Aiming at the problem that the existing privacy protection histogram publishing methods based on grouping to suppress differential noise errors cannot effectively balance the group approximation error and the Differential Privacy (DP) Laplacian error, resulting in the lack of histogram availability, a High-Precision Histogram Publishing method (HPHP) was proposed. First, the constraint inference method was used to achieve the histogram ordering under the premise of satisfying the DP constraints. Then, based on the ordered histogram, the dynamic programming grouping method was used to generate groups with the smallest total error on the noise-added histogram. Finally, the Laplacian noise was added to each group mean. For the convenience of comparative analysis, the privacy protection histogram publishing method with the theoretical minimum error (Optimal) was proposed. Experimental analysis results between HPHP, DP method with noise added directly, AHP (Accurate Histogram Publication) method and Optimal show that the Kullback-Leibler Divergence (KLD) of the histogram published by HPHP is reduced by 90% compared to that of AHP method and is close to the effect of Optimal. In conclusion, under the same pre-conditions, HPHP can publish higher-precision histograms on the premise of ensuring DP.

In order to improve the performance of face recognition under non-uniform illumination conditions, a face recognition method based on Patterns of Monogenic Oriented Magnitudes (PMOM) was proposed. Firstly, multi-scale monogenic filter was used to get monogenic magnitude maps and orientation maps of a face image. Secondly, a new operator named PMOM was proposed to decompose the monogenic orientation and magnitude into several PMOM maps by accumulating local energy along several orientations, then Local Binary Pattern (LBP) was used to get LBP feature map from each PMOM map. Finally, LBP feature maps were divided into several blocks, and the concatenated histogram calculated over each block was used as the face feature. The experimental results on the CAS-PEAL and the YALE-B face databases show that the proposed approach improves the performance significantly for the image face with illumination variations. Other advantages of our approach include its simplicity and generality. Its parameter setting is simple and does not require any training steps or lighting assumption and can be implemented easily.

Concerning the disadvantages of traditional face recognition methods, such as high dimension of extracted feature, higher computational complexity, a new method of face recognition combining monogenic filtering with Local Quantiztative Pattern (LQP) was proposed. Firstly, the multi-modal monogenic features of local amplitude, local orientation and local phase were extracted by a multi-scale monogenic filter; secondly, the LQP operator was used to get LQP feature maps by encoding the three kinds of monogenic features in each pixel; finally, the LQP feature maps were divided into several blocks, from which spatial histograms were extracted and connected as the face feature. ORL and CAS-PEAL face databases were used to test the proposed algorithm and the recognition rates were higher than all the other methods used in the experiments. The results validate that the proposed method has higher recognition accuracy and can reduce the computational complexity significantly.

In order to use the magnitude and phase information of filtered image for face recognition, a new method fusing Monogenic local phase and local magnitude was proposed. Firstly, the authors encoded the phase using the exclusive or (XOR) operator, and combined the orientation and scale information. Then the authors divided the phase pattern maps and binary pattern maps based on magnitude into blocks. After that, they extracted the histograms from blocks. Secondly, they used the block-based Fisher principle to reduce the feature dimension and improve the discrimination ability. At last, the authors fused the cosine similarity of magnitude and phase at score level. The phase method Monogenic Local XOR Pattern (MLXP) reached the recognition rate of 0.97 and 0.94, and the fusing method recognition rate was 0.99 and 0.979 on the ORL and CAS-PEAL face databases respectively and the fusing method outperformed all the other methods used in the experiment. The results verify that the MLXP method is effective. And the method fusing the Monogenic magnitude and phase not only avoids the Small Sample Size (3S) problem in conventional Fisher discrimination methods, but also improves the recognition performance significantly with smaller time and space complexity.