An analysis of the transition proportion for binarization in handwritten historical documents

• The minimum-error-rate (MER) based on transition sets is similar to the actual MER.
• We show that the transition proportion has a small influence in the normal threshold.
• The transition proportion is a feature to calculate the stroke width on a document.
• The transition proportion is a feature that identify regions of interest.
• Gray-intensity histograms are lognormally distributed rather than normally distributed.

In this paper, we will present a mathematical analysis of the transition proportion for the normal threshold (NorT) based on the transition method. The transition proportion is a parameter of NorT which plays an important role in the theoretical development of NorT. We will study the mathematical forms of the quadratic equation from which NorT is computed. Through this analysis, we will describe how the transition proportion affects NorT. Then, we will prove that NorT is robust to inaccurate estimations of the transition proportion. Furthermore, our analysis extends to thresholding methods that rely on Bayes rule, and it also gives the mathematical bases for potential applications of the transition proportion as a feature to estimate stroke width and detect regions of interest. In the majority of our experiments, we used a database composed of small images that were extracted from DIBCO 2009 and H-DIBCO 2010 benchmarks. However, we also report evaluations using the original (H-)DIBCO׳s benchmarks.