Shape assembly composes complex shapes geometries by arranging simple part geometries and has wide applications in autonomous robotic assembly and CAD modeling. Existing works focus on geometry reasoning and neglect the actual physical assembly process of matching and fitting joints, which are the contact surfaces connecting different parts. In this paper, we consider contacting joints for the task of multi-part assembly. A successful joint-optimized assembly needs to satisfy the bilateral objectives of shape structure and joint alignment. We propose a hierarchical graph learning approach composed of two levels of graph representation learning. The part graph takes part geometries as input to build the desired shape structure. The joint-level graph uses part joints information and focuses on matching and aligning joints. The two kinds of information are combined to achieve the bilateral objectives. Extensive experiments demonstrate that our method outperforms previous methods, achieving better shape structure and higher joint alignment accuracy.

Batch Normalization (BN) and its variants have delivered tremendous success in combating the covariate shift induced by the training step of deep learning methods. While these techniques normalize feature distributions by standardizing with batch statistics, they do not correct the influence on features from extraneous variables or multiple distributions. Such extra variables, referred to as metadata here, may create bias or confounding effects (e.g., race when classifying gender from face images). We introduce the Metadata Normalization (MDN) layer, a new batch-level operation which can be used end-to-end within the training framework, to correct the influence of metadata on feature distributions. MDN adopts a regression analysis technique traditionally used for preprocessing to remove (regress out) the metadata effects on model features during training. We utilize a metric based on distance correlation to quantify the distribution bias from the metadata and demonstrate that our method successfully removes metadata effects on four diverse settings: one synthetic, one 2D image, one video, and one 3D medical image dataset.