\lambda {\bigg( {\Big\Vert \nabla D\Big(   \alpha I_C + (1-\alpha) I_{TD}  \Big) \Big\Vert}_2-1 \bigg)}^2,$$ where $\alpha$ is a randomly generated number from uniform distribution $U[0,1]$. Since there is no pre-trained model involved in the generator network $G$, the whole training takes a long time and the loss blows up. In order to further enforce the $1$-Lipschitz assumption in the critic network $D$, we further impose the weight constraint $\lambda$. The weight is clipped in the interval $[-c, c]$. Together with this weight constraint, the training becomes more stable.

![The generator network $G$ has the U-net architecture, and the critic network $D$ is the conventional convolutional neural network. The subsampled frames are concatenated before passing through the generator network.[]{data-label="fig:net"}](G_net.png "fig:") ![The generator network $G$ has the U-net architecture, and the critic network $D$ is the conventional convolutional neural network. The subsampled frames are concatenated before passing through the generator network.[]{data-label="fig:net"}](D_net.png "fig:")

Experiments
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Dataset
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The dataset for training is collected from Flicker. It consists of 1500 images of buildings and 1000 images of chimneys. All collected images are resized to 256x256 and are synthetically deformed by our data augmentation algorithm. More specifically, each image is deformed to produce 100 deformed video 