of the local areas and entire points. Previous approaches [@Achlioptas2017latent; @yang2018foldingnet; @Deng2018ppffoldnet] usually use simple fully-connected (FC) layers or MLP layers to build the decoder. However, the expressive ability of the decoder is largely limited without considering the relationship among features. In this work, we propose a progressive decoding way which can be regarded as a reverse process of the encoding. The first step is to generate local region features from the global feature. To propagate the global feature $\bm{g}$ to region features, a simple interpolation operation is first engaged in the decoder. The local region feature $\bm{l}_i$ is calculated by $$\bm{l}_i = \frac{c}{(p_i-p_0)^2}\bm{g}, i \in [1,M],$$ where $c$ ($c={10}^{-10}$) is a constant. Here, $p_0 = (0,0,0)$ is the centroid of the input point cloud after the normalization processing. And $p_i$ is the centroid point of the corresponding local region. By the simple interpolation operation, the spatial distribution information of local region can be integrated to facilitate the feature decoding. The interpolated local region features are then concatenated with skip linked local region features from the encoder. The concatenated features are passed through another MLP layer into a $M \times D$ feature matrix.

![The decoding process of the RNN layer.[]{data-label="fig:rnn"}](RNN.pdf){height="2cm" 