We present an integrated approach to imaging the progress of air displacement by spontaneous imbibition of oil into sandstone. We combine Computerized Tomography (CT) scanning and neural network image processing. The main aspects of our approach are I) visualization of the distribution of oil and air saturation by CT, II) interpretation of CT scans using neural networks, and III) reconstruction of 3-D images of oil saturation from the CT scans with a neural network model. The neural networks developed here construct 3-D images of fluid distribution at any time and/or location within the core. One neural network model interpolates between the CT images for a given position at different time levels and extrapolates beyond the interval of time during which the images were collected. Likewise, the network interpolates spatially between images at a given time. After interpolation and extrapolation, other network models have been developed to reconstruct the three-dimensional distribution of oil in the core. Excellent agreement between the actual images and the neural network predictions is found.