There are various situations where image data is binary: character recognition, result of image segmentation etc. As a first contribution, we compare Gaussian based principal component analysis (PCA), which is often used to model images, and "binary PCA" which models the binary data more naturally using Bernoulli distributions. Furthermore, we address the problem of data alignment. Image data is often perturbed by some global transformations such as shifting, rotation, scaling etc. In such cases the data needs to be transformed to some canonical aligned form. As a second contribution, we extend the binary PCA to the "transformation invariant mixture of binary PCAs" which simultaneously corrects the data for a set of global transformations and learns the binary PCA model on the aligned data.