In a Fully Convolutional Network (FCN), different layers require specific initialization strategies to optimally support spatial predictions. The transposed convolutional layer, which is responsible for upsampling the feature maps back to the original input image size, is initialized using the upsampling of bilinear interpolation (e.g., via a bilinear kernel). Conversely, the $$1 \times 1$$ convolutional layer, which transforms the number of channels to correspond to the target classes, is initialized using Xavier initialization.

```python
# PyTorch
W = bilinear_kernel(num_classes, num_classes, 64)
net.transpose_conv.weight.data.copy_(W)
```

```python
# MXNet
W = bilinear_kernel(num_classes, num_classes, 64)
net[-1].initialize(init.Constant(W))
net[-2].initialize(init=init.Xavier())
```

Claude

To restore the spatial dimensions of feature maps to the original input image size in a Fully Convolutional Network (FCN), a transposed convolutional layer is employed. If the spatial dimensions need to be increased by a factor of $$s$$, the transposed convolution is configured with a stride of $$s$$. To achieve the exact original dimensions, the padding is set to $$s/2$$ (assuming $$s/2$$ is an integer), and the height and width of the convolution kernel are set to $$2s$$. For instance, to upscale a feature map by $$32$$ times, the stride is $$32$$, the padding is $$16$$, and the kernel size is $$64$$.

```python
# PyTorch
net.add_module('transpose_conv', nn.ConvTranspose2d(num_classes, num_classes,
                                    kernel_size=64, padding=16, stride=32))
```

```python
# MXNet
net.add(nn.Conv2DTranspose(num_classes, kernel_size=64, padding=16, strides=32))
```

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