Curvature Diversity-Driven Deformation and Domain Alignment for Point Cloud

Unsupervised Domain Adaptation (UDA) is crucial for reducing the need for extensive manual data annotation when training deep networks on point cloud data. A significant challenge of UDA lies in effectively bridging the domain gap. To tackle this challenge, we propose $\mathbf{\text{C}}$urvature $\mathbf{\text{D}}$iversity-Driven $\mathbf{\text{N}}$uclear-Norm Wasserstein $\mathbf{\text{D}}$omain Alignment (CDND). Our approach first introduces a $\mathit{\text{Curv}}\mathit{\text{ature}}\mathit{\text{Diversity-driven}}\mathit{\text{Deformation}}\mathit{\text{Rec}}\mathit{\text{onstruction}}\mathit{\text{(CurvRec)}}$ task, which effectively mitigates the gap between the source and target domains by enabling the model to extract salient features from semantically rich regions of a given point cloud. We then propose $\mathit{\text{D}}\mathit{\text{eformation-based}}\mathit{\text{N}}\mathit{\text{uclear-norm}}\mathit{\text{W}}\mathit{\text{asserstein}}\mathit{\text{D}}\mathit{\text{iscrepancy}}\mathit{\text{(D-NWD)}}$, which applies the Nuclear-norm Wasserstein Discrepancy to both $\mathit{\text{deformed}}\mathit{\text{and}}\mathit{\text{original}}$ data samples to align the source and target domains. Furthermore, we contribute a theoretical justification for the effectiveness of D-NWD in distribution alignment and demonstrate that it is $\mathit{\text{generic}}$ enough to be applied to $\mathbf{\text{any}}$ deformations. To validate our method, we conduct extensive experiments on two public domain adaptation datasets for point cloud classification and segmentation tasks. Empirical experiment results show that our CDND achieves state-of-the-art performance by a noticeable margin over existing approaches.