We propose two nuclear- and L2,1-norm regularized 2D neighborhood preserving projection (2DNPP) methods for extracting representative 2D image features. 2DNPP extracts neighborhood preserving features by minimizing a Frobenius norm-based reconstruction error that is very sensitive noise and outliers in given data. To make the distance metric more reliable and robust, and encode the neighborhood reconstruction error more accurately, we minimize the nuclear- and L2,1-norm-based reconstruction error, respectively and measure it over each image. Technically, we propose two enhanced variants of 2DNPP, nuclear-norm-based 2DNPP and sparse reconstruction-based 2DNPP. Besides, to optimize the projection for more promising feature extraction, we also add the nuclear- and sparse L2,1-norm constraints on it accordingly, where L2,1-norm ensures the projection to be sparse in rows so that discriminative features are learnt in the latent subspace and the nuclear-norm ensures the low-rank property of features by projecting data into their respective subspaces. By fully considering the neighborhood preserving power, using more reliable and robust distance metric, and imposing the low-rank or sparse constraints on projections at the same time, our methods can outperform related state-of-the-arts in a variety of simulation settings.