# Image Projective Invariants

arXiv: https://arxiv.org/abs/1707.05950 · HTML: https://mlsanity.com/paper/1707.05950/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Jul 2017.

## Built on by (most cited first, 4 of 4)

- [A Survey of Orthogonal Moments for Image Representation: Theory, Implementation, and Evaluation](https://mlsanity.com/paper/2103.14799/) (2021)
- [Gaussian-Hermite Moment Invariants of General Multi-Channel Functions](https://mlsanity.com/paper/2201.00877/) (2022)
- [Image Moment Invariants to Rotational Motion Blur](https://mlsanity.com/paper/2303.14566/) (2023)
- [Entropy Transformer Networks: A Learning Approach via Tangent Bundle Data Manifold](https://mlsanity.com/paper/2307.12517/) (2023)

## Abstract (arXiv)

In this paper, we propose relative projective differential invariants (RPDIs) which are invariant to general projective transformations. By using RPDIs and the structural frame of integral invariant, projective weighted moment invariants (PIs) can be constructed very easily. It is first proved that a kind of projective invariants exists in terms of weighted integration of images, with relative differential invariants as the weight functions. Then, some simple instances of PIs are given. In order to ensure the stability and discriminability of PIs, we discuss how to calculate partial derivatives of discrete images more accurately. Since the number of pixels in discrete images before and after the geometric transformation may be different, we design the method to normalize the number of pixels. These ways enhance the performance of PIs. Finally, we carry out some experiments based on synthetic and real image datasets. We choose commonly used moment invariants for comparison. The results indicate that PIs have better performance than other moment invariants in image retrieval and classification. With PIs, one can compare the similarity between images under the projective transformation without knowing the parameters of the transformation, which provides a good tool to shape analysis in image processing, computer vision and pattern recognition.