The general edge weighted Hausdorff distance has limited effects on improving the noise robustness, because single-scale edge detection operator itself is sensitive to noise which lesds to little difference between the real and false edge. A novel weighted Hausdorff distance algorithm was proposed based on multi-scale edge measure fusion (EFWHD). Multi-scale edge measure was extracted and then evidence theory was brought in. The basic belief assignment of multi-scale edge measure was constructed by a new method of bidirectional exponent and then fused by Conflict-Redistribution DSmT. To distinguish the real edge and high-frequency noise furtherly, the general weighted hausdorff distance formula was modified and the new formula was proposed which can use the fused edge measure more effectively. Simulation with both optical and SAR images shows that the edge detection method of this paper suppresses noise effectively, meanwhile preserving rich details and the contrast tests are processed to verify the efficiency of improving noise robustness.