Lorenz Curve-Based Entropy Thresholding on Circular Histogram

Abstract

Circular histogram thresholding is a new threshold selection method in color image segmentation. However, the method of the existing circular histogram thresholding based on the Otsu Criteria lacks the generality of using the circular histogram. In order to improve the effectiveness and reduce the complexity of thresholding on circular histogram, this paper firstly introduces the Lorenz curve into circular histogram. Then the circular histogram is expanded into the linearized histogram in clockwise or anticlockwise direction by the optimal index of the Lorenz curve. In the end, the entropy thresholding of the linearized circular histogram is adopted to choose the optimal threshold to obtain the object of color images. Many experimental results show that the proposed method has better effectiveness and adaptability than the existing circular thresholding utilizing Otsu Criteria. INDEX TERMS Color image segmentation, circular histogram thresholding, entropy method, Lorenz-curve type technique.

Recursive Algorithms of Maximum Entropy Thresholding on Circular Histogram

“…e running time of the recursive algorithm of maximum entropy thresholding for circular histogram linearization is also recorded. Here, two different methods will be used to linearize the circular histogram: one is to traverse the breakpoints in an exhaustive way and then use the recursive algorithm of the traditional maximum entropy thresholding for the linearized histogram, and the other is to use Kang et al's [13] Lorenz curve method to find the optimal breakpoint, then break the circular histogram at that point, and then use the recursive algorithm of traditional maximum entropy thresholding. More intuitive to show their differences, the average running time of each method in these eight images will be calculated, and the bar chart is shown in Figure 5.…”

“…en, the selection criterion of the optimal threshold pair of circular maximum entropy thresholding is [13]…”

“…Recently, Kang et al [13,14] proposed two ways on circular histogram thresholding based on the maximum entropy principle. In the first way, the circular histogram was converted into a linear histogram at the appropriate breakpoint using Lorenz curve, and then the traditional maximum entropy thresholding method was used to segment.…”

“…It can be found from the literature [13,14] that the entropy-based method on circular histogram may be much better than the Otsu-based method. However, separating the circular histogram into two classes needs two thresholds, so it takes O(L 2 ) time to use maximum entropy thresholding on circular histogram.…”

Automatic Image Thresholding Based on Shannon Entropy Difference and Dynamic Synergic Entropy

“…Among these methods, image thresholding is a simple, yet effective, way of separating targets from the background, when the gray levels of the pixels belonging to targets are substantially different from the gray levels of the pixels belonging to the background [1], [13]- [15]. Image thresholding is also one of the most commonly used low-level image processing methods in various image analysis systems [1], [16]- [19]. Image thresholding compares the gray level of each pixel in a gray level image with a selected threshold to determine whether the pixel belongs to the targets or the background.…”