Existing surface reconstruction algorithms taking a gradient field as input enforce the integrability constraint. While enforcing integrability allows the subsequent integration to produce surface heights, current algorithms suffer from the one or more of following disadvantages: they can only handle dense per-pixel gradients, smooth out sharp features in a non-integrable field, or produce severe surface distortion. In this thesis, we present a method which does not based on integrability enforcement, and reconstructs a 3D continuous surface from a gradient field which can be dense or sparse. The key of our approach is the use of kernel basis functions, which transfers the continuous surface reconstruction problem into high dimensional space where a closed-form solution exists. This lea...[ Read more ]

Existing surface reconstruction algorithms taking a gradient field as input enforce the integrability constraint. While enforcing integrability allows the subsequent integration to produce surface heights, current algorithms suffer from the one or more of following disadvantages: they can only handle dense per-pixel gradients, smooth out sharp features in a non-integrable field, or produce severe surface distortion. In this thesis, we present a method which does not based on integrability enforcement, and reconstructs a 3D continuous surface from a gradient field which can be dense or sparse. The key of our approach is the use of kernel basis functions, which transfers the continuous surface reconstruction problem into high dimensional space where a closed-form solution exists. This leads to a neat and straightforward implementation while producing better results than traditional techniques. In particular, the use of kernel functions as basis functions to represent a continuous surface avoids unnecessary discretization and finite approximation, both will lead to surface distortion, which are typical problems arising from the use of Fourier or Wavelet bases widely adopted by previous representative approaches. We perform exhaustive comparison with classical and recent methods on benchmark and challenging data sets to demonstrate that our method produces accurate surface reconstruction, while preserving salient features and robust to noise.