Reconstruction from Range Data

Huong Quynh Dinh and Greg Turk
Graphics, Visualization, and Usability Center
College of Computing
Georgia Institute of Technology

We use variational implicit surfaces to generate smooth and seamless models from sparse, noisy, and non-uniform range data. Data acquisition techniques from computer vision, such as stereo range images and space carving, produce three dimensional point sets that are imprecise and non-uniform when compared to laser or optical range scanners. Traditional reconstruction algorithms designed for dense and precise data cannot be used on stereo range images and carved volumes. Our method constructs a three dimensional implicit surface, formulated as a summation of weighted radial basis functions. Three primary advantages of our technique are: (1) the implicit functions we construct can well estimate the surface in regions where there is little data; (2) the reconstructed surface is insensitive to noise in data acquisition because we can allow the surface to approximate, rather than exactly interpolate, the data; and (3) the reconstructed surface is detailed, yet smooth, because we use radial basis functions that achieve multiple orders of smoothness.

The implicit function, f(x), we construct is formulated as follows:

n is the number of constraint points, or observed data points. We construct a linear system by applying the equation above to the n constraint points. f(x) is the observed data value at constraint x (f(x) = 0 for surface constraints). We solve for the unknown weights, w.

The figures above is a comparison of our reconstruction with existing reconstruction algorithms. The leftmost figure is from an interactive viewer showing the space-carved range data that we use as input to our reconstruction algorithm. The figure in the middle is a variational implicit surface reconstructed using the thin-plate radial basis function, and the final figure on the right is our new method of reconstruction using a basis function which achieves multiple orders of smoothness.

Our research addresses the following issues in reconstruction from range data:

• Volumetric Regularization
• Interpolation Vs. Approximation
• A Radial Basis Function for Multiple Orders of Smoothness
• Constraint Specification
• Reconstruction from Synthetic Range Images
• Reconstruction from Real Space Carved Data
• Search Space for Lambda, Phi, and Delta
• Model Coloring
• Acknowledgements & References