基于局部—全局方法的三角网格优化算法

在基于网格形变的图像缩放算法中，表示图像的网格质量对于这类算法的结果有着很大的影响。为了改善图像网格质量，提出一种基于局部—全局方法的平面三角网格优化算法。在局部阶段利用自定义的最相似规则，为网格中的每一个三角形单元求取与之最相似的正三角形，得到一组目标仿射变换函数；全局阶段采用尽可能刚性方法，利用最小二乘法求取一组满足最小变形能量函数的最优解，使得最终生成的网格由尽可能相似于正三角形的三角形构成。同时，在优化过程中加入约束控制，保护网格中的重要区域不发生改变。实验结果表明，优化后的网格质量得到了明显的改善，有助于图像缩放算法后续工作的进行。

Local-global algorithm for triangular mesh optimization

In the image resizing algorithm based on mesh deformation, the mesh quality is crucial. A new local-global based triangular mesh optimization algorithm was proposed to improve the quality of the triangular mesh representing the image being resized. In the local step, the equilateral triangle, which is most similar to each triangle in the mesh, was obtained using custom rules, and a set of objectives affine transformation function was got. While in the global step, the optimal position of each node was solved by least-square method based on as rigid as possible method to minimize the value of the deformation energy function. Simultaneously, constrained control was added in optimization process to protect the critical areas of the grid from changing. The experimental results demonstrate that the quality of the planar triangular mesh is greatly improved.