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This paper, presents a novel unsupervised dimensionality reduction approach called variance difference embedding (VDE) for facial feature extraction. The proposed VDE method is derived from maximizing the difference between global variance and local variance, so it can draw the close samples closer and simultaneously making the mutually distant samples even more distant from each other. VDE utilizes the maximum variance difference criterion rather than the generalized Rayleigh quotient as a class separability measure, thereby avoiding the singularity problem when addressing the sample size problem. The results of the experiments conducted on ORL database, Yale database and a subset of PIE database indicate the effectiveness of the proposed VDE method on facial feature extraction and classification.

A quaternion model for describing color image is proposed in order to evaluate its quality. Local variance distribution of luminance layer is calculated. Color information is taken into account by using quaternion matrix. The description method is a combination of luminance layer and color information. The angle between the singular value feature vectors of the quaternion matrices corresponding to the reference image and the distorted image is used to measure the structural similarity of the two color images. When the reference image and distorted images are of unequal size it can also assess their quality. Results from experiments show that the proposed method is better consistent with the human visual characteristics than MSE, PSNR and MSSIM. The resized distorted images can also be assessed rationally by this method.

Following the oscillating theory of Meyer, many image decomposition models have been proposed to split an image into two parts: structures and textures. But these models are not effective in the case of a noisy image, because both textures and noise are oscillating patterns. In this paper, we use the local variance measure to separate noise from textures. Firstly, we examine the relationship between dyadic BMO norm and local variance. Then, we give the wavelet representation of dyadic BMO norm and local variance, and further propose a method to distinguish between texture and noise in wavelet domain. In high frequency wavelet domain, we propose a decomposition model using local variance as constraints, while in low frequency domain, we use the shrinkage scheme to distinguish them. Finally, we present various numerical results on images to demonstrate the potential of our method.

It is dissatisfactory to implement wavelet threshold to de-noise only with wavelet coefficient magnitudes. In this paper two novel methods of wavelet threshold de-noising based on locale variances are presented. They use the wavelet coefficient magnitudes as well as the local variances, which denote the clustering properties of wavelet coefficients preferably. Some simulation results, obtained from recovering a signal embedded in the additive white noise in different signal-to-noise (SNR) settings, show the potential and effectiveness of the proposed methods.