2D Direction Histogram-Based Rényi Entropic Multilevel Thresholding

Abstract

2D histogram-based thresholding methods, in which the histogram is computed from local image features, have better performance than 1D histogram-based methods, but they take much more computation time. In this paper, we present a Rényi entropic multilevel thresholding (REMT) method based on a 2D direction histogram constructed from pixel values and local directional features. In addition to presenting a fast recursive method for REMT, we propose the Rényi entropic artificial bee colony multilevel thresholding (REABCMT) method to quickly find the optimal threshold values. In order to demonstrate the efficacy of REABCMT, three versions of this method are compared in terms of computation time and optimal threshold values. In addition, the segmentation performance of REABCMT is also evaluated by comparing it with two other methods to show its effectiveness. Moreover, in order to evaluate the efficiency and stability of using the ABC algorithm in the search for threshold values, genetic algorithm (GA) and particle swarm optimization (PSO), two common optimization algorithms, are also compared with it.

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.…”

“…A comparison of the parameters for the six state‐of‐the‐art methods clearly indicates among them that some of these methods show highest values only for one or two performance parameters (underlined entries). For example, the method by Yimit and Hagihara [43] shows the highest value only for recall (0.7689) and similarity (0.632). Similarly, the method by Borjigin and Sahoo [44] offers the highest value only for precision (0.7980) and the Yi et al method [45] possess the highest value only for f‐measure (0.6590).…”

“…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, these methods showed less performance due to the lack of gradient orientation. To overcome this problem, Yimit and Hagihara [43] proposed a new method using Renyi's entropic multi‐level thresholding method based on the 2D histogram to compute the optimal threshold value. However, this method fails to handle illumination changes in the images.…”

“…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.…”