Image Projective Invariants

TL;DR

This paper introduces relative projective differential invariants (RPDIs) and projective weighted moment invariants (PIs) that are invariant under projective transformations, improving image retrieval and classification accuracy without needing transformation parameters.

Contribution

The paper presents a novel class of projective invariants based on RPDIs and integral invariants, with methods to enhance their stability and discriminability in discrete images.

Findings

PIs outperform traditional moment invariants in image retrieval.

The proposed invariants are stable and discriminative under projective transformations.

Experiments confirm improved classification accuracy using PIs.

Abstract

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.