For omni-directional imaging based cooperative robot vision system, panorama unrolling is an important problem. We present an eight direction symmetry reuse algorithm for this problem, principles of this algorithm are: 1) Treat the original image to be unrolled as a series of co-centric circles, and uniformly partition them into eight parts of symmetrical sector regions. 2) According to symmetry principle in spatial geometry, we construct the symmetrical transform relations pixel coordinates among these regions. So, we need compute only one region of pixel coordinate for panorama unrolling, by use of complex ray-trace coordinate mapping, while the other seven parts of regions can be determined by symmetrically reusing results from the first region, which reduces seven-eighths computational burden for ray-tracing method. Experiments indicate that, under the same precision, our algorithm improves 3.28 times of unrolling speed compared with ray-trace unrolling method. In omnidirectional video with look-up table method, the idea of eight direction symmetry reuse can also be used to reduce the look-up table size to only one-eighth of the original table.