Discontinuity-preserving Normal Integration with Auxiliary Edges
<|reference_start|>Discontinuity-preserving Normal Integration with Auxiliary Edges: Many surface reconstruction methods incorporate normal integration, which is a process to obtain a depth map from surface gradients. In this process, the input may represent a surface with discontinuities, e.g., due to self-occlusion. To reconstruct an accurate depth map from the input normal map, hidden surface gradients occurring from the jumps must be handled. To model these jumps correctly, we design a novel discretization scheme for the domain of normal integration. Our key idea is to introduce auxiliary edges, which bridge between piecewise-smooth patches in the domain so that the magnitude of hidden jumps can be explicitly expressed. Using the auxiliary edges, we design a novel algorithm to optimize the discontinuity and the depth map from the input normal map. Our method optimizes discontinuities by using a combination of iterative re-weighted least squares and iterative filtering of the jump magnitudes on auxiliary edges to provide strong sparsity regularization. Compared to previous discontinuity-preserving normal integration methods, which model the magnitudes of jumps only implicitly, our method reconstructs subtle discontinuities accurately thanks to our explicit representation of jumps allowing for strong sparsity regularization.<|reference_end|>
@article{kim2024discontinuity-preserving,
    title={Discontinuity-preserving Normal Integration with Auxiliary Edges},
    author={Hyomin Kim, Yucheol Jung, Seungyong Lee},
    journal={arXiv preprint arXiv:2404.03138},
    year={2024},
    archivePrefix={arXiv},
    eprint={2404.03138},
    primaryClass={cs.CV cs.GR}
}