# ALReg: Registration of 3D Point Clouds Using Active Learning
## 3 Method
### Active Selection  
For the training set \(\mathcal{D}_{t}\) very few labeled superpoints \(\mathcal{S}_{\mathcal{L}}\) are initially selected randomly, and the selected registration network is trained with these labeled superpoints. At certain points of the training process, an acquisition score is calculated for each superpoint in \(\mathcal{D}_{U}\) and according to their sorted scores, some of them are included in \(\mathcal{D}_{L}\). It should be remarked that, for every selection phase, only one unlabeled superpoint from each training sample is selected. Otherwise, the algorithm may select the newly labeled superpoints so that there could be an unbalance among point counts. Considering that our main focus for ALReg is to decrease training time, creating batches for variable-sized samples will be more time-consuming than the mentioned setup. The full framework is depicted in Figure 2.  
In this study, we present two different acquisition scoring mechanisms: \(ALReg_{DIV}\) and \(ALReg_{UNC}\) focusing on diversity and uncertainty respectively.  
**ALRegDiv**: To calculate the diversity of a superpoint, the acquisition functions in ReDAL and SSDR-AL are unsuitable here since ReDAL benefits from color discontinuity and SSDR-AL uses class distributions. Thus, to obtain diversity scores, following a similar approach to [28], a feature diversity metric is calculated. Diversity score of an unlabeled superpoint \(S_{i}\in S_{U}(X_{j})\) is calculated as  
\[D(s)=\min_{s_{k}\in S_{L}(X_{j})}||F(s_{i})-F(s_{k})|| \tag{9}\]  
where \(F\) denotes the encoder features from the selected network.  
**ALRegUNC**: To calculate the uncertainty of a superpoint, a Monte Carlo Dropout (MCDO) [80] approach is followed. Since dropout is a specific type of Bayesian neural network (BNN), after each layer of the encoder layer, a dropout layer is placed to obtain varying outputs for the same points. Since it is not a classification task, the uncertainty metrics presented before are unusable. Thus, a variance-based uncertainty metric used for BNNs with latent variables [81; 82] could be applied to our problem.  
For the data point \(x\) and the network output \(y\), total uncertainty in terms of variance could be written as  
\[\sigma^{2}(y|x)=\sigma^{2}_{q(W)}(E[y|W,x])+E_{q(W)}[\sigma^{2}(y|W,x)] \tag{10}\]  
where \(q(W)\) represents the posterior approximation according to weights \(W\). Here, the first term represents epistemic uncertainty and the second term represents aleatoric uncertainty. The aleatoric uncertainty term could be calculated by \(M\times N\) network passes. The network weights \(W\) are sampled M times (corresponding to using M different MCDO setups) and the variable is sampled N times (corresponds to use N different point sets from a selected superpoint). For a feature vector with size K, means of variances are calculated for each of the K features and their average will indicate the uncertainty of the selected superpoint \(U(s)\).  
The procedure is explained in Algorithm 1.  
Figure 2: The ALReg Framework. In training time, only the labeled superpoints \(D_{L}\) are used. In the active selection phase, uncertainty scores and network features are obtained to select new superpoints for labeling.