Improvement in the Between-Class Variance Based on Lognormal Distribution for Accurate Image Segmentation

There are various distributions of image histograms where regions form symmetrically or asymmetrically based on the frequency of the intensity levels inside the image. In pure image processing, the process of optimal thresholding tends to accurately separate each region in the image histogram to obtain the segmented image. Otsu's method is the most used technique in image segmentation. Otsu algorithm performs automatic image thresholding and returns the optimal threshold by maximizing between-class variance using the sum of Gaussian distribution for the intensity level in the histogram. There are various types of images where an intensity level has right-skewed histograms and does not fit with the between-class variance of the original Otsu algorithm. In this paper, we proposed an improvement of the between-class variance based on lognormal distribution, using the mean and the variance of the lognormal. The proposed model aims to handle the drawbacks of asymmetric distribution, especially for images with right-skewed intensity levels. Several images were tested for segmentation in the proposed model in parallel with the original Otsu method and the relevant work, including simulated images and Medical Resonance Imaging (MRI) of brain tumors. Two types of evaluation measures were used in this work based on unsupervised and supervised metrics. The proposed model showed superior results, and the segmented images indicated better threshold estimation against the original Otsu method and the related improvement.