2D shape deformation using nonlinear least squares optimization
2D shape deformation using nonlinear least squares optimization
复制标题
DOI：
10.1007/s00371-006-0054-y
复制
发表时间：
2006-09
期刊：
影响因子：
--
通讯作者：
Y. Weng;Weiwei Xu;Yanchen Wu;Kun Zhou;B. Guo
中科院分区：
文献类型：
--
作者：
Y. Weng;Weiwei Xu;Yanchen Wu;Kun Zhou;B. Guo
提出了一种新的基于非线性最小二乘优化的二维形状变形算法。该算法的目的是保持两个局部形状属性：边界曲线的拉普拉斯坐标和形状内部的局部区域，它们共同表示为一个非二次能量函数。用迭代的Gauss-牛顿法来最小化这个非线性能量函数。结果是一个交互式的形状变形系统，它可以获得物理上看似合理的结果，这是以前的线性最小二乘方法难以实现的。除了保留局部形状属性的算法外，我们还提出了一种保持形状全局面积的方案，这对于变形不可压缩对象是有用的。
This paper presents a novel 2D shape deformation algorithm based on nonlinear least squares optimization. The algorithm aims to preserve two local shape properties: the Laplacian coordinates of the boundary curve and the local area of the shape interior, which are together represented in a non-quadratic energy function. An iterative Gauss–Newton method is used to minimize this nonlinear energy function. The result is an interactive shape deformation system that can achieve physically plausible results that are difficult to achieve with previous linear least squares methods. In addition to this algorithm that preserves local shape properties, we also introduce a scheme to preserve the global area of the shape, which is useful for deforming incompressible objects.