Volume-Preserving Parameterizations via Preconditioned Nonlinear Conjugate Gradient Method
提出一种通过最小化等体积能量来实现保体积参数化的方法，使用预处理非线性共轭梯度法求解，实验表明该方法在形状配准和体积变形中精度和效率更高。
Abstract A volume-preserving parameterization is a bijective mapping that maps a 3-manifold onto a canonical domain while preserving local volume. We formulate this problem as an unconstrained nonlinear optimization problem by introducing an isovolumetric energy that quantifies volumetric distortion. This energy is minimized using a preconditioned nonlinear conjugate gradient method, which is globally convergent when the line search satisfies the strong Wolfe conditions. Numerical experiments demonstrate that the proposed method achieves improved accuracy and efficiency, and it supports applications in shape registration and volumetric deformation.