Vision-based tactile sensors have recently shown promising contact information sensing capabilities in various fields, especially for dexterous robotic manipulation. However, dense contact geometry measurement is still a challenging problem. In this article, we update the design of our previous GelStereo tactile sensor and present a self-supervised contact geometry learning pipeline. Specifically, a self-supervised stereo-based depth estimation neural network (GS-DepthNet) is proposed to achieve real-time disparity estimation, and two specifically designed loss functions are proposed to accelerate the convergence of the network during the training process and improve the inference accuracy. Furthermore, extensive qualitative and quantitative experiments of perceived contact shape were performed on our GelStereo sensor. The experimental results verify the accuracy and robustness of the proposed contact geometry sensing pipeline. This updated GelStereo tactile sensor with dense contact geometric sensing capability has predictable application potential in the field of industrial and service robots.