Mean-Based Breakpoint Selection on Circular Histogram

Jiulun Fan,Jipeng Yang,Volodymyr Ponomaryov

doi:10.1155/2021/5966463

Jiulun Fan, Jipeng Yang + Show 1 more

Open Access

https://doi.org/10.1155/2021/5966463

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Abstract

Circular histogram represents the statistical distribution of circular data; the H component histogram of HSI color model is a typical example of the circular histogram. When using H component to segment color image, a feasible way is to transform the circular histogram into a linear histogram, and then, the mature gray image thresholding methods are used on the linear histogram to select the threshold value. Thus, the reasonable selection of the breakpoint on circular histogram to linearize the circular histogram is the key. In this paper, based on the angles mean on circular histogram and the line mean on linear histogram, a simple breakpoint selection criterion is proposed, and the suitable range of this method is analyzed. Compared with the existing breakpoint selection criteria based on Lorenz curve and cumulative distribution entropy, the proposed method has the advantages of simple expression and less calculation and does not depend on the direction of rotation.

Highlights

As a typical example of circular data, Hue(H) represents the basic colors of the image (H ∈ [0, 2π)); it can be expressed as a circular histogram, due to its periodicity
One is the criterion based on the Lorenz curve [20]; we discussed the relation between the area difference and the expansion direction and gave the optimal breakpoint selection criterion in the anticlockwise or clockwise direction. e other is the criterion based on the cumulative distribution entropy [21], and we built a circular histogram expansion model based on the cumulative distribution entropy and discussed the optimal breakpoint selection criteria under different expansion directions. ese two circular histogram expansion methods overcome the randomness of breakpoint selection
Angle mean is used to represent the average angle of a set of data on a circle; it is a circular statistical invariant on the circular histogram; it does not change with the rotation of the circular histogram

Summary

Introduction

As a typical example of circular data, Hue(H) represents the basic colors of the image (H ∈ [0, 2π)); it can be expressed as a circular histogram, due to its periodicity. E other is the criterion based on the cumulative distribution entropy [21], and we built a circular histogram expansion model based on the cumulative distribution entropy and discussed the optimal breakpoint selection criteria under different expansion directions.

Results

Conclusion