## 2 Three-Dimensional Object Segmentation and Labeling Algorithm
### Tceda  
In this paper, TCEDA [28] is used to detect edge information in images. The candidate edge points are detected by determining whether adjacent pixels with gradient changes have reasonable texture changes. Then, the edge texture extension method is used to delete relatively short line segments, thereby retaining effective contour edge points. TCEDA can avoid inappropriate threshold setting and retain large amounts of edge information as the object in the next processing step. TCEDA mainly involves three steps: image preprocessing, optimal edge thinning process, and edge texture construction processing. In image preprocessing, the input color image is converted into a gray-level image. Then, the 2D Gaussian function filter is used for smoothing to reduce the interference caused by noise on the image edge. Subsequently, the Sobel filter mask is used to calculate the gradient value of each pixel in the image. Finally, the gradient amplitude and angle of each pixel are calculated. In the optimal edge thinning process, the gradient amplitude and angle of each pixel are analyzed using the non-maximum suppression method to obtain the initial result of edge thinning. Subsequently, the redundant pixels processed by the non-maximum suppression method are removed using the thinning texture template process to obtain the optimal result of edge thinning. The non-maximum suppression method classifies the calculated gradient angles based on their similarity and compares the gradient amplitudes of adjacent pixels on both sides of the gradient direction of the processed pixel (center pixel). When the gradient amplitudes of the two adjacent points are both smaller than that of the center pixel, the center pixel and two adjacent points are labeled as candidate edge points; otherwise, they are not labeled. Subsequently, the thinning texture template is used to compare the texture of a 3 \(\times\) 3-pixel block of the candidate edge point in the raster-scan order. When the block texture conforms to the defined thinning texture template, the redundant pixel in the center of the block is deleted. The optimal edge thinning result can be obtained after all candidate edge points are processed. Because the optimal edge thinning process retains many short line segments and isolated points, the edge texture construction processing is used to delete these noises (short line segments and isolated points) and retain long line segments with extensible texture changes. The edge texture construction processing extends and constructs line segments by expanding the edge texture template established between adjacent blocks. In this process, the extended length of the edge line segment containing more than six edge points is retained to obtain the edge contour image. To show that TCEDA can detect more edge information than other edge detection methods, one of the experimental results of TCEDA is provided by referring to TCEDA [28]. The TCEDA was compared with the other four improved adaptive Canny edge detection algorithms which were proposed by [PERSON] and [PERSON] [29], [PERSON] et al. [30], [PERSON] et al. [31], and [PERSON] and [PERSON] [32]. The results of the TCEDA compared with the other four improved adaptive Canny edge detection algorithms, as shown in Figure 1. Figure 1f shows the TCEDA can be effectively preserved the edge, the texture on the tile, the seam line between the tiles, and the wrinkles of the jeans. Figure 1: Embossed tile image comparison results of different methods. (**a**) Original image (\(640\times 480\)) [33]; (**b**) [PERSON] and [PERSON]’s method (THH = 238, THL = 119); (**c**) [PERSON] et al. proposed method (THH = 238, THL = 20); (**d**) [PERSON] et al.’s method (THH = 102, THL = 31); (**e**) [PERSON] and [PERSON]’s method (THH = 74, THL = 29); (**f**) TCEDA [28]. Figure 2a,b is an image pair (Test image 1) obtained from the KITTI database [34]. Figure 2a is the compared image (left image \(I_{L}\)) and Figure 2b is the processing image (right image \(I_{R}\)).