We propose OptCtrlPoints, a data-driven framework designed to identify the optimal sparse set of control points for reproducing target shapes using biharmonic 3D shape deformation. Control-point-based 3D deformation methods are widely utilized for interactive shape editing, and their usability is enhanced when the control points are sparse yet strategically distributed across the shape. With this objective in mind, we introduce a data-driven approach that can determine the most suitable set of control points, assuming that we have a given set of possible shape variations. The challenges associated with this task primarily stem from the computationally demanding nature of the problem. Two main factors contribute to this complexity: solving a large linear system for the biharmonic weight computation and addressing the combinatorial problem of finding the optimal subset of mesh vertices. To overcome these challenges, we propose a reformulation of the biharmonic computation that reduces the matrix size, making it dependent on the number of control points rather than the number of vertices. Additionally, we present an efficient search algorithm that significantly reduces the time complexity while still delivering a nearly optimal solution. Experiments on SMPL, SMAL, and DeformingThings4D datasets demonstrate the efficacy of our method. Our control points achieve better template-to-target fit than FPS, random search, and neural-network-based prediction. We also highlight the significant reduction in computation time from days to approximately 3 minutes.

翻译：我们提出OptCtrlPoints，一个数据驱动框架，旨在为使用双调和3D形状变形再现目标形状时，确定最优稀疏控制点集。基于控制点的3D变形方法广泛应用于交互式形状编辑，当控制点稀疏且策略性地分布在形状上时，其可用性得以增强。基于此目标，我们引入一种数据驱动方法，可基于给定的一组可能形状变化，确定最合适的控制点集。该任务的主要挑战源于问题计算量大的特性，这主要由两个因素导致：求解双调和权重计算所需的大型线性系统，以及找到网格顶点最优子集的组合优化问题。为克服这些挑战，我们提出双调和计算的重构方法，将矩阵规模从依赖于顶点数减少为依赖于控制点数。此外，我们提出一种高效搜索算法，显著降低时间复杂度，同时仍能提供近乎最优的解。在SMPL、SMAL和DeformingThings4D数据集上的实验证明了我们方法的有效性。与FPS、随机搜索和基于神经网络的预测相比，我们的控制点在模板到目标的拟合中表现更优。我们还强调了计算时间从数天显著减少至约3分钟的改进效果。