  3D point-cloud recognition with PointNet and its variants has received
remarkable progress. A missing ingredient, however, is the ability to
automatically evaluate point-wise importance w.r.t.\! classification
performance, which is usually reflected by a saliency map. A saliency map is an
important tool as it allows one to perform further processes on point-cloud
data. In this paper, we propose a novel way of characterizing critical points
and segments to build point-cloud saliency maps. Our method assigns each point
a score reflecting its contribution to the model-recognition loss. The saliency
map explicitly explains which points are the key for model recognition.
Furthermore, aggregations of highly-scored points indicate important
segments/subsets in a point-cloud. Our motivation for constructing a saliency
map is by point dropping, which is a non-differentiable operator. To overcome
this issue, we approximate point-dropping with a differentiable procedure of
shifting points towards the cloud centroid. Consequently, each saliency score
can be efficiently measured by the corresponding gradient of the loss w.r.t the
point under the spherical coordinates. Extensive evaluations on several
state-of-the-art point-cloud recognition models, including PointNet, PointNet++
and DGCNN, demonstrate the veracity and generality of our proposed saliency
map. Code for experiments is released on
\url{https://github.com/tianzheng4/PointCloud-Saliency-Maps}.
