Theoretical Analysis of Power-law Transformation on Images for Text Polarity Detection

TL;DR

This paper provides a theoretical explanation for how power-law transformations affect image histograms and class separation, aiding text polarity detection in image binarization tasks.

Contribution

It offers a novel theoretical analysis of the power-law transformation's impact on histogram statistics and class variance in image binarization.

Findings

Power-law transformation influences between-class variance based on text polarity.

Theoretical insights explain empirical observations in histogram-based binarization.

Enhanced understanding of image preprocessing for text recognition.

Abstract

Several computer vision applications like vehicle license plate recognition, captcha recognition, printed or handwriting character recognition from images etc., text polarity detection and binarization are the important preprocessing tasks. To analyze any image, it has to be converted to a simple binary image. This binarization process requires the knowledge of polarity of text in the images. Text polarity is defined as the contrast of text with respect to background. That means, text is darker than the background (dark text on bright background) or vice-versa. The binarization process uses this polarity information to convert the original colour or gray scale image into a binary image. In the literature, there is an intuitive approach based on power-law transformation on the original images. In this approach, the authors have illustrated an interesting phenomenon from the histogram statistics of the transformed images. Considering text and background as two classes, they have observed that maximum between-class variance between two classes is increasing (decreasing) for dark (bright) text on bright (dark) background. The corresponding empirical results have been presented. In this paper, we present a theoretical analysis of the above phenomenon.