# Spot the Difference: Detection of Topological Changes via Geometric Alignment

arXiv: https://arxiv.org/abs/2106.08233 · HTML: https://mlsanity.com/paper/2106.08233/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 22 of its 54 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 22 of 22)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [U-Net: Convolutional Networks for Biomedical Image Segmentation](https://mlsanity.com/paper/1505.04597/) (2015)
- [Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift](https://mlsanity.com/paper/1502.03167/) (2015)
- [Variational Inference with Normalizing Flows](https://mlsanity.com/paper/1505.05770/) (2015)
- [Spatial Transformer Networks](https://mlsanity.com/paper/1506.02025/) (2015)
- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [VoxelMorph: A Learning Framework for Deformable Medical Image Registration](https://mlsanity.com/paper/1809.05231/) (2018)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Identifying the Best Machine Learning Algorithms for Brain Tumor Segmentation, Progression Assessment, and Overall Survival Prediction in the BRATS Challenge](https://mlsanity.com/paper/1811.02629/) (2018)
- [Optimal Transport for Domain Adaptation](https://mlsanity.com/paper/1507.00504/) (2015)
- [Unsupervised Learning for Fast Probabilistic Diffeomorphic Registration](https://mlsanity.com/paper/1805.04605/) (2018)
- [Quicksilver: Fast Predictive Image Registration - a Deep Learning Approach](https://mlsanity.com/paper/1703.10908/) (2017)
- [Occlusion Aware Unsupervised Learning of Optical Flow](https://mlsanity.com/paper/1711.05890/) (2017)
- [SurVAE Flows: Surjections to Bridge the Gap between VAEs and Flows](https://mlsanity.com/paper/2007.02731/) (2020)
- [Dreaming More Data: Class-dependent Distributions over Diffeomorphisms for Learned Data Augmentation](https://mlsanity.com/paper/1510.02795/) (2015)
- [Probabilistic Multilayer Regularization Network for Unsupervised 3D Brain Image Registration](https://mlsanity.com/paper/1907.01922/) (2019)
- [Self-Supervised Out-of-Distribution Detection in Brain CT Scans](https://mlsanity.com/paper/2011.05428/) (2020)
- [A Deep Network for Joint Registration and Reconstruction of Images with Pathologies](https://mlsanity.com/paper/2008.07628/) (2020)
- [Semantic similarity metrics for learned image registration](https://mlsanity.com/paper/2104.10051/) (2021)
- [Brain Extraction from Normal and Pathological Images: A Joint PCA/Image-Reconstruction Approach](https://mlsanity.com/paper/1711.05702/) (2017)
- [Efficient Registration of Pathological Images: A Joint PCA/Image-Reconstruction Approach](https://mlsanity.com/paper/1704.00036/) (2017)
- [Tackling the Problem of Large Deformations in Deep Learning Based Medical Image Registration Using Displacement Embeddings](https://mlsanity.com/paper/2005.13338/) (2020)

## Abstract (arXiv)

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 algorithm for the detection of changes in image topology. The model is based on a conditional variational auto-encoder and detects topological changes between two images during the registration step. We account for both topological changes in the image under spatial variation and unexpected transformations. Our approach is validated on two tasks and datasets: detection of topological changes in microscopy images of cells, and unsupervised anomaly detection brain imaging.