We present Deformable Voxel Grids (DVGs) for 3D shapes comparison and processing. It consists of a voxel grid which is deformed to approximate the silhouette of a shape, via energy-minimization. By interpreting the DVG as a local coordinates system, it provides a better embedding space than a regular voxel grid, since it is adapted to the geometry of the shape. It also allows to deform the shape by moving the control points of the DVG, in a similar manner to the Free Form Deformation, but with easier interpretability of the control points positions. After proposing a computation scheme of the energies compatible with meshes and pointclouds, we demonstrate the use of DVGs in a variety of applications: correspondences via cubification, style transfer, shape retrieval and PCA deformations. The first two require no learning and can be readily run on any shapes in a matter of minutes on modest hardware. As for the last two, they require to first optimize DVGs on a collection of shapes, which amounts to a pre-processing step. Then, determining PCA coordinates is straightforward and brings a few parameters to deform a shape.
翻译:我们为 3D 形状比较和处理提供了可变的 Voxel 网格(DVGs) 。 它由一个 voxel 网格组成, 以通过能量最小化来接近形状的光影。 通过将 DVG 解释为本地坐标系统, 它提供了比普通 voxel 网格更好的嵌入空间, 因为它适应形状的几何学, 还可以通过移动 DVG 控制点来变形, 与自由形式变形相似, 但控制点位置更容易解释。 在提出与 meshes 和 poluds 相容的能量计算方案之后, 我们展示了DVG 用于多种应用: 通过刻化、 风格转换、 形状检索和 CCA 变形等通信。 前两个网格不需要学习, 并且可以在小硬件的几分钟内运行任何形状。 最后两个网格需要首先优化 DVG 的形状收藏, 这相当于一个前步的形状。 确定一个直径的坐标, 直径的坐标是后一个形状。