Super-Resolution Surface Reconstruction from Few Low-Resolution Slices

TL;DR

This paper introduces a variational model with an Euler-Elastica regulariser for super-resolution surface reconstruction from few low-resolution slices, improving surface detail for numerical simulations.

Contribution

It proposes a novel variational model and two numerical algorithms specifically designed for super-resolution surface reconstruction from limited low-resolution data.

Findings

The model effectively enhances surface resolution in real-life examples.

Quantitative metrics show improved curvature consistency.

Algorithms outperform existing methods in accuracy and stability.

Abstract

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.