## 4 Training the Model
### Experiments  
We trained the model using the KITTI and the NYU_V2 data sets under the following different scenarios:  
1. Using the KITTI data set considering the positive definite metric. 2. Using the KITTI data set considering the anisotropic metric. 3. Using the KITTI data set, considering the biased infinity Laplacian and the anisotropic metric. 4. Using the KITTI data set, considering the double biased infinity Laplacian and the anisotropic metric. 5. Using NYU_V2 downsampled 4\(\times\) considering the positive definite metric. 6. Using NYU_V2 downsampled 4\(\times\) considering the anisotropic metric. 7. Using NYU_V2 downsampled 8\(\times\) considering the positive definite metric. 8. Using NYU_V2 downsampled 8\(\times\) considering the anisotropic metric. 9. Using NYU_V2 downsampled 16\(\times\) considering the positive definite metric. 10. Using NYU_V2 downsampled 16\(\times\) considering the anisotropic metric. 11. Using the KITTI data set, we varied the number of images in the training set considering the anisotropic metric. Considering each trained model from **(1)** to **(12)**, we performed the experiments on the KITTI and NYU_V2 data sets, as summarized in Table 5. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Experiment** & **Used Metric** & **Training Set** & **Experiment** \\
**Number** & & & & \\ \hline \hline
1 & positive definite & KITTI training set & Interpolation of the complete KITTI \\  & Metric & & data set \\  & & & & data set \\
2 & anisotropic metric & KITTI training set & Interpolation of the complete KITTI \\  & & & data set \\
3 &
\begin{tabular}{c} anisotropic metric + \\ biased infinity \\ Laplacian \\ \end{tabular} & KITTI training set & Interpolation of the complete KITTI \\  & & & data set \\
4 & \
\begin{tabular}{c} double biased infinity \\ Laplacian \\ \end{tabular} & KITTI training set &
\begin{tabular}{c} Interpolation of the complete KITTI \\ data set \\ data set \\ \end{tabular} \\  & & & data set \\
5 & \begin{tabular}{c} positive definite \\ Metric \\ \end{tabular} & \
\begin{tabular}{c} NYU\_V2 4\(\times\) training \\ set \\ \end{tabular} &
\begin{tabular}{c} UPSampling of the \\ complete NYU\_V2 \\ 4\(\times\) data set \\ \end{tabular} \\  & & & & 4\(\times\) data set \\
6 & \begin{tabular}{c} Anisotropic Metric \\ set \\ \end{tabular} & \
\begin{tabular}{c} NYU\_V2 4\(\times\) training \\ set \\ \end{tabular} &
\begin{tabular}{c} UPSampling of the \\ complete NYU\_V2 \\ 4\(\times\) data set \\ \end{tabular} \\  & & & & 10\(\times\) data set \\
7 & \begin{tabular}{c} positive definite \\ Metric \\ \end{tabular} & \
\begin{tabular}{c} NYU\_V2 8\(\times\) training \\ set \\ \end{tabular} &
\begin{tabular}{c} UPSampling of the \\ complete NYU\_V2 \\ 8\(\times\) data set \\ \end{tabular} \\  & & & & 8\(\times\) data set \\
8 & \begin{tabular}{c} Anisotropic Metric \\ \end{tabular} & \
\begin{tabular}{c} NYU\_V2 16\(\times\) \\ training set \\ \end{tabular} &
\begin{tabular}{c} UPSampling of the \\ complete NYU\_V2 \\ 16\(\times\) data set \\ \end{tabular} \\  & & & & 10\(\times\) data set \\
10 & \begin{tabular}{c} Anisotropic Metric \\ \end{tabular} & \
\begin{tabular}{c} NYU\_V2 16\(\times\) \\ training set \\ \end{tabular} &
\begin{tabular}{c} UPSampling of the \\ complete NYU\_V2 \\ 16\(\times\) data set \\ Interpolation of the \\ complete KITTI data \\ \end{tabular} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Experiments performed with our model in order to obtain MSE + MAE. Figure 11 shows an example of the subsampled depth map. In Figure 11, we show the ground truth acquired with a Kinect sensor. In Figure 11, we show the subsampled depth map; we took one sample every other \(8\times 8\) square pixel. Figure 11 shows a cropped area of Figure 11 and a subsampled version of Figure 11.  
Experiment number 11 considers a varying number of images in the training set. We trained the model using sets containing 3 to 18 images. In Figure 12, we show the \(MSE+MAE\) error for different numbers of images.