For endoscopic medical treatment, measuring the size and shape of lesions, such as tumors, is important. We are developing a 3D endoscope system to measure the shape and size of living tissues based on active stereo. In previous works, our group attached a pattern projector outside the endoscope head. Since this increased the diameter of the endoscope, the burden and the risks of the patients would increase. In this paper, we set the pattern projector inside the instrument channel of the endoscope instead of mounting it outside, so that it can be deployed whenever required. This does not increase the size of the endoscope and facilitates the measuring process. However, since the projector is not physically fixed to the endoscope anymore prior to the operation, we propose an 'auto-calibration' technique where extrinsic parameters are calibrated intra-operatively from a point marker on the projector observed simultaneously on the target surface. In the experiment, we show that the external parameters were successfully calibrated to obtain 3D reconstructions properly with the overall systems. The accuracy of the auto-calibration was validated by confirming that the epipolar constraints were kept, and a 3D reconstruction of a human tissue was demonstrated.