@MastersThesis{Matyskova-TR-2007-07,
  UPDATE  = { 2007-03-16 },
author =      {Mat{\'y}skov{\'a}, Martina},
supervisor =  {Kostliv{\'a}, Jana},
language =    {czech},
title =       {Filtrace diskr{\'e}tn{\'\i}ho povrchu},
e_title =     {Discrete Surface Fairing},
school =      {MFF, Charles University},
address =     {Prague, Czech Republic},
year =        {2007},
month =       {February},
day =         {5},
type =        {{MSc Thesis CTU--CMP--2007--07}},
issn =        {1213-2365},
pages =       {109},
figures =     {43},
authorship =  {100},
psurl       = {[Matyskova-TR-2007-07.pdf]},
project =     {1ET101210406},
annote =      {This thesis proposes a new method for fairing of surfaces,
               which are represented by a triangulated mesh. Motivation
               for our task is a 3D reconstruction, which results in a
               triangulated mesh. Such mesh is typically corrupted by
               noise (due to data and processing inaccuracy), which is
               required to be faired out. We solve the problem on a
               discrete surface, where two criteria for optimization are
               defined: surface curvature and non-uniformity. The
               curvature deals with surface smoothness, while the
               non-uniformity with surface regularity. The problem of
               fairing is solved by a discrete diffusion. Since our aim is
               to fair surfaces with boundaries, first we describe the
               fairing of curves, then fairing of closed surfaces, and
               finally fairing of surfaces with boundary (which is in fact
               a combination of the former ones). We have tested the
               algorithm's performance on synthetic as well as real data
               with good results. The experiments showed that our proposed
               algorithm is robust, stable and does not shrink an object,
               while its main surface characteristics are preserved. },
keywords =    {surface fairing, mesh smoothing, approximation of curvature},
}