# Cross-Domain Echocardiography Segmentation with Multi-Space Joint Adaptation
## 1 Introduction  
Cardiovascular disease (CVD) is the leading cause of death among adults worldwide. Echocardiography, the non-invasive imaging inspection tool, is widely applied in the clinical routine of CVDs [1]. The analysis of echocardiography is often used clinically for appraising cardiac morphology and function. For example, the ejection fraction (EF) [2] of the left ventricle (LV) is one of the famous clinical indices to quantify the LV systolic function. The LVEF can be calculated by the volume of the left ventricle. The width of the left ventricular myocardium also contains pathological information. The exact segmentation of the left ventricle endocardium (LV\({}_{\text{endo}}\)) and the left ventricle epicardium (LV\({}_{\text{epi}}\)) provides the clinical quantitative measures mentioned above. However, manual echocardiography labeling requires a doctor with rich clinical expertise to spend a lot of time, which seriously affects diagnostic efficiency. Smart health [3, 4] can assist clinical diagnosis, such as automatic echocardiography segmentation. Automatic echocardiography segmentation remains an unresolved challenge due to the low signal-to-noise ratio and low contrast. The boundaries between anatomical structures are ambiguous and sometimes missing in echocardiography, and the performance of traditional segmentation methods [5, 6] is not satisfactory. The development of deep learning [1, 7] has promoted automatic echocardiography segmentation. The U-Net [8] has provided a good idea for medical image segmentation. Further, the RU-Net [9] merges two U-Nets as an attention mechanism to obtain the region of interest (ROI) in the image. The first U-Net is used for preprocessing to simplify the ultrasound image, and the second U-Net is corrected on this basis in order to producethe final segmentation result. Then, the Res-U [10] network couples the advantages of the ResNet and U-Net to denoise the ultrasound images. More recently, some methods have adopted echocardiography prior knowledge to help with LV segmentation. The anatomical constrained neural network (ACNN) [11] incorporates the prior knowledge of the heart anatomy structures to enhance the constraints on the segmentation boundaries. [PERSON] et al. [12] propose a network that combines deep learning and a shape-driven deformable model for LV segmentation. [PERSON] et al. [13] propose the multi-constraint aggregation learning (MCAL), which judges the boundary by anatomical knowledge and gives the boundary region a higher weight. [PERSON] et al. [14] deform illogical results with a variational autoencoder that learns the cardiac shape. Ensemble learning also plays a role in echocardiography segmentation. The TRSA-Net [15] adopts an innovative co-attention learning structure for both segmentation and quantification tasks. The CLAS [16] achieves temporal-consistent segmentation on echocardiographic sequences with co-learning from the appearance and shape. As a result of the diverse imaging devices and imaging protocols, echocardiography datasets are greatly different from each other in domain styles, such as grayscale distribution. Figure 1 shows an example of echocardiography from diverse centers. These images are inconsistent in the grayscale distribution and spatial texture. This discrepancy causes the segmentation network trained on one dataset (source domain) to not be able to exert effectively on another dataset (target domain) directly. This problem is expected to be mitigated via unsupervised domain adaptation, i.e., unpaired image-to-image translation. It causes one domain image to be visually similar to another domain image, while preserving the content information in the source images. Domain adaptation models based on the generative adversarial network (GAN) have been widely used in natural image processing. The SAGAN for image-to-image translation [17] introduces a self-attention network to the GAN and bidirectionally translates the style feature with the global information.