that it extracts local depth information, and therefore, the existence of depth discontinuities does not affect the estimation on the smooth portion of the face. This is illustrated in Figure \[fig:depth\_extraction\_verification\] (a)-(b), where a larger facial patch is fed into the network. The decomposition module is composed exclusively of convolutional layers, and therefore, images of arbitrary size can be evaluated. Figure \[fig:depth\_extraction\_verification\]-(a) shows the input to the network, and Figure \[fig:depth\_extraction\_verification\]-(b) the first channel of the output (for compactness we display only the x-partial derivative). As we can see, the existence of depth discontinuities does not affect the prediction in the interior of the face (we consider the prediction outside this region as noise and we replace it by $0$ for visualization).

![Is the network really extracting depth information? In this figure we show the output of the network for two inputs generated using identical facial texture but different depth ground truth data. (a) Image obtained when the projected pattern is projected over the face with the real texture and the real 3D profile. (b) Output of the network when we input (a) (only the x-partial derivative is displayed for compactness). (c) Image obtained when the projected pattern is projected 