# Differential and integral invariants under Mobius transformation

arXiv: https://arxiv.org/abs/1808.10083 · HTML: https://mlsanity.com/paper/1808.10083/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2018.

## Built on by (most cited first, 2 of 2)

- [Dynamic Graph Unlearning: A General and Efficient Post-Processing Method via Gradient Transformation](https://mlsanity.com/paper/2405.14407/) (2024)
- [A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation](https://mlsanity.com/paper/2103.14799/) (2021)

## Abstract (arXiv)

One of the most challenging problems in the domain of 2-D image or 3-D shape is to handle the non-rigid deformation. From the perspective of transformation groups, the conformal transformation is a key part of the diffeomorphism. According to the Liouville Theorem, an important part of the conformal transformation is the Mobius transformation, so we focus on Mobius transformation and propose two differential expressions that are invariable under 2-D and 3-D Mobius transformation respectively. Next, we analyze the absoluteness and relativity of invariance on them and their components. After that, we propose integral invariants under Mobius transformation based on the two differential expressions. Finally, we propose a conjecture about the structure of differential invariants under conformal transformation according to our observation on the composition of the above two differential invariants.