Reconstruction of 3D Human Facial Images Using Partial Differential Equations

Abstract

Abstract-One of the challenging problems in geometric modeling and computer graphics is the construction of realistic human facial geometry.Such geometry are essential for a wide range of applications, such as 3D face recognition, virtual reality applications, facial expression simulation and computer based plastic surgery application. This paper addresses a method for the construction of 3D geometry of human faces based on the use of Elliptic Partial Differential Equations (PDE). Here the geometry corresponding to a human face is treated as a set of surface patches, whereby each surface patch is represented using four boundary curves in the 3-space that formulate the appropriate boundary conditions for the chosen PDE. These boundary curves are extracted automatically using 3D data of human faces obtained using a 3D scanner. The solution of the PDE generates a continuous single surface patch describing the geometry of the original scanned data. In this study, through a number of experimental verifications we have shown the efficiency of the PDE based method for 3D facial surface reconstruction using scan data. In addition to this, we also show that our approach provides an efficient way of facial representation using a small set of parameters that could be utilized for efficient facial data storage and verification purposes.

Surface Modeling Using Partial Differential Equations: A Survey

“…In addition to the work carried out by Bloor and Wilson, using PDE-based surface modelling in generating three-dimensional models was also greatly promoted by Ugail et al Their work applied PDE-based approaches in optimisation of thin-walled structures [42], modelling of oedemous limbs and venous ulcers [43], reconstruction of 3D human facial images [44], shape morphing between different geometric objects [45], parametric design of aircraft geometry [46], surface profiling of micro-scale structures [47], modelling of the compaction behaviour of cylindrical pharmaceutical tablets [48], and facial geometry parameterisation [49].…”

A note on visual pattern recognition by Gaussian curvature mapping

“…This permits an object to be generated and controlled by a very few parameters such as boundary-value conditions and global coefficients associated with an elliptic PDE [5]. We start following the approach of Elyan and Ugail [6] where "the geometry corresponding to a human face is treated as a set of surface patches, whereby each surface patch is represented using four boundary curves in the 3space that formulate the appropriate boundary conditions for the chosen PDE. These boundary curves are extracted automatically using 3D data of human faces obtained using a 3D scanner.…”

Interactive Surface Design and Manipulation Using PDE-Method through Autodesk Maya Plug-in

“…Nevertheless, when modeling complex objects, four curves hardly provide sufficient information to depict such objects precisely (i.e. human face, [17]). In such cases more than one surface patch is needed, each of which represented and controlled by a group of boundary curves (four curves/ surface patch).…”