Super-Resolution Surface Reconstruction from Few Low-Resolution Slices
This work addresses a domain-specific need for improved surface resolution in imaging applications, such as blood vessel analysis, but appears incremental as it builds on existing variational models.
The paper tackles the problem of reconstructing high-resolution surfaces from low-resolution segmented imaging data, which is crucial for applications like finite element analysis, by proposing a new variational model with an Euler-Elastica-based regularizer and two numerical algorithms, showing effectiveness through quantitative comparisons using standard deviations of Gaussian and mean curvatures.
In many imaging applications where segmented features (e.g. blood vessels) are further used for other numerical simulations (e.g. finite element analysis), the obtained surfaces do not have fine resolutions suitable for the task. Increasing the resolution of such surfaces becomes crucial. This paper proposes a new variational model for solving this problem, based on an Euler-Elastica-based regulariser. Further, we propose and implement two numerical algorithms for solving the model, a projected gradient descent method and the alternating direction method of multipliers. Numerical experiments using real-life examples (including two from outputs of another variational model) have been illustrated for effectiveness. The advantages of the new model are shown through quantitative comparisons by the standard deviation of Gaussian curvatures and mean curvatures from the viewpoint of discrete geometry.