852 research outputs found
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Reconstructing Surfaces by Volumetric Regularization Using Radial Basis Functions
We present a new method of surface reconstruction that generates smooth and seamless models from sparse, noisy, nonuniform, and low resolution range data. Data acquisition techniques from computer vision, such as stereo range images and space carving, produce 3D point sets that are imprecise and nonuniform when compared to laser or optical range scanners. Traditional reconstruction algorithms designed for dense and precise data do not produce smooth reconstructions when applied to vision-based data sets. Our method constructs a 3D implicit surface, formulated as a sum 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
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Reconstructing Surfaces Using Anisotropic Basis Functions
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 implicit 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 field of principle directions across the 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
3D shape based reconstruction of experimental data in Diffuse Optical Tomography
Diffuse optical tomography (DOT) aims at recovering three-dimensional images of absorption and scattering parameters inside diffusive body based on small number of transmission measurements at the boundary of the body. This image reconstruction problem is known to be an ill-posed inverse problem, which requires use of prior information for successful reconstruction. We present a shape based method for DOT, where we assume a priori that the unknown body consist of disjoint subdomains with different optical properties. We utilize spherical harmonics expansion to parameterize the reconstruction problem with respect to the subdomain boundaries, and introduce a finite element (FEM) based algorithm that uses a novel 3D mesh subdivision technique to describe the mapping from spherical harmonics coefficients to the 3D absorption and scattering distributions inside a unstructured volumetric FEM mesh. We evaluate the shape based method by reconstructing experimental DOT data, from a cylindrical phantom with one inclusion with high absorption and one with high scattering. The reconstruction was monitored, and we found a 87% reduction in the Hausdorff measure between targets and reconstructed inclusions, 96% success in recovering the location of the centers of the inclusions and 87% success in average in the recovery for the volumes
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