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A novel fusion scheme for volumetric medical imagery based on first-order local variational information is presented. The authors first define the contrast of a volumetric image with an arbitrary number of bands, which corresponds with the 3D gradient in the special case of a single-band image with a Euclidean metric. This contrast of multi-band image is regarded as the target contrast field. The next step is to look for a single-band volumetric image as the fusion result, which will have the closest gradient field to the contrast of the input multi-band image. It is a functional extremum problem. Using the variational approach, it leads directly to its Euler-Lagrange equation. By iteration of gradient descent, the final result can be obtained. Experimental results are presented to support the performance of the method.