This study proposes a fast 3D dynamic programming expansion to find a shortest surface in a 3D matrix. This algorithm can detect boundaries in an image sequence. Using phantom image studies with added uniform distributed noise from different SNRs, the unsigned error of this proposed method is investigated. Comparing the automated results to the gold standard, the best averaged relative unsigned error of the proposed method is 0.77% (SNR = 20 dB), and its corresponding parameter values are reported. We further apply this method to detect the boundary of the real superficial femoral artery (SFA) in MRI sequences without a contrast injection. The manual tracings on the SFA boundaries are performed by well-trained experts to be the gold standard. The comparisons between the manual tracings and automated results are made on 16 MRI sequences (800 total images). The average unsigned error rate is 2.4% (SD = 2.0%). The results demonstrate that the proposed method can perform qualitatively better than the 2D dynamic programming for vessel boundary detection on MRI sequences.