## 2 Methods
### Experiments
#### 2.3.2 Implementation Details  
**Input:** All the cine cardiac images employed slice-wise normalization in the range \([0,1]\) by subtracting the mean slice intensity from each pixel intensity, then dividing it by the difference between the maximum and minimum slice intensity. All images were resampled to 1.37 mm\({}^{2}\)/pixel. Images were cropped to \(192\times 192\times 1\) pixels before feeding to the models. We applied data augmentation on-the-fly during training as shown in Figure 7, which includes random rotations up to 90 degrees, random zooms up to 20%, random horizontal shifts up to 20%, random horizontal and/or vertical flips, and noise addition (Figure 7). **Baselines Architecture:** As the disentangled encoder in the skeletal block, we use a modified U-Net-like architecture, EPU-Net++, and as a sentiency encoder, we use VAE. As the reconstruction block, we use FiLM- and SPADE-based decoder as used in [49]. **Generator-Discriminator Network:** Our segmentation generator network consists of 3 convolution layers with \(3\times 3\) kernel and {64, 64, 1} channels in the stride of 1. Each convolution layer is followed by a batch normalization [50] layer along with a LeakyReLU [51] except the last layer. We use the structure similar to DCGAN [52] for the discriminator network. **EvoNorm-Projection skip connections:** In our skeleton encoder, we replace the standard skip connection with a normalized-projection operation using \(EvoNorm2D+1\times 1-Conv+Gaussian-dropout\), as in Figure 4. This new normalization layer adds together two types of statistical moments-batch variance, and instance variance, both of which capture both the global and local information across images without having any explicit activation function [53]. The proposed projection operation helps in reducing the learnable weights and also allows intricate learnability of cross-channel information. **Additional Factors:** The performance of semi-supervised models trained for image segmentation can be significantly impacted by the proper selection of regularizer, optimizer, and hyper-parameters. The model implemented in Keras was initialized with the He normal initializer and trained for 100 epochs with a batch size of 4. We trained all the components iteratively with the Adam optimizer with a 0.0001 learning rate to minimize the objective function. All experiments were conducted on a machine equipped with two NVIDIA RTX 2080 Ti GPU (each 11 GBs memory). The detailed training procedure is presented in Algorithm 1. **Training:** In our semi-supervised setup, we trained the network on varying proportions of labeled data: 1%, 10%, 20%, 30%, 50%, and 90% as a labeled set and used the rest of the data as the training unlabeled set to hold \(|\mathcal{D}_{\mathcal{L}}|\leq|\mathcal{D}_{\mathcal{UL}}|\). In Section 3, we include an ablation study to investigate the importance of adding different loss components in our model \(\mathcal{C}\)_f_SL which is comprised of all the three loss functions: WSBF, MIM, Adv-GM. (Definitions are provided in Sections 2.1.2 and 2.1.3.) We experimented an ablation study containing four of the variants of our proposed model \(\mathcal{C}\)_f_SL. The variants are described as follows: \({}^{1}\)C_f_SL, without weighted-soft focal loss (WSFL); \({}^{2}\)C_f_SL, without adversarial-Geman-McClure loss (Adv-GM); \({}^{3}\)C_f_SL, dice and cross-entropy loss only; and \({}^{4}\)C_f_SL, without mutual information minimizer loss (MIM). Here, we utilize the same backbones as the baselines with the only exceptions being different loss functions. To clarify our point, in \({}^{1}\)C_f_SL, we removed the weighted soft focal loss (WSFL) from the weighted soft background focal loss (WSBF), while keeping the background focal dice loss (BFD), mutual information minimizer loss (MIM) and adversarial-Geman-McClure (adv-GM) the same as before.