## 1 Introduction  
Three-dimensional reconstruction technologies are widely applied in many fields, such as reverse engineering, robot vision, medical surgery, intelligent manufacturing, and in the entertainment industry [1; 2; 3; 4; 5]. The technologies could be classified into three categories: time-of-flight (TOF), stereo vision, and structured light (SL) [6]. SL techniques have many advantages over the other methods in terms of high accuracy, robustness, simplicity and low cost [7; 8]. The available projection patterns for SL techniques could be the single-line [3; 9], multi-line [10; 11] or surface pattern [12; 13]. By projecting surface pattern onto the object and capturing the corresponding deformed patterns modulated by the object profile, 3D information could be reconstructed more effectively than with the other two patterns [6; 12]. According to the codification strategies, the surface patterns can be roughly categorized into two classes: temporal-based and spatial-based schemes [14]. The temporal-based approaches have advantages in terms of high accuracy and robustness. These approaches adopt the binary code method [7; 15] or the phase shifting method [16; 17; 18]. However, the approaches have to conduct multi-shots to capture the patterns in a time series. So, the temporal-based techniques are not suitable for dynamic scenes. In contrast, the spatial-based approaches only implement a single-shot, which is favorable for 3D reconstruction of dynamic scenes [19]. Among spatial-based methods, the encoding scheme, such as the De Bruijn sequence [20], M-arrays [21] and pseudo-random codes [22], is a commonly used strategy [7] These methods encode the features by different heights, widths, orientations, or compactness for a unique identity. However, the uniqueness of the local code-wordretrieval is hard to guarantee, due to perspective distortion [23]. Differing from spatial-coded patterns, coding-free patterns are always simple and periodic. The methods using coding-free patterns are more robust, insensitive to distortion, and low-cost [24]. Grid pattern is a typical surface pattern. Some researchers have studied methods with a grid pattern in recent decades [6; 25; 26; 27; 28; 29; 30]. [PERSON] et al. [25] employed a chromatic grid pattern with six different colors to identify lines, where three colors are assigned for horizontal lines, and the other three for vertical lines. The De Bruijn sequence with order determines the three colors of three adjacent lines. [PERSON] et al. [26] used a periodic color-encoded grid pattern to achieve more accurate retrieval correspondence. [PERSON] et al. [31] proposed a grid pattern with two colors to distinguish the vertical and horizontal lines. Then coplanarity constraint and epipolar constraint are utilized to retrieve the correspondence. All of these methods require projecting a chromatic pattern for correspondence retrieval. [PERSON] et al. [24] investigated the depth sensing method by using a coding-free binary grid pattern based on a camera and a DLP projector stereo platform. A coarse-to-fine line detection strategy was applied for extracting the grid. A graph-based topological labeling algorithm was proposed to determine the topological coordinates of the intersections of the grid. By using the topology of the grid and the epipolar constraint, the corresponding pixels between the projected and captured pattern were matched. Then the 3D reconstruction was implemented, based on the triangular stereo model. However, low calibration accuracy of the camera-projector stereo system may occur and influence the correspondence determination with epipolar constraint. The sub-grid pixel matching is realized by solving an over-determined system of equation. The least square solution should be calculated in every sensing process. This paper aimed to provide a simple and effective single-shot 3D reconstruction approach using the grid pattern-based structured-light vision method.