# Reconstructing Surfaces

- "Reconstructing Surfaces Using Anisotropic Basis Functions"
- Huong Quynh Dinh, Greg Slabaugh and Greg Turk
- International Conference on Computer Vision (ICCV) 2001
- Vancouver, Canada
- July 9-12, 2001
- pp. 606-613

Full Paper (PDF, 1.2 Mbytes).

## Abstract

Point sets obtained from computer vision techniques are often
noisy and non-uniform. We present a new method of surface reconstruction
that can handle such data sets using anisotropic basis functions. Our
reconstruction algorithm draws upon the work in variational implict
surfaces for constructing smooth and seamless 3D surfaces.

Implicit functions are often formulated as a sum of weighted basis
functions that are radially symmetric. Using radially symmetric basis
functions inherently assumes, however, that the surface to be
reconstructed is, everywhere, locally symmetric. Such an assumption is
true only at planar regions, and hence, reconstruction using isotropic
basis is insufficient to recover objects that exhibit sharp features. We
preserve sharp features using anisotropic basis that allow the surface to
vary locally. The reconstructed surface is sharper along edges and at
corner points. We determine the direction of anisotropy at a point by
performing principal component analysis of the data points in a small
neighborhood. The resulting surface is smoothed through tensor filtering.

We have applied the anisotropic basis functions to reconstruct surfaces
from noisy synthetic 3D data and from real range data obtained from
space carving.

Reconstruction from synthetic data using isotropic basis functions.

Reconstruction using anisotropic basis functions.

Data from voxel carving of the Ghirardelli Square model.

Comparison between isotropic, anisotropic and filtered anisotropic
reconstructions.

Comparisons between two photos of the real model and the reconstructed
images using anisotropic basis functions.

Go to
Greg Turk's Home Page.