# BRUL`E: Barycenter-Regularized Unsupervised Landmark Extraction

arXiv: https://arxiv.org/abs/2006.11643 · HTML: https://mlsanity.com/paper/2006.11643/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 20 Jun 2020.

## Built on by (most cited first, 5 of 5)

- [Align Your Intents: Offline Imitation Learning via Optimal Transport](https://mlsanity.com/paper/2402.13037/) (2024)
- [Optimal MRI Undersampling Patterns for Ultimate Benefit of Medical Vision Tasks](https://mlsanity.com/paper/2108.04914/) (2021)
- [ENOT: Expectile Regularization for Fast and Accurate Training of Neural Optimal Transport](https://mlsanity.com/paper/2403.03777/) (2024)
- [Landmarks Augmentation with Manifold-Barycentric Oversampling](https://mlsanity.com/paper/2104.00925/) (2021)
- [Unsupervised Landmark Discovery Using Consistency Guided Bottleneck](https://mlsanity.com/paper/2309.10518/) (2023)

## Abstract (arXiv)

Unsupervised retrieval of image features is vital for many computer vision tasks where the annotation is missing or scarce. In this work, we propose a new unsupervised approach to detect the landmarks in images, validating it on the popular task of human face key-points extraction. The method is based on the idea of auto-encoding the wanted landmarks in the latent space while discarding the non-essential information (and effectively preserving the interpretability). The interpretable latent space representation (the bottleneck containing nothing but the wanted key-points) is achieved by a new two-step regularization approach. The first regularization step evaluates transport distance from a given set of landmarks to some average value (the barycenter by Wasserstein distance). The second regularization step controls deviations from the barycenter by applying random geometric deformations synchronously to the initial image and to the encoded landmarks. We demonstrate the effectiveness of the approach both in unsupervised and semi-supervised training scenarios using 300-W, CelebA, and MAFL datasets. The proposed regularization paradigm is shown to prevent overfitting, and the detection quality is shown to improve beyond the state-of-the-art face models.