Modeling Image Tone Dichotomy with the Power Function

TL;DR

The article shows dichotomy image space as a viable way to extract rich information from images despite poor contrast linked to tone, lightness, and color perception and a comparison with state-of-the-art methods in image enhancement provides evidence of the method's value.

Abstract

The primary purpose of this paper is to present the concept of dichotomy in image illumination modeling based on the power function. In particular, we review several mathematical properties of the power function to identify the limitations and propose a new mathematical model capable of abstracting illumination dichotomy. The simplicity of the equation opens new avenues for classical and modern image analysis and processing. The article provides practical and illustrative image examples to explain how the new model manages dichotomy in image perception. The article shows dichotomy image space as a viable way to extract rich information from images despite poor contrast linked to tone, lightness, and color perception. Moreover, a comparison with state-of-the-art methods in image enhancement provides evidence of the method's value.

Figures (11)

• Figure 1: Subexposed images are too-dark photographs with very little detail because the sensor receives insufficient light. Note that the proposed model correctly recovers tone dichotomy, allowing us to observe the snowy plover in its habitat.
• Figure 2: A photograph is overexposed when the sensor receives too much light. Consequently, the picture is too bright, and details in the highlights are lost. Note that the model can create a correctly contrasted image feeling just bright or dark enough.
• Figure 3: The exposure is often problematic, and the image contains a mixture of underexposed and overexposed regions. Note that the transformation recovers the heron details, strikingly balancing the shadows and highlights.
• Figure 4: This collage shows the results of computing the entropy of Figures \ref{['fig1']}, \ref{['fig2']}, and \ref{['fig3']}, considering the original image, and after applying adaptive gamma and dichotomy functions.
• Figure 5: These charts provide the histograms computed from the results of Figure \ref{['fig7']}.

Theorems & Definitions (19)

• Definition 1
• Definition 2
• Lemma 1
• Lemma 2
• Lemma 3
• Lemma 4
• Lemma 5
• Theorem 1
• proof : Proof of Theorem 1
• Lemma 6