  Point cloud models with neural network architectures have achieved great
success and have been widely used in safety-critical applications, such as
Lidar-based recognition systems in autonomous vehicles. However, such models
are shown vulnerable to adversarial attacks which aim to apply stealthy
semantic transformations such as rotation and tapering to mislead model
predictions. In this paper, we propose a transformation-specific smoothing
framework TPC, which provides tight and scalable robustness guarantees for
point cloud models against semantic transformation attacks. We first categorize
common 3D transformations into three categories: additive (e.g., shearing),
composable (e.g., rotation), and indirectly composable (e.g., tapering), and we
present generic robustness certification strategies for all categories
respectively. We then specify unique certification protocols for a range of
specific semantic transformations and their compositions. Extensive experiments
on several common 3D transformations show that TPC significantly outperforms
the state of the art. For example, our framework boosts the certified accuracy
against twisting transformation along z-axis (within 20$^\circ$) from 20.3$\%$
to 83.8$\%$. Codes and models are available at
https://github.com/chuwd19/Point-Cloud-Smoothing.
