Several studies have attempted to identify the isotropy boundary (IB) defining the limit between the adiabatic and nonadiabatic trajectories of the trapped protons along closed magnetic field lines. This boundary is an indicator of the amount of magnetic field line stretching in the magnetotail. Previous studies were based on in situ measurements, resulting in spatially and temporally restricted samples. To overcome these limitations, we propose to use global data obtained with the FUV spectrographic proton auroral imager (SI12) on board the IMAGE satellite. We determine at each magnetic local time the position of an optical boundary related to the IB and thereby to the stretching of the magnetic field lines. We show that the correspondence between the latitude of the maximum proton precipitation observed by SI12 and the IB measured by Defense Meteorological Satellite Program satellites is statistically established and depends on the magnetic local time. The relation between the position of the maximum proton precipitation as well as the intensity of this maximum and the magnetic field distortion is determined by comparison with GOES 8 data. We suggest that SI12 images can be used as a tool to globally determine the isotropy boundary and to monitor the level of stretching in the magnetotail.