Huang Hung-Tsai, Li Zi-Cai, Wei Yimin, Suen Ching Yee
Department of Data Science and Analytics, I-Shou University, Kaohsiung 84001, Taiwan.
Department of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, Taiwan.
J Imaging. 2025 Jan 8;11(1):14. doi: 10.3390/jimaging11010014.
This paper is devoted to numerical algorithms based on harmonic transformations with two goals: (1) face boundary formulation by blending techniques based on the known characteristic nodes and (2) some challenging examples of face resembling. The formulation of the face boundary is imperative for face recognition, transformation, and combination. Mapping between the source and target face boundaries with constituent pixels is explored by two approaches: cubic spline interpolation and ordinary differential equation (ODE) using Hermite interpolation. The ODE approach is more flexible and suitable for handling different boundary conditions, such as the clamped and simple support conditions. The intrinsic relations between the cubic spline and ODE methods are explored for different face boundaries, and their combinations are developed. Face combination and resembling are performed by employing blending curves for generating the face boundary, and face images are converted by numerical methods for harmonic models, such as the finite difference method (FDM), the finite element method (FEM) and the finite volume method (FVM) for harmonic models, and the splitting-integrating method (SIM) for the resampling of constituent pixels. For the second goal, the age effects of facial appearance are explored to discover that different ages of face images can be produced by integrating the photos and images of the old and the young. Then, the following challenging task is targeted. Based on the photos and images of parents and their children, can we obtain an integrated image to resemble his/her current image as closely as possible? Amazing examples of face combination and resembling are reported in this paper to give a positive answer. Furthermore, an optimal combination of face images of parents and their children in the least-squares sense is introduced to greatly facilitate face resembling. Face combination and resembling may also be used for plastic surgery, finding missing children, and identifying criminals. The boundary and numerical techniques of face images in this paper can be used not only for pattern recognition but also for face morphing, morphing attack detection (MAD), and computer animation as Sora to greatly enhance further developments in AI.
本文致力于基于调和变换的数值算法，目标有两个：（1）通过基于已知特征节点的融合技术进行面部边界公式化；（2）一些具有挑战性的面部相似示例。面部边界的公式化对于人脸识别、变换和组合至关重要。通过两种方法探索源面部边界与目标面部边界之间具有组成像素的映射：三次样条插值和使用埃尔米特插值的常微分方程（ODE）。ODE方法更灵活，适用于处理不同的边界条件，如夹紧和简单支撑条件。针对不同的面部边界探索了三次样条和ODE方法之间的内在关系，并开发了它们的组合。通过使用融合曲线生成面部边界来进行面部组合和相似处理，并且通过数值方法对面部图像进行转换以用于调和模型，例如用于调和模型的有限差分法（FDM）、有限元法（FEM）和有限体积法（FVM），以及用于组成像素重采样的分裂积分法（SIM）。对于第二个目标，探索面部外观的年龄效应以发现通过整合老年人和年轻人的照片和图像可以生成不同年龄的面部图像。然后，针对以下具有挑战性的任务。基于父母及其子女的照片和图像，我们能否获得一张尽可能与他/她当前图像相似的合成图像？本文报道了令人惊叹的面部组合和相似示例以给出肯定答案。此外，引入了父母及其子女面部图像在最小二乘意义下的最优组合，以极大地促进面部相似处理。面部组合和相似处理还可用于整形手术、寻找失踪儿童和识别罪犯。本文中面部图像的边界和数值技术不仅可用于模式识别，还可用于面部变形、变形攻击检测（MAD）和计算机动画（如索拉），以极大地促进人工智能的进一步发展。
