
\section{Introduction}
\label{sec:intro}

Due to the increased prevalence of neurodegenerative diseases and their effects on cognitive function, the study of such diseases is a highly active research field. As the leading cause of dementia~\cite{alzheimer_dementia}, Alzheimer's disease (AD) is a particular focus of research advancements. However, the complex pathogenesis and progression mechanisms of AD remain only partially understood. 

Magnetic resonance imaging (MRI) has shown use in the non-invasive tracking of AD-associated brain changes, such as hippocampal and amygdala atrophy and ventricular dilation~\cite{alzheimer,10.1002/jmri.21049}. Notably, several supervised machine learning methods utilizing MRI have been proposed which yield improvements in AD identification~\cite{supervised1,supervised2,supervised4}. However, such methods are restricted by the need for large, annotated data sets. In contrast, unsupervised anomaly detection techniques~\cite{chen2018unsupervised,ganomaly,fanogan,zimmerer_uad} offer a promising solution by modeling the distribution of healthy brain images to identify and localize anomalies without relying on labeled data. 

Nevertheless, unsupervised approaches face challenges in accurately analyzing structural abnormalities, particularly regions of atrophy, which are critical in AD research~\cite{bercea2022ra}. Classical techniques using multi atlas-based deformable registration~\cite{koikkalainen2011multi} and morphometry methods~\cite{deformation-based-morph,deformation-based-morph-2} have been proposed to analyze these structural changes. However, such methods allow analysis to be conducted only on a population-level, for instance as deviations from an atlas.

In this work, we propose Morphological Autoencoders for Alzheimer’s Disease Detection (\textit{MORPHADE}), a novel unsupervised anomaly detection framework based on deformable autoencoders (AEs) ~\cite{bercea2023aes} which leverages deformation networks to generate patient-specific anomaly maps from 3D T1-weighted MRI brain scans. These anomaly maps allow not only AD detection, but also crucially reveal the location and degree of atrophy. Our main contributions are as follows:
\begin{itemize}
    \item We use deformation fields in an unsupervised framework to analyze AD-related changes in the brain. To the best of our knowledge, this is the first use of such an approach using deep learning in the context of AD.
    \item We extend deformable autoencoders to 3D, utilize adversarial training and propose a dual-deformation strategy to improve reconstruction fidelity and the localization of atrophy.
    \item We accurately identify AD-affected brain regions, aligning our findings with clinical expectations.
    \item We assess AD severity by correlating our findings with clinical medial temporal lobe atrophy scores, evaluated by a board-certified clinical expert.
    \item Through comprehensive validation, we demonstrate superior performance in AD detection compared to unsupervised and even supervised baselines.
\end{itemize}




