Abstract

A typical curve reconstruction problem is to generate a continuous linear representation of a curve from a set of unorganized sampling points on the curve. These unorganized points should be joined by edges in the order in which they appear on the curve. There are many methods to reconstruct curves from existing point clouds. Most of the existing algorithms are designed based on concepts from computational geometry. The current algorithms have difficulties in reconstructing curves with sharp corners or noisy points and they depend on predefined parameters. The present thesis proposes a different way to reconstruct curves, that is, to reconstruct curves based on the experiments of human vision. The curves should be reconstructed in the same manner that human beings perceive them. In the present thesis, statistical experiments are conducted to construct a vision function. A software system, based on that vision function, is developed to simulate human vision for curve reconstruction. The experiments investigate the relationships between points and the relationship between points and curves, by using methods from Design of Experiments (DOE), ANOVA and the multivariate non-linear regression model. The errors between the predicted values using the regression model and the observed values from vision experiments follow normal distribution. The algorithm based on the constructed vision function uses the key factors as input to identify curves for given points. Examples show that the curve reconstruction results using this new algorithm are advantageous by comparison the results with from existing algorithms.