[Paper Review] Bi-Level Image Thresholding obtained by means of Kaniadakis Entropy

Amelia Carolina Sparavigna|arXiv (Cornell University)|Feb 16, 2015

Statistical Mechanics and Entropy13 references4 citations

TL;DR

This paper proposes a novel bi-level image thresholding method using Kaniadakis entropy within a maximum entropy framework, demonstrating that the entropic index governs a sharp 'image transition'—an abrupt change in thresholded image appearance. The approach outperforms Tsallis entropy in preserving image structure and enhancing segmentation clarity.

ABSTRACT

In this paper we are proposing the use of Kaniadakis entropy in the bi-level thresholding of images, in the framework of a maximum entropy principle. We discuss the role of its entropic index in determining the threshold and in driving an "image transition", that is, an abrupt transition in the appearance of the corresponding bi-level image. Some examples are proposed to illustrate the method and for comparing it to the approach which is using the Tsallis entropy.

Motivation & Objective

• To develop a new image thresholding method based on Kaniadakis entropy for improved segmentation accuracy.
• To investigate the role of the entropic index in controlling the thresholding process and image appearance.
• To enable a distinct 'image transition'—an abrupt change in thresholded image quality—through tuning the entropic index.
• To compare the performance of Kaniadakis entropy with Tsallis entropy in bi-level thresholding.
• To validate the method on real image datasets and demonstrate its effectiveness in preserving image structure.

Proposed method

• Adopt a maximum entropy principle using Kaniadakis entropy to determine optimal bi-level thresholds.
• Define the Kaniadakis entropy function with a parameterized entropic index κ that controls the shape of the entropy curve.
• Formulate the thresholding problem as an optimization task maximizing Kaniadakis entropy under intensity distribution constraints.
• Use numerical optimization to find the threshold that maximizes the Kaniadakis entropy for a given image.
• Introduce a transition mechanism where small changes in κ induce abrupt changes in the thresholded image output.
• Compare results with Tsallis entropy-based thresholding using identical image datasets and evaluation criteria.

Experimental results

Research questions

• RQ1 How does the entropic index κ in Kaniadakis entropy influence the threshold selection in bi-level image segmentation?
• RQ2 Can Kaniadakis entropy induce a distinct 'image transition'—an abrupt change in image appearance—when varying κ?
• RQ3 How does Kaniadakis entropy-based thresholding compare to Tsallis entropy in preserving image structure and segmentation quality?
• RQ4 What is the sensitivity of the thresholding outcome to variations in the entropic index κ?
• RQ5 Does Kaniadakis entropy offer advantages in handling complex or noisy image intensities compared to Tsallis entropy?

Key findings

• The entropic index κ in Kaniadakis entropy controls a sharp transition in the appearance of the thresholded image, enabling distinct segmentation states.
• Small variations in κ lead to abrupt changes in the thresholded output, indicating a high sensitivity that can be exploited for adaptive segmentation.
• Kaniadakis entropy produces clearer and more structured bi-level images compared to Tsallis entropy in tested examples.
• The method successfully identifies optimal thresholds by maximizing Kaniadakis entropy under the maximum entropy principle.
• The proposed approach demonstrates superior performance in preserving image details and contrast compared to the Tsallis-based alternative.
• The transition behavior induced by κ suggests potential for dynamic thresholding in adaptive image processing systems.