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Cengiz Öztireli, Gaël Guennebaud, Markus Gross
Point Set Surfaces
Point Set Surfaces are meshless surface representations. Since reconstructing such a surface from point
samples requires a smoothing step, the resulting surfaces lack the very important surface features such as
sharp edges and corners. In this work, our primary aim is to remove this limitation and produce smooth
surfaces that still preserve the important high frequency details.
Features
The surface definition we developed achieves high quality feature preservation with controllable sharpness
tuned by a single parameter. In addition, it has many other significant improvements over the existing definitions.
The main features of our definition are:
The novel surface definition has built-in handling of noise, outliers and high frequency features without no user interaction
or further processing. Only a simple formula needs to be computed, and a simple spatial data structure such as a
kd-tree is needed to speed up computations. This results in a very efficient and easy-to-implement algorithm suitable for real time applications.
Method
The way to this definition was to first cast implicit surface fitting by moving least squares as a
local regression problem, and then use robust statistical techniques from the regression literature. This gives
a non-least squares error function to solve, for which an iterative solution is required. Fortunately, regression
literature offers an easy and convergent technique called iteratively reweighted least squares for the solution.
If surface is smooth around a point, then only one iteration is needed for it to converge. In the non-smooth regions,
typically 2-3 iterations are needed. The end result is a smooth surface that handles both noise and outliers and at the
same time preserves details and features.
- C. Öztireli, G. Guennebaud, M. Gross, Feature Preserving Point Set Surfaces based on Non-Linear Kernel Regression, Proceedings of Eurographics (Munich, Germany, March 30 - April 3, 2009), Computer Graphics Forum, vol. 28, no. 2, pp. 493-501
[Abstract]
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