Binary data comparison using similarity indices and principal components analysis

This work is a study of binary data, especially binary images sources of information widely used. In general, comparing two binary images that represent the same content is not always easy because an image can undergo transformations like: Translation, rotation, affinity, resolution change and scale or change in appearance. In this paper, we will try to solve the translation and rotation problems. For translation case, the similarity indices are used between the image rows or blocks. In the case of rotation, first the coordinate’s contours are extracted, then we compute the covariance matrix used in the Principal Components Analysis (PCA) and the corresponding eigen values which are invariant to this type of movement. We also, compare our approach having complexity O(M+N) to Hausdorff Distance (HD) that has complexity of O(M×N) for an M×N image. In our approach, HD is used only to compare distance between 1D signatures.