Aiming at the problems in the best basis selection, this paper presents a novel criterion based on the statistical measurement of the curvature wavelet coefficient to dynamically select the single best basis of the quad-tree wavelet packet transformation. The selected single best basis works as an extracted feature for biometric periocular recognition system. The proposed method first extracts the mean curvature of wavelet coefficients inside the quad-tree wavelet packet transform. Second, the method finds the most distinctive features based on the largest standard deviation and dynamically selects the extracted curvature wavelet coefficients as the single best basis. Third, the selected single curvature best basis works as an extracted feature, and then it is combined with the histogram of oriented gradients method. Finally, the support vector machine is employed to perform classification. Two datasets of two-dimensional periocular digital images are tested against the proposed method. To show the extended ability, we analyze the curvature best basis method against wavelet functions and characteristics and test the proposed method against the plain face and masked face recognition. The proposed method achieves the highest performance results inside periocular recognition (97.53% accuracy for UBIPr-1 and 97.77% accuracy for EYB-P1), masked face recognition (98.11% accuracy), and plain face recognition (98.26% accuracy). The proposed method is robust against glasses occlusion, artificial geometry transformations, Gaussian and salt pepper noise. Comparison with other works in a similar recognition system shows that our proposed curvature best basis method yields the highest performance results.INDEX TERMS Best basis, curvature, periocular recognition, wavelet packet transform.