GmFace: A Mathematical Model for Face Image Representation Using Multi-Gaussian
This work addresses the problem of face modeling for computer vision applications, but it appears incremental as it builds on existing Gaussian-based methods.
The authors tackled the challenge of mathematically representing human faces by proposing GmFace, a multi-Gaussian function model, and achieved this by designing GmNet to optimize parameters, enabling face image transformations through simple computations.
Establishing mathematical models is a ubiquitous and effective method to understand the objective world. Due to complex physiological structures and dynamic behaviors, mathematical representation of the human face is an especially challenging task. A mathematical model for face image representation called GmFace is proposed in the form of a multi-Gaussian function in this paper. The model utilizes the advantages of two-dimensional Gaussian function which provides a symmetric bell surface with a shape that can be controlled by parameters. The GmNet is then designed using Gaussian functions as neurons, with parameters that correspond to each of the parameters of GmFace in order to transform the problem of GmFace parameter solving into a network optimization problem of GmNet. The face modeling process can be described by the following steps: (1) GmNet initialization; (2) feeding GmNet with face image(s); (3) training GmNet until convergence; (4) drawing out the parameters of GmNet (as the same as GmFace); (5) recording the face model GmFace. Furthermore, using GmFace, several face image transformation operations can be realized mathematically through simple parameter computation.