## 1 Introduction
### Overview of the Proposed Method  
To further address some of the shortcomings associated with existing methods, our efforts focus on learning meaningful spatial features utilizing a disentangler with a mutual information minimizer (MIM) to improve the adversarially trained generative models for improving semi-supervised segmentation and reconstruction results. Our proposed method builds on several recent and key research findings in the fields of generative models, semi-supervised learning, and representation learning via disentanglement. We believe that the proposed framework's reliance on as little as 1% labeled data for training, in concert with the high segmentation accuracy achieved, comparable to the fully or semi-supervised models, renders the proposed work an attractive solution for medical image segmentation, where access to vast expert-annotated data is expensive and often difficult to gain access to. We approach this problem using a method that is based on disentangled representations and utilizes data from multiple scanners with varying intensities and contrast (Figure 1). Our method is intended to address multi-scanner unlabeled-data issues, such as intensity differences, and a lack of sufficient annotated data. Learning good data representations for medical imaging tasks ensures the preservation of relevant information and the removal of irrelevant information from the data to improve the interpretability of the learned features. Our model disentangles the input image into spatial and non-spatial space. These spatial features are represented as categorical feature maps, with each category corresponding to input pixels that are spatially similar and are from the same organ part. This semantic similarity aids in learning to be generalized the anatomical representation to any modality from different scanners. Furthermore, the non-spatial features capture the image's global intensity information, which aids the renderer in painting the anatomy in the reconstructed image. Finally, because annotating data is time-consuming and expensive, the ability to learn this decomposition through disentanglement using a small number of labels is critical in medical image analysis. In light of these needs, here we propose a semi-supervised (C\({}_{d}\)SL) model for learning disentangled representations that combines recent developments in semi-supervised learning-generative models and adversarial learning. We aim to factorize the representation of an image pair into two parts: a shared representation that captures the common information between images and an exclusive representation that contains the specific information of each image. Furthermore, in order to achieve representation disentanglement, we propose to minimize mutual information between shared and exclusive representations. Moreover, we use feature-wise linear modulation (FiLM) [38] to distinguish the domain-invariant information from the domain-specific information, as well as a spatially adaptive normalization (SPADE) [39]-based decoder to guide the synthesis of more texture information to restrain the posterior collapse of the VAE and spatial information. To illustrate its adequacy, our model is applied to two of the foremost critical tasks in medical imaging--segmentation of cardiac structures and reconstruction of the original image--and both assignments are handled by the same model. Our model leverages a large amount of unannotated data from the ACDC ([[https://www.creatis.insa-lyon.fr/Challenge/acdc/databases.html](https://www.creatis.insa-lyon.fr/Challenge/acdc/databases.html)]([https://www.creatis.insa-lyon.fr/Challenge/acdc/databases.html](https://www.creatis.insa-lyon.fr/Challenge/acdc/databases.html)), accessed on 2 October 2021) dataset to learn the interpretable representations through judicious choices of common factors that serve as strong prior knowledge for more complicated problems--the segmentation of cardiac structures. Figure 2 shows a simplified data view of our proposed model.