I am trying to learn a piecewise affine transform model where the input images are converted via the transform into output data. One example transformation would be (first to second) –
 
The input images, are however, neither simple down samples with borders, nor distortion free rectangles, which is why I need piecewise affine transform to work.
I use the following code to “learn” the transform but obviously i am going wrong somewhere as the loss is stuck from the very first epoch( i use MSE loss)
class Net(nn.Module):

    def __init__(self):
        super(Net, self).__init__()
        # Spatial transformer localization-network
        self.localization = nn.Sequential(
            nn.Conv2d(3, 8, kernel_size=7),
            nn.MaxPool2d(2, stride=2),
            nn.ReLU(True),
            nn.Conv2d(8, 10, kernel_size=5),
            nn.MaxPool2d(2, stride=2),
            nn.MaxPool2d(2, stride=2),
            nn.ReLU(True)
        )

        # Regressor for the 3 * 2 affine matrix
        self.fc_loc = nn.Sequential(
            nn.Linear(10 * 30 * 30, 360),
            nn.ReLU(True),
            nn.Linear(360, 3 * 2)
        )

        # Initialize the weights/bias with identity transformation
        self.fc_loc[2].weight.data.zero_()
        

    # Spatial transformer network forward function
    def stn(self, x):

        xs = self.localization(x)
        xs = xs.view(-1, 30* 10 * 30)
        theta = self.fc_loc(xs)
        theta = theta.view(-1, 2, 3)
        
        grid = F.affine_grid(theta, x.size())
        print(x.shape)
        x = F.grid_sample(x, grid)
        return x

    def forward(self, x):
        # transform the input
        x = self.stn(x)


Code is heavily borrowed for the pytorch STN example as I first wanted to try out things before stepping it up.
Any help would be highly appreciated 
Edit:
This is the output from the model –

The loss is stuck as the output is same, no matter what the input 
Are there any constraints for defining the grid ? Something that maybe I can teach the model–which it would take a long time to learn by itself.