Learning Day 70: 3D U-Net with 3D convolution layers, V-Net, DenseNet, FC-DenseNet

Background

• Continue from Day 69 regarding U-Net, one problem with biomedical imaging is that different slices at different locations would appear very differently, thus U-Net is not able to identify the target region
• What if we directly feed the 3D data into a U-Net?

3D U-Net

• It employs 3D convolution layers to take in 3-dimension imaging data
• Besides 3D conv layers, the principle of 3D U-Net is very similar to U-Net

3D U-Net architecture (ref)

3D convolution

• It is very similar to 2D convolution, just that we need to imagine 1 more dimension
• A 2D convolution operation

An illustration of a 2D convolution operation

• A 3D convolution operation with a 3D input of 1 input channel

Single-channel 3D input with a 3D filter

• A 3D convolution operation with 3D input of input channel, c = 3. In this case, the input is actually 4-dimension. The filter is 5-dimension.

3-channel 3D input (4-dimension) with 3 x 3-channel 3D filter (5-dimension)

V-Net

• Added ResNet-like shortcut
• Same loss function (DICE coefficient)
• Include “down” conv layer (conv with stride=2)
• Make use of 1x1x1 conv layer prior to softmax for classification between background and foreground
• PReLU activation where the gradient at y<0, a, is learnable

ReLU (left), Leaky ReLU (middle) and PReLU (right) (ref)

V-Net architecture (ref)

DenseNet

• Focus on fully utilising the feature maps
• Reduce the no. of parameters
• Not prone to overfitting even for small dataset
• There are extra connections between all layers. I.e. Current layer’s input includes outputs from all previous layer
• Eg. Input X0 →Output H1, Input X0 &X1 →Output H2

An illustration of a dense block (ref)

FC-DenseNet

• The architecture is still similar to U-Net
• Just replace the original conv blocks withe dense block
• Skip connections exist only at the scaling down side (left), not at the scaling up side (right) of the network
• Skip connections are to avoid feature loss

An illustration of FC-DenseNet architecture (ref)

Reference

Unless otherwise stated, all presented contents are summarised from this course for personal learning purposes