Stitching Images Back Together

When a large visual is scanned into a computer in pieces, or printed out across multiple sheets of paper, distortions are often introduced in the scanning or printing process that make it impossible to fully reconstruct the original visual ideally. For clarity, we refer to the pieces of the visual as images, and the whole visual as the picture. Typically, either scanning or printing is done with some overlap between adjacent images, that makes it possible to find very good relative locations for placing any pair of images that were adjacent. Unfortunately, the distortion often means that not all of the pairwise relative locations can be achieved simultaneously. We present a graph theoretic approach to this problem. This approach is purely local in the sense that we only use the fact that any given pair of adjacent images can be stitched together perfectly, i.e., all features match, due to the offset data from pairwise correlation. At present, these local correlations are used for stitching following a certain pattern. We propose different patterns which should give better global results. To that end, we formulate the problem in a graph theoretic way and introduce some error measures. We determine lower bounds for the different measures of error. We find and compare several alternative stitching patterns which have smaller errors than the one currently used.