width="8cm"}

RNN Layer
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Given the feature of local regions, we want to decode the scale level features. Due to the multi-scale setting, the features of different scales in a local region can be regarded as a feature sequence with length $T$. As we all know that recurrent neural network [@hochreiter1997long] has shown excellent performances in processing sequential data. Thus, a RNN decoding layer is employed to generate the multi-scale area features. The decoding process is shown in Figure \[fig:rnn\]. We first replicate the local region feature $\bm{l}_i$ for $T$ times, and the replicated local region features are feed into the RNN layer by $$\bm{h}_t = f(\bm{h}_{t-1}, \bm{l}_i^t), t \in [1,T],$$ where $f$ is a non-linear activation function and $t$ is the index of RNN step. Therefore, the predicted $t^{th}$ area feature $\bm{a}_t$ can be calculated by $$\bm{a}_t = \bm{W}_\theta \bm{h}_t.$$ Here, $\bm{W}_d$ is a learnable weight matrix. To generate the points inside each local area, several FC layers are adopted to reconstruct the points. The local area $\bm{A}^{'}_t$ is reconstructed by $$\bm{A}^{'}_t = \bm{W}_{\theta_t}\bm{a}_t + b_{\theta_t},$$ where $\bm{W}_{\theta_t}$, $b_{\theta_t}$ are weights of the FC layer. Based on the reconstructed local areas, another FC layer is applied to incrementally reconstruct 