The Application of the 25-Grid Point 3D Biharmonic Equation in Human Face Recognition

Abstract

The paper used mathematical methods to create a model of human face images. Human face recognition has emerged as a major issue, occupying an active area in a variety of fields. It has strong ties to the broader field of pattern recognition and is in high demand in commercial and security applications that use biometric systems. The fundamental issue in face recognition is the difficulty in numerically solving the fourth-order Biharmonic Equation to generate an Elliptic Surface. Combining Elliptic Surface discrete numbers with human face images is similarly difficult. The research looked at the effectiveness of solving the three-dimensional Biharmonic Equation in the field of human face identification, as well as the modelling of face images in order to identify people based on their facial information. The procedure included dividing the surface using the forward finite differences approach to obtain the coefficient matrices of the grid points that form the elliptic surface, and then extracting human face photos from a database using a 3D camera. MATLAB was then used to extract the statistic data information and plot the curves of these data from the images. It has been found that the 25-grid point's surface is conservative field.