Face recognition is one of the most popular biometric today. However, there are still challenges in the development of a robust, real-time face recognition system. Several challenges can be listed as poor illumination, rotations of the face and deformations on the face caused by factors like aging. The most frequent deformations on the face are due to facial expressions that indicate the emotional state of the person. A robust face recognition system should perform well under facial expression deformations. In this paper, we focus on this challenge of face recognition and analyzed the performance of the well known feature extractor Local Binary Patterns (LBPs) under varying facial expressions. The facial expressions considered are the six basic expressions which are anger, disgust, fear, happiness, sadness and surprise. The system is tested on BU-3DFE database. The simulation results show that the LBP features form a strong base for expression invariant face recognition and are open to further improvements.

The wavelet transformation is a mathematical method developed over the past decades to be adapted for applications in the fields of science and engineering. The wavelet transform can be applied in the field of numerical analysis to solve the differential equation. This paper is concerned with applying Haar wavelet methods to solve an ordinary differential equation for an RLC series circuit with a known initial state. The matrix construction calculations are proposed in a simple way. Three numerical mathematical examples are shown that include second-order differential equations with variable and constant coefficients. The results showed that the proposed method is quite reasonable while comparing the solution of second order systems by Haar wavelet method with the exact solution in the context of serial RLC circuit. Moreover, the use of Haar waves is found to be simple, accurate, with flexible and appropriate arithmetic computational costs.

The discrete wavelet transform is commonly used as a denoising step for many applications, like biomedical applications which are usually suffering from low SNR of the recorded signal. However, the choice of appropriate threshold value for DWT coefficients plays significant role in reconstructing the denoised signal. This paper presents a design of real-time wavelet denoising architecture which is suitable for wide range of real-time denoising applications. In this design, an adaptive thresholding approach based on feedback control loop is proposed to make the architecture more applicable for real-time wavelet denoising. This thresholding method considers a noise level estimator module based on first detail coefficients level 𝑑1 to calculate the unknown standard deviation of background noise. The proposed architecture is developed using MATLAB to simulate the suggested denoising method. The performance of the proposed denoising method is studied in terms of integral gain 𝐺 of feedback control and window size 𝑀 with respect to the improvement in SNR and settling time. The results imply that the proposed denoising architecture is suitable for real-time denoising applications with acceptable improvement in SNR approximately 8 dB.