# Texture Construction Edge Detection Algorithm
## 1 Introduction
To effectively reduce the problem of edge discontinuity or loss, the Canny algorithm [9] proposes using high-threshold and low-threshold values instead of a single threshold. Since the higher gradient value is a more pronounced edge, [PERSON] uses the hysteresis effect to track pixels that are held between the high and low thresholds, as possible for object edge retention. To find the best threshold, some scholars have proposed a method for detecting high and low thresholds for Canny [9] edge detection; for example, [PERSON] and [PERSON] [10] used the Otsu method for the gradient magnitude histogram after non-maximum suppression. The calculated gradient magnitude histogram is used to obtain the high threshold and sets one-half of the high threshold as a low threshold. However, since the low threshold setting is determined by the high threshold, it has not been accurately calculated by statistical analysis. Therefore, it is inaccurate in terms of the setting, which may still lead to edge loss. [PERSON] et al. [11] also used the Otsu method to analyze the gradient magnitude histogram after non-maximum suppression. They first obtained the high-threshold value and then excluded the gradient value greater than the high threshold and performed the second operation on the statistical result to obtain a low threshold. The proposed method of the iteration threshold effectively improves the edge detection discontinuity and detection errors. [PERSON] et al. [12] proposed using the mean squared error (MSE) [13] to automatically detect the high and low thresholds. First, one uses the MSE to quantify the gradient magnitude histogram after non-maximum suppression. To perform the operation, one first obtains the high threshold, then excludes the gradient larger than the high threshold, and finally performs the second operation on the statistical result to obtain the low threshold. The proposed method improves the edge detection effect in high- and low-brightness images. In addition, the gradient magnitude histogram proposed by [PERSON] and [PERSON] [14] uses a differential operation to obtain the adaptive high and low thresholds after non-maximum suppression. The high threshold is obtained by the first zero bin of the amplitudes difference, and the low threshold is set to 0.4 times the high threshold. The method improved the ability of noise reduction and made the edge more obvious, but the low threshold is still dependent on the calculation of the high-threshold value and the setting is less accurate and may still lead to loss of the edge. [PERSON] et al. [15] used the method proposed by [PERSON] et al. [16] to adaptively solve the high and low thresholds by the operation of two statistical values in the gradient histogram after non-maximum suppression: one is the average value of the probability density function and the other is the variation in the probability density function. The proposed method has better continuity at the detected edge. Although the Canny [9] algorithm uses a high- and low-threshold strategy to preserve the edges more flexibly, there is still a common problem of threshold setting. A pixel with a gradient value larger than the high-threshold is used as the starting point of the edge. Therefore, the high-threshold value directly affects the edge detection result and the low-threshold value is the lower limit of the gradient value of the edge detection. When the threshold value is set too high, the edge texture with a lower gradient value is filtered out. Conversely, when the setting is too low, too much noise or too many false edges are left. Because of the variability of the image, a fixed set of high and low thresholds cannot effectively be used to preserve the rich edge information in the image. Therefore, finding the edge of the object in the image by setting the threshold value is an insurmountable problem. To solve the excessive or effective edge texture loss caused by unsuitable threshold value setting, the texture construction edge detection algorithm (TCEDA) is proposed as the edge construction algorithm.