POP Image Fusion -- Derivative Domain Image Fusion without Reintegration

There are many applications where multiple images are fused to form a single summary greyscale or colour output, including computational photography (e.g. RGB-NIR), diffusion tensor imaging (medical), and remote sensing. Often, and intuitively, image fusion is carried out in the derivative domain. Here, a new composite fused derivative is found that best accounts for the detail across all images and then the resulting gradient field is reintegrated. However, the reintegration step generally hallucinates new detail (not appearing in any of the input image bands) including halo and bending artifacts. In this paper we avoid these hallucinated details by avoiding the reintegration step. Our work builds directly on the work of Socolinsky and Wolff who derive their equivalent gradient field from the per-pixel Di Zenzo structure tensor which is defined as the inner product of the image Jacobian. We show that the x-and y-derivatives of the projection of the original image onto the Principal characteristic vector of the Outer Product (POP) of the Jacobian generates the same equivalent gradient field. In so doing, we have derived a fused image that has the derivative structure we seek. Of course, this projection will be meaningful only where the Jacobian has non-zero derivatives, so we diffuse the projection directions using a bilateral filter before we calculate the fused image. The resulting POP fused image has maximal fused detail but avoids hallucinated artifacts. Experiments demonstrate our method delivers state of the art image fusion performance.