  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.
