In the area of 3D shape analysis, the geometric properties of a shape have long been studied. Instead of directly extracting representative features using expert-designed descriptors or end-to-end deep neural networks, this paper is dedicated to discovering distinctive information from the shape formation process. Concretely, a spherical point cloud served as the template is progressively deformed to fit the target shape in a coarse-to-fine manner. During the shape formation process, several checkpoints are inserted to facilitate recording and investigating the intermediate stages. For each stage, the offset field is evaluated as a stage-aware description. The summation of the offsets throughout the shape formation process can completely define the target shape in terms of geometry. In this perspective, one can derive the point-wise shape correspondence from the template inexpensively, which benefits various graphic applications. In this paper, the Progressive Deformation-based Auto-Encoder (PDAE) is proposed to learn the stage-aware description through a coarse-to-fine shape fitting task. Experimental results show that the proposed PDAE has the ability to reconstruct 3D shapes with high fidelity, and consistent topology is preserved in the multi-stage deformation process. Additional applications based on the stage-aware description are performed, demonstrating its universality.

通过一种渐进变形的方法，本论文利用球形点云为模板来提取阶段感知的描述信息，进而实现对3D形状的高精度重构。

云球: 通过渐进变形实现的三维形状表示