# Benchmarking Anomaly Detection Methods for Extacardiac Findings in Cardiac MRI
## 2 Related Work  
Anomaly detection methods can be categorized based on their learning principles into unsupervised, semi-supervised, and open-set supervised approaches (Figure 1) [10]. Unsupervised AD methods, the most prevalent category, use a curated dataset comprising only normal images to model the normal class, detecting anomalies as deviations from this learned distribution without supervision on what constitutes an anomaly [18; 23; 34]. In contrast, semi-supervised AD methods incorporate normal, abnormal, and unlabeled samples to define a compact cluster representing normality [23; 35]. Within this category, one-class semi-supervised AD methods rely exclusively on normal and unlabeled samples [23]. Finally, open-set supervised methods utilize labeled normal and abnormal samples by combining supervised with unsupervised mechanisms. They may use abnormal samples to either serve as negative samples to refine the modeling of the normal class distribution [33] or explicitly guide the model in recognizing abnormal patterns in images [27]. Given the broad range and diversity of the methods addressed in this study, the rest of this section provides a concise overview of the benchmarked AD methods, along with other relevant approaches from the literature. This overview is intended to provide sufficient background to understand the subsequent sections of the manuscript. For a more detailed explanation of the methods used in this work, the readers are referred to the original papers or relevant AD review articles. According to [18], unsupervised AD methods can be further divided into four categories: image reconstruction, feature modeling, attention-based, and self-supervised methods [18]. Image reconstruction methods typically employ autoencoder (AE) networks to learn the underlying data distribution while enforcing a low-dimensional latent space to prevent identity mappings. [PERSON] and [PERSON] [36] enhanced the regularization effect on these networks by introducing the variational autoencoder (VAE), modeling a likelihood distribution of the data conditioned on latent variables, which is simpler than explicitly modeling the data distribution. However, VAEs often produce blurry reconstructions, which prompted [PERSON] et al. [14] to developed a restoration framework, known as r-VAE, that selectively refines abnormal regions (i.e., those with low ELBO values) using maximum a posteriori estimation. This approach penalizes deviations from both the input image and a learned normality distribution. To further mitigate blurry reconstructions, generative adversarial networks (GANs) leverage adversarial loss to enhance image realism. In this context, [PERSON] et al. proposed anoGAN [37], which seeks to find the latent representation of the most similar normal and realistic version of the query image. This is achieved by optimizing a loss function that penalizes reconstruction errors and discrepancies in discriminator-based classification, where the discriminator is trained to distinguish normal from abnormal images based on similarity to the training data. Later, the same authors proposed f-anoGAN [38], a more efficient version that, instead of computing the latent representation through iteratively backpropagating the loss with frozen model parameters, directly maps the image to the latent space through an encoder network. They also adopted a Wasserstein GAN to enhance training stability and mitigate mode collapse. Beyond convolutional neural networks, [PERSON] et al. [15] introduced a hierarchical transformer AE network with skip connections (H-TAE-S), which enables simultaneous learning of local and global features by leveraging the long-range dependencies captured by transformer architectures. More recently, denoising diffusion probabilistic models (DDPMs) and diffusion models in general emerged as state-of-the-art techniques in image reconstruction. These  
Figure 1: Categories of AD methods and their respective training image setups. Adapted from [23].