Spot the Difference: Topological Anomaly Detection via Geometric Alignment

Geometric alignment appears in a variety of applications, ranging from domain adaptation, optimal transport, and normalizing flows in machine learning; optical flow and learned augmentation in computer vision and deformable registration within biomedical imaging. A recurring challenge is the alignment of domains whose topology is not the same; a problem that is routinely ignored, potentially introducing bias in downstream analysis. As a first step towards solving such alignment problems, we propose an unsupervised topological difference detection algorithm. The model is based on a conditional variational auto-encoder and detects topological anomalies with regards to a reference alongside the registration step. We consider both a) topological changes in the image under spatial variation and b) unexpected transformations. Our approach is validated on a proxy task of unsupervised anomaly detection in images.