Feature-preserving mesh reconstruction from point clouds is challenging. Implicit methods tend to fit smooth surfaces and cannot be used to reconstruct sharp features. Explicit reconstruction methods are sensitive to noise and only interpolate sharp features when points are distributed on feature lines. We propose a watertight surface reconstruction method based on optimal transport that can accurately reconstruct sharp features often present in CAD models. We formalize the surface reconstruction problem by minimizing the optimal transport cost between the point cloud and the reconstructed surface. The algorithm consists of initialization and refinement steps. In the initialization step, the convex hull of the point cloud is deformed under the guidance of a transport plan to obtain an initial approximate surface. Next, the mesh surface was optimized using operations including vertex relocation and edge collapses/flips to obtain feature-preserving results. Experiments demonstrate that our method can preserve sharp features while being robust to noise and missing data.

Mesh-based image warping techniques typically represent image deformation using linear functions on triangular meshes or bilinear functions on rectangular meshes. This enables simple and efficient implementation, but in turn, restricts the representation capability of the deformation, often leading to unsatisfactory warping results. We present a novel, flexible polygonal finite element (poly-FEM) method for content-aware image warping. Image deformation is represented by high-order poly-FEMs on a content-aware polygonal mesh with a cell distribution adapted to saliency information in the source image. This allows highly adaptive meshes and smoother warping with fewer degrees of freedom, thus significantly extending the flexibility and capability of the warping representation. Benefiting from the continuous formulation of image deformation, our poly-FEM warping method is able to compute the optimal image deformation by minimizing existing or even newly designed warping energies consisting of penalty terms for specific transformations. We demonstrate the versatility of the proposed poly-FEM warping method in representing different deformations and its superiority by comparing it to other existing state-of-the-art methods.