As-rigid-as-possible shape deformation and interpolation

摘要

We provide a detailed analysis of the 2D deformation algorithm based on non-linear least squares optimization, and prove that different mesh structure is of critical importance to deforming result. Based on triangle mesh, preserving the length of edges during deforming is enough to preserve the local, global and boundary properties of the shape. Sufficient theoretical analysis and experiments proved the advantage of the algorithm: (1) It is more stable. The constraint of edges length is strong enough to preserve the stability of triangle, thus the local and global structure are stable. (2) Due to less constraints, the calculating cost is reduced and the performance is improved. (3) The problem of parameter adjusting is solved in the approach. Further more, the algorithm has the ability to control facial expression and to adjust the area of shape etc. In addition, a new approach to shape interpolation is presented. The inputs of the shape interpolation algorithm are bitmap represented images without any topology information in both the original and the target shapes. The strategy is to extract the topology of the original shape, and set up the correspondence between the original and the target shapes, which is to find the matching contour vertices between the original and target shapes. And the shape deformation algorithm is applied using the interpolation of the matching vertices as controlling points. The algorithm guarantees as-rigid-as-possible and rotation invariant shape interpolation. The interpolated shapes have the same topology structure with the original and the target shapes. Experiments indicate that the algorithm is stable and well performed.