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，一种数据驱动的框架，旨在为使用双调和三维形状变形再现目标形状时，识别最优的稀疏控制点集。基于控制点的三维变形方法广泛用于交互式形状编辑，当控制点稀疏但策略性地分布在形状上时，其可用性会得到增强。基于此目标，我们引入了一种数据驱动方法，可以在给定一组可能的形状变化时，确定最合适的控制点集。该任务面临的主要挑战源于其计算密集型特性。两个主要因素导致了这一复杂性：求解用于双调和权重计算的大型线性系统，以及寻找网格顶点最优子集的组合优化问题。为克服这些挑战，我们提出了一种双调和计算的重构方法，可减少矩阵规模，使其依赖于控制点数量而非顶点数量。此外，我们提出了一种高效的搜索算法，在提供接近最优解的同时显著降低了时间复杂度。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大幅缩短至约3分钟。