Standard principal component analysis (PCA) is frequently applied to a set of 1D vectors. For a set of 2D objects such as images, a 2DPCA approach that computes principal components of row-row and column-column covariance matrices would be more appropriate. A new 2DPCA method for low numerical rank matrices and based on orthogonal triangular (QR) factorization is proposed in this paper. The QR-based 2DPCA displays more efficiency in terms of computational complexity. We also propose and discuss a new updating schema for 2DPCA called 2DIPCA showcasing its numerical stability and speed. The proposed methods are applied to image compression and recognition and show their outperformances over a bunch of 1D and 2D PCA methods in both the batch and incremental modes. Experiments are performed on three benchmark face databases. Results reveal that the proposed methods achieve relatively substantial results in terms of recognition accuracy, compression rate and speed.