## 1 Introduction
[21] used the gray-level difference at fixed intervals in consecutive images to extract the edges of moving objects, calculated the depth information of the edge points of moving objects, clustered the depth information, and segmented different objects. Although the object segmentation techniques proposed by [PERSON] et al. [20] and [PERSON] et al. [21] do not rely on object recognition, they rely on the motion or gray-level difference of objects in consecutive images. [PERSON] and [PERSON] [22] proposed a 3D fuzzy clustering method to perform clustering analysis for different planes and curved surfaces using the 3D information of images. This method can be applied to segment overlapping objects from static images without complex backgrounds. However, the clustering method requires setting the initial number of categories and repeating the iterative computational analysis. Therefore, this method is prone to classification errors and consumes a lot of computation time. [PERSON] et al. [23] proposed an improved robust estimator and genetic algorithm that uses depth gradient images to analyze different surface regions and uses the surface models of 3D planes and curved surfaces to detect and extract all planes and curved surfaces from 3D images sequentially and iteratively. [PERSON] et al. [24] used adaptive surface models to segment 3D point clouds into a preset number of geometric surfaces, which were used as the initial setting for image segmentation. Then, they merged similar adjacent surfaces together, recalculated the relevant parameters, and repeated the process until the termination condition was met. This type of method that fits the object surface with 3D surface models to segment different objects also consumes a lot of computation time and is unsuitable for the complex environment. After object segmentation, the position and label of each object must be analyzed and recorded for subsequent recognition or analysis. The most widely used object labeling method is the connected component labeling algorithm proposed by [PERSON] and [PERSON] [25]. First, this method converts all pixels of the objects that are segmented from the 2D image into a binary image, merges adjacent pixels into the same object in sequence,and assigns label numbers to distinguish different objects, thereby achieving the purpose of labeling the position and region of the objects. However, this method requires large amounts of memory to record labels. [PERSON] [26] used a multi-scan to reduce the amount of memory used in the labeling process as well as a forward and backward mask to scan the binary image alternately. Although no additional memory was required to record labels, more execution time was required. Many researchers have subsequently proposed improved methods [27], such as the four-scan, two-scan, one-scan, contour-tracing labeling, and hybrid object labeling algorithms. Although these methods can reduce memory usage or speed up the operation, they can only connect objects in 2D images without integrating the distance information for the overlapping objects. In summary, the use of 3D information can indeed effectively segment the overlapping objects in images. Compared with dynamic object segmentation, static object segmentation does not require much time to analyze consecutive images. Therefore, this paper proposes a 3D object segmentation and labeling algorithm for static images to segment and label objects simultaneously, to realize object segmentation and labeling in unknown environments. The remainder of this paper is organized as follows. Section 2 introduces the 3D object segmentation algorithm. Section 3 presents the relevant experimental results. The applications and contributions of the proposed algorithm are summarized in Section 4.