# Ricci flow-based brain surface covariance descriptors for diagnosing Alzheimer's disease

arXiv: https://arxiv.org/abs/2403.06645 · HTML: https://mlsanity.com/paper/2403.06645/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 51 references that are in the map.
- First posted on arXiv 11 Mar 2024.

## Builds on (most cited first, 6 of 6)

- [Community Detection on Networks with Ricci Flow](https://mlsanity.com/paper/1907.03993/) (2019)
- [Multimodal Representations Learning and Adversarial Hypergraph Fusion for Early Alzheimer's Disease Prediction](https://mlsanity.com/paper/2107.09928/) (2021)
- [Characterization Multimodal Connectivity of Brain Network by Hypergraph GAN for Alzheimer's Disease Analysis](https://mlsanity.com/paper/2107.09953/) (2021)
- [Morphological feature visualization of Alzheimer's disease via Multidirectional Perception GAN](https://mlsanity.com/paper/2111.12886/) (2021)
- [Spherical Parameterization Balancing Angle and Area Distortions](https://mlsanity.com/paper/1810.09031/) (2018)
- [CAMEL: Curvature-Augmented Manifold Embedding and Learning](https://mlsanity.com/paper/2303.02561/) (2023)

## Built on by (most cited first, 3 of 3)

- [Covariance Descriptors Meet General Vision Encoders: Riemannian Deep Learning for Medical Image Classification](https://mlsanity.com/paper/2511.04190/) (2025)
- [MicroRicci: A Greedy and Local Ricci Flow Solver for Self-Tuning Mesh Smoothing](https://mlsanity.com/paper/2506.15571/) (2025)
- [Entropy-Enhanced Conformal Features from Ricci Flow for Robust Alzheimer's Disease Classification](https://mlsanity.com/paper/2510.18396/) (2025)

## Abstract (arXiv)

Automated feature extraction from MRI brain scans and diagnosis of Alzheimer's disease are ongoing challenges. With advances in 3D imaging technology, 3D data acquisition is becoming more viable and efficient than its 2D counterpart. Rather than using feature-based vectors, in this paper, for the first time, we suggest a pipeline to extract novel covariance-based descriptors from the cortical surface using the Ricci energy optimization. The covariance descriptors are components of the nonlinear manifold of symmetric positive-definite matrices, thus we focus on using the Gaussian radial basis function to apply manifold-based classification to the 3D shape problem. Applying this novel signature to the analysis of abnormal cortical brain morphometry allows for diagnosing Alzheimer's disease. Experimental studies performed on about two hundred 3D MRI brain models, gathered from Alzheimer's Disease Neuroimaging Initiative (ADNI) dataset demonstrate the effectiveness of our descriptors in achieving remarkable classification accuracy.