Gray-Level Image Transitions Driven by Tsallis Entropic Index

TL;DR

This paper explores how the Tsallis entropic index influences image thresholding, revealing abrupt transitions in image appearance analogous to physical phase transitions, with implications for image segmentation techniques.

Contribution

It demonstrates the impact of the Tsallis entropic index on thresholding, highlighting abrupt image transitions and their analogy to physical system phase changes.

Findings

Threshold values can change abruptly when the entropic index is in (0,1)

Gray-level image transitions resemble physical order or texture transitions

The entropic index influences the appearance of bi-level and multi-level images

Abstract

The maximum entropy principle is largely used in thresholding and segmentation of images. Among the several formulations of this principle, the most effectively applied is that based on Tsallis non-extensive entropy. Here, we discuss the role of its entropic index in determining the thresholds. When this index is spanning the interval (0,1), for some images, the values of thresholds can have large leaps. In this manner, we observe abrupt transitions in the appearance of corresponding bi-level or multi-level images. These gray-level image transitions are analogous to order or texture transitions observed in physical systems, transitions which are driven by the temperature or by other physical quantities.