Reconstructing Surfaces by Volumetric Regularization

We present a new method of surface reconstruction that generates 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 space carved volumes. Our method constructs a three dimensional implicit surface, formulated as a summation of weighted radial basis functions. We achieve three primary advantages over existing algorithms: (1) the implicit functions we construct estimate the surface well 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 locally detailed, yet globally smooth, because we use radial basis functions that achieve multiple orders of smoothness