tests.

Hard Mining [@simo2015discriminative] only trains the hardest samples with the largest hinge loss and thus also speeds up training. However, the percentage of samples trained in each batch is fixed and does not adapt to the requirements of the training data like in our approach. With our data, Hard Mining becomes unstable with a mining factor above 2 i.e. the loss of negative samples becomes much larger than the loss of positive samples. This leads to poor performance ($r = 96.61\%$ for Hard Mining x4). We think this has to do with the fact that the hardest of our negative samples are much harder to train than the hardest positive samples. Some patches are e.g. fully white due to overexposure (negative training has no effect here). Also, many of our negative samples have, in contrast to the samples of [@simo2015discriminative], a very small spatial distance to their positive counterpart. This makes their training even harder (We report most failures for small distances, see supplementary material), while positive samples do not change.

![ The distribution of $L_2$ errors for different for $L_t$ and $L_g$ for positive samples $p^+_2$ and negative samples $p^-_2$ with distance of 10 pixels to the corresponding 