Surface reconstruction in computer vision.
Sarvajit S. Sinha · Deep Blue (University of Michigan) · 1991
This thesis presents algorithms for visual surface reconstruction from scattered data, explicitly dealing with the common sources of error in current algorithms: noise, outliers and discontinuities in the data. We have drawn from three separate areas--approximation theory, robust statistics and computer vision to create algorithms to fit a surface to scattered data (such as from stereo). We have also utilized differential geometry to compute a stable mathematical model for a class of objects with piece-wise smooth surfaces. This thesis concentrates on a two-stage algorithm for surface reconstruction from sparse data. We present methods to handle noise, outliers and discontinuities in a common framework. The basic paradigm is to clean and grid (the first stage), and then to fit the data with a discontinuity preserving spline (the second stage). The first stage consists of a robust local approximation algorithm to both remove outliers in the data and create a grid from the original scattered data points which preserves discontinuities. The second stage uses a weighted bicubic tensor-product B-spline as a finite element, and as a surface descriptor for a global adaptive regularized approximation to the data. The weighted bicubic approximating spline is able to fit data with step discontinuities with little distortion in the approximated surface. Data for experiments in this thesis have been chosen from various sources. For example, visual processes provide information only at scattered points in the visual field. These are the geometric and photometric edges in the scene. We fit the scattered data obtained from different stereo algorithms to obtain complete information about the visible surfaces in the scene. We also deal with data from a variety of active range sensors. Having obtained a dense representation of the data, we build a viewpoint invariant principal patch representation. This is based on the orthogonal lines of principal curvature. By computing these curves from a range image, we show that it is possible to construct a mesh which can later be repatched using generic CAD surface primitives that are virtually free of tensor product artifacts and possess desired inter-surface continuity.