**3.3 Representation of motion correlation between real surgical instruments and their digital twin models**

The motion of the digital twin surgical instrument and the real surgical instrument is homologous but not synchronous, and the motion deviation of the two needs to be extracted to ensure remote operation safety. In the abovementioned fused environment of real and twin scenes, intelligent algorithms are used to establish the expression of the twin and real instruments in the image coordinate system based on the principle of projective geometry, and the spatial deviation between them is described by pixel difference. Based on this, the transparency of the twin instrument is controlled by the deviation, with smaller deviations resulting in greater transparency and larger deviations resulting in greater visibility. Without interfering with the doctor, the delay of the remote instrument is visually displayed to the doctor.
