Parameterization-Free Projection For Geometry Reconstruction

Daniel Cohen-Or                   Hillel Tal-Ezer

ACM Transactions on Graphics (SIGGRAPH 2007)

Example videos of the projection operator:

Abstract:

We introduce a Locally Optimal Projection operator (LOP) for

surface approximation from point-set data. The operator is parameterization

free, in the sense that it does not rely on estimating a local

normal, fitting a local plane, or using any other local parametric

representation. Therefore, it can deal with noisy data which clutters

the orientation of the points. The method performs well in cases

of ambiguous orientation, e.g., if two folds of a surface lie near

each other, and other cases of complex geometry in which methods

based upon local plane fitting may fail. Although defined by a

global minimization problem, the method is effectively local, and it

provides a second order approximation to smooth surfaces. Hence

allowing good surface approximation without using any explicit or

implicit approximation space. Furthermore, we show that LOP is

highly robust to noise and outliers and demonstrate its effectiveness

by applying it to raw scanned data of complex shapes.

Technical Report:

Examples:

 Left: A prism point-cloud contaminated with ghost geometry noise. Middle: MLS. Right: LOP. In both the point-set is projected onto itself. A noisy point-cloud of a surface with three holes (a). The red points in (b) are projected onto the point-set in (a). The results of the MLS and LOP projections are shown in (c),(d), respectively.

 This example depicts the distribution of point by LOP operator. (a): Starting from a crude initial guess (red points projected onto the green point-set), the operator iteratively (b–d) distribute the points regularly while respecting the geometry faithfully. Hole-puncher scan which consists of a few registered scans suffering from bad alignment, noise and outliers. (a) shows an example of two scans which where registered using ICP. (b),(d-top) are the whole input data seen from two angles. Note the high noise and ghost geometry. The corresponding LOP reconstruction is depicted in (c),(d-bottom). Note the zoomed-in views in (e) and (f).