PolyShape Representation

PolyShape processing results on some samples of ModelNet-10 dataset based on √3-subdivision. Sqrt1 to Sqrt3 refer to the output of the PolyShape procedure after each level of subdivision. Note that V and F refer to the number of vertices and faces for each shape.

Probability Distributions/h4>

Joint and marginal distributions. Visualization of (a) the learned joint distributions and (b) the marginal distributions approximated by polynomial functions of degreed 2 on the ModelNet-10 with the √3-subdivision.

Polynomial Convolution (PolyConv)

Classification accuracy (Acc%), testing time, andnumber of parameters in only convolution layers on theModelNet-10 with both subdivision strategies for the var-ious convolution operations in PolyNet.

3D Shape Classification

Classification accuracy (Acc%) and mean Aver-age Precision (mAP%) of PolyNet compared to the state-of-the-art methods based on different representations on theModelNet-10 and the ModelNet-40 datasets.

3D Shape Retrieval

The retrieved shapes for the given queries using PolyNet. The blue models in the first column are the queries. The retrieved results in green are from the same category as the query, while the results in red are from different categories. From left to right, the results are ordered with a descending rank.