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Mathematical Problems in Engineering
Volume 2014 (2014), Article ID 932695, 13 pages
Research Article

Minimum Error Thresholding Segmentation Algorithm Based on 3D Grayscale Histogram

1School of Software, Jiangxi Normal University, Nanchang 330022, China
2Department of Computer Application, Faculty of Information Science and Technology, Southwest Jiaotong University, Chengdu 610031, China
3Department of Electronic & Information Engineering, Faculty of Electrical Engineering, Southwest Jiaotong University, Chengdu 610031, China

Received 25 October 2013; Revised 5 December 2013; Accepted 9 December 2013; Published 14 January 2014

Academic Editor: Su-Qun Cao

Copyright © 2014 Jin Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Threshold segmentation is a very important technique. The existing threshold algorithms do not work efficiently for noisy grayscale images. This paper proposes a novel algorithm called three-dimensional minimum error thresholding (3D-MET), which is used to solve the problem. The proposed approach is implemented by an optimal threshold discriminant based on the relative entropy theory and the 3D histogram. The histogram is comprised of gray distribution information of pixels and relevant information of neighboring pixels in an image. Moreover, a fast recursive method is proposed to reduce the time complexity of 3D-MET from to , where stands for gray levels. Experimental results demonstrate that the proposed approach can provide superior segmentation performance compared to other methods for gray image segmentation.