![Thesis Master](/img/d7b3cdd1-94a5-4978-a673-de087b211036/thesis-master.png?fm=jpg&q=80&fit=max&crop=200%2C120%2C0%2C0)
Cengiz Öztireli1
1ETH Zurich
We propose a new implicit Moving Least Squares (MLS) surface definition that preserves high frequency details including sharp features and reduces many artifacts present with existing MLS surface definitions. The new definition is stable under sparse sampling and sharpness of features is controllable. Although it is defined iteratively, convergence rate is high and computation is efficient. Since it is in an analytic form, derivatives such as curvatures are computed trivially and accurately. To derive this definition, we show that MLS surfaces can be interpreted as a Local Kernel Regression (LKR) on the implicit function defining the surface. This opens the way to adapt techniques from kernel regression literature to improve MLS surfaces. We use one such technique, robust kernel regression, to derive our new MLS surface definition. Many other possible methods that can be utilized to improve MLS surfaces are also pointed out.
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