吴涛(湛江师范学院信息科学与技术学院, 湛江 524048)
目的 图像阈值化将灰度图像转换为二值图像，被广泛应用于多个领域。因实际工程应用中固有的不确定性，自动阈值选择仍然是一个极具挑战的课题。针对图像自动阈值化问题，提出了一种利用粗糙集的自适应方法。方法 该方法分析了基于粗糙集的图像表示框架，建立了图像粗糙粒度与局部灰度标准差的相互关系，通过最小化自适应粗糙粒度准则获得最优的划分粒度。进一步在该粒度下构造了图像目标和背景的上下近似集及其粗糙不确定度，通过搜索灰度级最大化粗糙熵获得图像最优灰度阈值，并将图像目标和背景的边界作为过渡区，利用其灰度均值作为阈值完成图像二值化。结果 对本文方法通过多个图像分3组进行了实验比较，包括3种经典阈值化方法和一种利用粗糙集的方法。其中，本文方法生成的可视化二值图像结果远远优于传统粗糙集阈值化方法。此外，也采用了误分率、平均结构相似性、假阴率和假阳率等指标进一步量化评估与比较相关实验结果。定性和定量的实验结果表明，本文方法的图像分割质量较高、性能稳定。结论 本文方法适应能力较好，具有合理性和有效性，可以作为现有经典方法的有力补充。
Adaptive rough entropy method for image thresholding
Wu Tao(School of Information Science and Technology, Zhanjiang Normal University, Zhanjiang 524048, China)
Objective 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. Method 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. Result 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. Conclusion 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.