Topological Analysis of Image Reconstruction Based on Polar Complex Exponential Transform

Abstract

Image moments are an important tool used for image reconstruction. An image can be represented in terms of image moments, which is known as image reconstruction from its moments. To construct an image from the moments, a question often arises that how many moments are required for the reconstruction of image. Theoretically, many image moments may be required for accurately reconstructing an image. However, since image moment construction can be computationally challenging, often in practice only a finite number of moments are used for the image reconstruction. The difference in reconstructed and original image for many numbers of images can lead to a satisfying answer. However, accurate reconstruction may not often be possible, and we are often relying on other approaches to find similarity between the original image and reconstructed image. We used a similarity based on a topological data analysis tool known as the persistence diagram, determining the bottleneck distance between the original and the reconstructed image as the measure of similarity. Our investigation was conducted on the common images utilized in image processing tasks. The findings indicate that there is no direct correlation between the number of moments and the quality of image reconstruction. It is necessary to choose an appropriate number of moments, which may be very small, instead of calculating a high number of image moments.

Received: 30 April 2024 | Revised: 2 July 2024 | Accepted: 29 July 2024

Conflicts of Interest

The authors declare that they have no conflicts of interest to this work.

Data Availability Statement

Data sharing is not applicable to this article as no new data were created or analyzed in this study.

Author Contribution Statement

Manoj Kumar Singh: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Visualization, Project administration. Deepika Saini: Conceptualization, Methodology, Validation, Formal analysis, Investigation, Resources, Data curation, Writing – original draft, Writing – review & editing, Visualization. Sanoj Kumar: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Resources, Writing – original draft, Writing – review & editing, Visualization, Supervision, Project administration.