Image thresholding based on gray level‐fuzzy local entropy histogram

Abstract

The thresholding method utilizes only the gray level information of image but ignores the spatial information between pixels. Thus, it sometimes produces incorrect segmentation results. In this paper, a novel histogram, called gray level-local fuzzy entropy (GLLFE) histogram, is proposed to incorporate spatial information into the thresholding process. First, the proposed method transfers the pixel's gray level to a fuzzy set through a fuzzy membership function. Second, the local fuzzy entropy of each pixel is calculated and the GLLFE histogram is constructed by combining the local fuzzy entropy and gray level. Finally, a two-dimensional threshold vector is determined according to the maximum entropy principle. The local fuzzy entropy can not only characterize the spatial correlation but also suppress the noise and enhance the weak edge. Experimental results show that the performance of the proposed method is good.

Highly efficient neoteric histogram–entropy‐based rapid and automatic thresholding method for moving vehicles and pedestrians detection

“…The efficiency of the proposed HEBT method has been assessed by comparing it with six other state‐of‐the‐art histogram–entropy‐based automatic threshold methods, where all the experiments have been implemented with the three‐frame differencing segmentation algorithm. The six state‐of‐the‐art methods studied are: a GLLFE histogram method [40], a grey‐level‐histogram and local‐entropy information method [41], Renyi's entropic multi‐level thresholding method based on a 2D histogram [43], a grey‐level and local‐average histogram along with Tsallis–Handra–Charvat entropy method [44], a new entropic thresholding method based on the 2D histogram constructed using a Gabor filter [45], and a generalised entropy‐based thresholding method based on Masi entropy [46]. The comparisons between the HEBT method and the other state‐of‐the‐art methods are made in terms of segmented images and performance parameters: average recall, average precision, average similarity, average f‐measure, and computation time.…”

“…From top to bottom: challenges. Displayed video clips (a) Raw images, (b) Ground truth images, (c) – (i) Segmentation results obtained by the method as in references Yimit and Hagihara [43], Chen et al [41], Zheng et al [40], Shubham and Bhandari [46], Borjigin and Sahoo [44], Yi et al [45], HEBT methods…”

“…However, the histogram‐based and the entropy‐based two methods, when applied separately, have lost some of the fine details of the images such as points, lines, diagonal information, and edges. To overcome this problem, the combined histogram–entropy‐based methods are widely developed [38–41]. Due to their simplicity and capacity to deal with the spatial correlation among the pixels, the combined histogram–entropy methods are considered to be efficient [24].…”

“…However, the GLGM method showed a negative effect on recognising the image edges. Further, a grey‐level‐local fuzzy entropy (GLLFE) histogram has been proposed by Zheng et al [40] to estimate the threshold value by transferring the pixels grey level to a fuzzy set through a fuzzy membership function and by combining the local fuzzy entropy and grey‐level pixels. Another approach by combining the grey‐level histogram and local‐entropy information to estimate the threshold value has been introduced by Chen et al [41].…”

“…Therefore, the overall contributions of this study include: (i) applying 1D bimodal histogram to calculate prior probabilities of the object and the background pixels of grey‐scale image; (ii) applying the Gaussian distribution function to 1D bimodal histogram for misclassification error removal, and to calculate the probability density function; (iii) calculating the Shannon entropy of the grey‐scale image and its application to reduce the computational time in estimating most probable and accurate threshold value. To validate the efficiency of our HEBT method, extensive experimental analysis is done using the newly developed HEB threshold method on real‐time moving vehicles and pedestrians datasets – change detection 2012 dataset containing 25 videos [47] (hereafter referred as CD‐2012), change detection 2014 dataset containing 22 videos [47] (hereafter referred as CD‐2014), and Wallflower dataset containing 7 videos [48] – and the performance is compared with six state‐of‐the‐art histogram–entropy‐based automatic thresholding techniques [40, 41, 43–46]. In these comparison studies, all the thresholding methods including our own HEBT method, are implemented with the three‐frame differencing segmentation method (the one used in the work of [2]) for object detection from complex and coarse images.…”