local regions and then show these centroids. By summing attention map by column in the region level, the attention value of each centroid is caculated. For example, a $256 \times 256$ attention map is translated to a 256-dimension attention vector, when the number of sampled centroids is 256. Then, both the size and the color of centroids are associated with the attention values. Therefore, the centroids with lighter colors and larger sizes indicate larger attention values. As depicted in Figure \[fig:attetnion\], we show some examples of the region level attention. Figure \[fig:attetnion\] shows that the self-attention in the region level tends to on special local regions at conspicuous locations such as edges, corners or protruding parts.

![Some examples of the attention in the scale level. The abscissa represents the 4 scales $[s_1,s_2,s_3,s_4]$ around each centroid in a point cloud and the ordinate indicates the index of 256 centroids, where each subfigure represents a 3D object.[]{data-label="fig:sl_attention"}](sl_attention.pdf){width="7cm" height="6cm"}

![Some examples of the attention in the point level, where the four subfigures in each row represent the four scales of a local region.[]{data-label="fig:pl_attention"}](pl_attention.pdf){width="7cm" height="6cm"}

Similarly, we also show some examples of the scale level attention in Figure \[fig:sl\_attention\] and the point level attention 