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Vein segmentation and projection correction constitute the core algorithms of an auxiliary venipuncture device, responding to accurate venous positioning to assist puncture and reduce the number of punctures and pain of patients. This paper proposes an improved U-Net for segmenting veins and a coaxial correction for image alignment in the self-built vein projection system. The proposed U-Net is embedded by Gabor convolution kernels in the shallow layers to enhance segmentation accuracy. Additionally, to mitigate the semantic information loss caused by channel reduction, the network model is lightweighted by means of replacing conventional convolutions with inverted residual blocks. During the visualization process, a method that combines coaxial correction and a homography matrix is proposed to address the non-planarity of the dorsal hand in this paper. First, we used a hot mirror to adjust the light paths of both the projector and the camera to be coaxial, and then aligned the projected image with the dorsal hand using a homography matrix. Using this approach, the device requires only a single calibration before use. With the implementation of the improved segmentation method, an accuracy rate of 95.12% is achieved by the dataset. The intersection-over-union ratio between the segmented and original images is reached at 90.07%. The entire segmentation process is completed in 0.09 s, and the largest distance error of vein projection onto the dorsal hand is 0.53 mm. The experiments show that the device has reached practical accuracy and has values of research and application. Full article