For a segmentation method to be useful it must be fast

easy to use

and produce high quality segmentations. It is clear that only few algorithms can offer this combination under various conditions. Thresholding is a popular image segmentation method that converts a gray level image into a binary image

and it has been widely applied in many fields. However

uncertainty is an inherent part of image thresholding in real world applications

and the automatic selection of optimum thresholds is still a challenge. In order to select the optimal threshold for image segmentation

an adaptive method based on rough set is proposed. The proposed method analyzes the rough set-based framework for image representation

establishes the relation between image rough granularity and local grayscale standard deviation

and obtains the optimal partition granularity by minimizing the adaptive rough granularity criteria. Next

the method defines the upper and lower approximation for image object and background

as well as the corresponding rough measure

and then produces the optimal grayscale by searching gray levels to maximize rough entropy. Finally

taking the boundary of object and background as transition region

the method achieves image thresholding according to the mean grayscale of the transition region. We have developed a program for the proposed method using MATLAB. The proposed method needs no input parameter

and its time complexity is approximately linear related to the size of the original image. Theoretically

the proposed method is efficient

and the segmented result is produced within 5 seconds for an image with the length and width of 256 in practice. By three groups of experiments on a variety of synthetic and real images

whose gray level are all 256

the performance of the proposed method is compared with the published results from three traditional state-of-art algorithms

and a rough set-based algorithm is also involved in the comparison

which have also been implemented under MATLAB 2007b environment. On one hand

we provide a qualitative comparison of our output against these relative algorithms. Compared with the rough set-based algorithm

the experimental results suggest the proposed method is effective to yield the approximately ideal results

that is

ground-truth images. On the other hand

the quantitative results are also reported using five measure metrics

including misclassification error

mean structural similarity

false negative rate

and false positive rate

which always lies between 0 and 1. Compared with three traditional state-of-art algorithms

the proposed method outperforms the other methods

demonstrating the highest score in most cases. The proposed method obtains the adaptive window size to construct rough set related with the upper and lower approximation for the image object and the background

and then segments the image based on the transition region determined by the rough set. These processes are proved to improve the segmentation result. In summary

it is indicated by the quantitative and qualitative experiments that

the proposed method performs good and robust image thresholding results

especially for non-destructive testing images. We can conclude that

our technique based on rough entropy has preferable adaptive performance and is superior to other existing methods. The proposed method is reasonable and effective

and can be as a powerful alternative to the traditional methods.