System (100; 200; 300; 400) for measuring an external profile of a part or an internal profile of a hollow part, comprising: - a part whose internal or external profile is to be measured, - a sensor (110, 110'; 210; 310; 410) comprising a probe (120; 220; 320; 420), a first reference element (130; 230; 330; 430) fixedly coupled with the probe (120; 220; 320; 420) via a support portion (114; 214; 314; 414), a base (112; 212; 312; 412) and a guide system (140; 240; 340; 440) connecting the probe (120; 220; 320; 420) with the base (112; 212; 312; 412), allowing relative movement between them along at least one degree of freedom defining a measurement direction, - said sensor (110, 110'; 210; 310; 410) being arranged relative to the part so that during the movement of the sensor relative to the part in a direction different from the measurement direction, said probe (120; 220; 320; 420) is able to follow the internal or external contour of the part, while the first reference element (130; 230; 330; 430) is able to remain outside the part, following a path reproducing the path of the probe (120; 220; 320; 420) along the internal or external contour of the part, and - an image-taking device capable of taking images representing at least a portion of the outside of the part and the first reference element (130; 230; 330; 430), - calculating means configured to - detect the relative displacement between the first reference element (130; 230; 330; 430) and the portion of the outside of the part in said measurement direction by comparing the images taken by the image-taking device, and - deduce a relative displacement between the probe (120; 220; 320; 420) and the base (112; 212; 312; 412) which corresponds to an offset in the measurement direction along the measured profile of the part from said relative displacement between the first reference element (130; 230; 330; 430) and the portion of the outside of the part in said measurement direction. - a part whose internal or external profile is to be measured, - a sensor (110, 110'; 210; 310; 410) comprising a probe (120; 220; 320; 420), a first reference element (130; 230; 330; 430) fixedly coupled with the probe (120; 220; 320; 420) via a support portion (114; 214; 314; 414), a base (112; 212; 312; 412) and a guide system (140; 240; 340; 440) connecting the probe (120; 220; 320; 420) with the base (112; 212; 312; 412), allowing relative movement between them along at least one degree of freedom defining a measurement direction, - said sensor (110, 110'; 210; 310; 410) being arranged relative to the part so that during the movement of the sensor relative to the part in a direction different from the measurement direction, said probe (120; 220; 320; 420) is able to follow the internal or external contour of the part, while the first reference element (130; 230; 330; 430) is able to remain outside the part, following a path reproducing the path of the probe (120; 220; 320; 420) along the internal or external contour of the part, and - an image-taking device capable of taking images representing at least a portion of the outside of the part and the first reference element (130; 230; 330; 430), - calculating means configured to - detect the relative displacement between the first reference element (130; 230; 330; 430) and the portion of the outside of the part in said measurement direction by comparing the images taken by the image-taking device, and - deduce a relative displacement between the probe (120; 220; 320; 420) and the base (112; 212; 312; 412) which corresponds to an offset in the measurement direction along the measured profile of the part from said relative displacement between the first reference element (130; 230; 330; 430) and the portion of the outside of the part in said measurement direction.