  Detecting 3D keypoints from point clouds is important for shape
reconstruction, while this work investigates the dual question: can shape
reconstruction benefit 3D keypoint detection? Existing methods either seek
salient features according to statistics of different orders or learn to
predict keypoints that are invariant to transformation. Nevertheless, the idea
of incorporating shape reconstruction into 3D keypoint detection is
under-explored. We argue that this is restricted by former problem
formulations. To this end, a novel unsupervised paradigm named SNAKE is
proposed, which is short for shape-aware neural 3D keypoint field. Similar to
recent coordinate-based radiance or distance field, our network takes 3D
coordinates as inputs and predicts implicit shape indicators and keypoint
saliency simultaneously, thus naturally entangling 3D keypoint detection and
shape reconstruction. We achieve superior performance on various public
benchmarks, including standalone object datasets ModelNet40, KeypointNet, SMPL
meshes and scene-level datasets 3DMatch and Redwood. Intrinsic shape awareness
brings several advantages as follows. (1) SNAKE generates 3D keypoints
consistent with human semantic annotation, even without such supervision. (2)
SNAKE outperforms counterparts in terms of repeatability, especially when the
input point clouds are down-sampled. (3) the generated keypoints allow accurate
geometric registration, notably in a zero-shot setting. Codes are available at
https://github.com/zhongcl-thu/SNAKE
