As-rigid-as-possible shape deformation and interpolation

Yang, H, Guo, H, Fu, X, Chen, F, Wang, Y and Li, H (2008) 'As-rigid-as-possible shape deformation and interpolation.' Journal of Visual Communication and Image Representation, 19 (4). pp. 245-255. ISSN 1047-3203

Official URL:


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.

Item Type: Article
Keywords: Triangle mesh; Edge length constraint; Global properties; Local properties; Boundary properties; Contour vertices matching
Divisions: Bath School of Design
Identification Number:
Date Deposited: 03 Jul 2013 10:11
Last Modified: 05 Jan 2022 16:07
URI / Page ID:
Request a change to this item or report an issue Request a change to this item or report an issue
Update item (repository staff only) Update item (repository staff only)