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Deep Convolutional Neural Networks (CNNs) i.e. Residual Networks (ResNets) have been used successfully for many computer vision tasks, but are difficult to scale to 3D volumetric medical data. Memory is increasingly often the bottleneck when training 3D Convolutional Neural Networks (CNNs). Recently, invertible neural networks have been applied to significantly reduce activation memory footprint when training neural networks with backpropagation thanks to the invertible functions that allow retrieving its input from its output without storing intermediate activations in memory to perform the backpropagation. Among many successful network architectures, 3D Unet has been established as a standard architecture for volumetric medical segmentation. Thus, we choose 3D Unet as a baseline for a non-invertible network and we then extend it with the invertible residual network. In this paper, we proposed two versions of the invertible Residual Network, namely Partially Invertible Residual Network (Partially-InvRes) and Fully Invertible Residual Network (Fully-InvRes). In Partially-InvRes, the invertible residual layer is defined by a technique called additive coupling whereas in Fully-InvRes, both invertible upsampling and downsampling operations are learned based on squeezing (known as pixel shuffle). Furthermore, to avoid the overfitting problem because of less training data, a variational auto-encoder (VAE) branch is added to reconstruct the input volumetric data itself. Our results indicate that by using partially/fully invertible networks as the central workhorse in volumetric segmentation, we not only reduce memory overhead but also achieve compatible segmentation performance compared against the non-invertible 3D Unet. We have demonstrated the proposed networks on various volumetric datasets such as iSeg 2019 and BraTS 2020.

Variational Level Set (VLS) has been a widely used method in medical segmentation. However, segmentation accuracy in the VLS method dramatically decreases when dealing with intervening factors such as lighting, shadows, colors, etc. Additionally, results are quite sensitive to initial settings and are highly dependent on the number of iterations. In order to address these limitations, the proposed method incorporates VLS into deep learning by defining a novel end-to-end trainable model called as Deep Recurrent Level Set (DRLS). The proposed DRLS consists of three layers, i.e, Convolutional layers, Deconvolutional layers with skip connections and LevelSet layers. Brain tumor segmentation is taken as an instant to illustrate the performance of the proposed DRLS. Convolutional layer learns visual representation of brain tumor at different scales. Since brain tumors occupy a small portion of the image, deconvolutional layers are designed with skip connections to obtain a high quality feature map. Level-Set Layer drives the contour towards the brain tumor. In each step, the Convolutional Layer is fed with the LevelSet map to obtain a brain tumor feature map. This in turn serves as input for the LevelSet layer in the next step. The experimental results have been obtained on BRATS2013, BRATS2015 and BRATS2017 datasets. The proposed DRLS model improves both computational time and segmentation accuracy when compared to the the classic VLS-based method. Additionally, a fully end-to-end system DRLS achieves state-of-the-art segmentation on brain tumors.