obtained derivatives disparity map edges equation estimate filter Gaussian curvature global grid location Grimson ill-posed problem integration iterative least squares linear lines of curvature lines of principal M-estimators median of squares method minimizes MLMS algorithm Multiview neighborhood noise number of knots object optimal outliers output parameters piecewise pixels polynomial preserving discontinuities principal curvature principal patches provides quadratic variation R.M.S. error range image regions regression representation residual RMS error scattered data scene shown in figure shows smoothing splines smoothness norm solution solve space spline fit stabilizing functional stereo pair subsamples surface fitting surface model surface reconstruction synthetic image tensor product term Terzopoulos theorem thesis thin-plate spline two-stage algorithm umbilic points unweighted viewpoint weighted bicubic spline weighted spline weighting function zero