Abstract: We describe a relationship between integral images and
differential images. First, we derive a simple difference filter from
conventional integral image. In the derivation, we show that an
integral image and the corresponding differential image are related
to each other by simultaneous linear equations, where the numbers
of unknowns and equations are the same, and therefore, we can
execute the integration and differentiation by solving the simultaneous
equations. We applied the relationship to an image fusion problem,
and experimentally verified the effectiveness of the proposed method.