## 1 Introduction  
As a routine medical procedure, the success rate of venipuncture is not solely dependent on the medical staff's skill and experience [1]. Various objective factors can also affect the outcome, such as dark skin, a thick subepidermal fat layer, and poor lighting conditions, all of which can decrease the success rate [2]. Due to their high precision and sensitivity, venipuncture robots [3] are starting to emerge. With the continuous development of technology, the most important vein segmentation algorithm has been continuously updated. Currently, most vein projectors employ near-infrared imaging principles to capture vein images [4]. By using a near-infrared camera, the features of the veins in near-infrared images are more distinct compared to those appearing blue-green under natural light. The obtained image is transmitted to a processor for enhancement and segmentation processing. Finally, the segmented binary image is fed back to the dorsal of the hand by the projector, allowing the medical staff to perform vein puncture through the projected image. Regarding the entire hand vein imaging process, this paper makes improvements to the vein segmentation and projection correction algorithms. Furthermore, a system is developed to validate the method, yielding a better result. Since the development of the first assisted vein puncture device [5], there has been an increasing demand for accuracy in projection results. Usually, the obtained NIR images are accompanied by severe noise, because veins are hidden underneath the skin and fat and the NIR light penetrates the skin to a limited depth. Although the pixel's brightness in the vein and dorsal is different, the overall contrast of the image is low, and the edges of the veins are often blurry [6]. Furthermore, the camera and projector are not located in the same position, resulting in a misalignment of the projected image with the dorsal hand. Therefore, this paper investigates two critical techniques in vein projector technology: image segmentation and projection correction. For the image segmentation problem, the core idea of the traditional methods is to design a feature extractor. However, the extractor requires the manual setting of certain parameters, which may not be suitable for different application scenarios. Additionally, manually designed feature extractors may fail to capture complex image features, resulting in poor segmentation accuracy and low robustness. Subsequently, regarding projection correction algorithms, most of the existing methods align the projected image with the dorsal by using the homography matrix. However, the hand has a larger curvature towards the edges, resulting in less accurate projection results. Furthermore, as the supporting surface, the hand is not fixed, therefore, any change in its position will lead to changes in the homography matrix [7]. To address these issues, this paper utilizes corresponding solutions, which are also the main contributions, as follows:  
1. The prior knowledge of Gabor kernels is integrated into U-Net to improve the network. Through the embedding of the Gabor kernel into the neural network, the feature extraction capability of the shallow network is enhanced. Consequently, this leads to improved accuracy in image segmentation and lays a foundation for later precise projection. 2. The proposed U-Net achieves a lightweight design by replacing conventional convolutions with inverted residual blocks. This operation mitigates the semantic information loss caused by channel reduction, while decreasing the parameter size, and is suitable for real-time projection. 3. During the projection process, this paper proposes a method that combines coaxial correction with the homography matrix. This approach enables the device to require only a single calibration before use. It enhances the accuracy of the vein projection system and simplifies the process of projection correction. 4.