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We studied the relativistic images caused by strong gravitational lensing inKerr black hole images, which carry some essential signatures about the blackhole space-time. We defined a new celestial coordinates whose origin is thecenter of black hole shadow to locate the relativistic images. Under theinfluences of the dragging effect caused by rotating black hole and theinclination angle of observer, the relative positions between the primary andsecondary images are different with the different Kerr spin parameter $a$ andthe observer's inclination angle $i$, so it can be used to determine the valueof $a$ and $i$. We provided the specific approach to measure the value of $a$and $i$ by the relativistic images. The time delays between the primary andsecondary images are different with the different $a$ and $i$. The time delaysin conjunction with the relative positions between the primary and secondaryimages could allow us to measure the value of $a$ and $i$ more precisely. Theserelativistic images are as unique as fingerprints for black hole space-time, bywhich one can further determine other parameters of all kinds of compactobjects and verify various theories of gravity. Our results provide a newmethod to implement parameter estimation in the study of black hole physics andastrophysics.

Determination of the spin parameter and the inclination angle by the relativistic images in black hole image