The histograms of oriented gradients (HOG) and co-occurrence HOG (CoHOG) algorithms are simple and intuitive descriptors. However, the HOG and CoHOG algorithms based on gradient computation still have some shortcomings: they ignore meaningful textural properties and are unstable to noise. In this paper, two new efficient HOG and CoHOG methods are proposed. The proposed algorithms are based on the Gaussian derivative filters, and the feature vectors are obtained by means of principal curvatures. The feature vectors are rotation invariant by means of the rotation invariance characteristic of principal curvatures (i.e. eigenvalues). The experimental results on the CUReT, ICTH-TIPS, KTH-11PS2-a, UIUC, Brodatz album, Kylberg and Xu datasets confirm that the developed algorithms have higher classification rates than state-of-the-art texture classification methods. The classification results also demonstrate that the developed algorithms are more stable to noise and rotation than the original HOG and CoHOG algorithms. (C) 2016 Elsevier B.V. All rights reserved.