Face Boundary Formulation for Harmonic Models: Face Image Resembling
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 fa...
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MDPI AG
2025-01-01
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| Series: | Journal of Imaging |
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| author | Hung-Tsai Huang Zi-Cai Li Yimin Wei Ching Yee Suen |
| author_facet | Hung-Tsai Huang Zi-Cai Li Yimin Wei Ching Yee Suen |
| author_sort | Hung-Tsai Huang |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-a090de710619411bbdc2cdcab22b302c |
| institution | Kabale University |
| issn | 2313-433X |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Journal of Imaging |
| spelling | doaj-art-a090de710619411bbdc2cdcab22b302c2025-01-24T13:36:16ZengMDPI AGJournal of Imaging2313-433X2025-01-011111410.3390/jimaging11010014Face Boundary Formulation for Harmonic Models: Face Image ResemblingHung-Tsai Huang0Zi-Cai Li1Yimin Wei2Ching Yee Suen3Department of Data Science and Analytics, I-Shou University, Kaohsiung 84001, TaiwanDepartment of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 80424, TaiwanShanghai Key Laboratory of Contemporary Applied Mathematics, Fudan University, Shanghai 200433, ChinaCenter for Pattern Recognition and Machine Intelligence, Concordia University, Montreal, QC H3G 1M8, CanadaThis 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.https://www.mdpi.com/2313-433X/11/1/14face boundary formulationblending curvesODE using Hermite interpolationsplitting–integrating methodharmonic modelsage effects |
| spellingShingle | Hung-Tsai Huang Zi-Cai Li Yimin Wei Ching Yee Suen Face Boundary Formulation for Harmonic Models: Face Image Resembling Journal of Imaging face boundary formulation blending curves ODE using Hermite interpolation splitting–integrating method harmonic models age effects |
| title | Face Boundary Formulation for Harmonic Models: Face Image Resembling |
| title_full | Face Boundary Formulation for Harmonic Models: Face Image Resembling |
| title_fullStr | Face Boundary Formulation for Harmonic Models: Face Image Resembling |
| title_full_unstemmed | Face Boundary Formulation for Harmonic Models: Face Image Resembling |
| title_short | Face Boundary Formulation for Harmonic Models: Face Image Resembling |
| title_sort | face boundary formulation for harmonic models face image resembling |
| topic | face boundary formulation blending curves ODE using Hermite interpolation splitting–integrating method harmonic models age effects |
| url | https://www.mdpi.com/2313-433X/11/1/14 |
| work_keys_str_mv | AT hungtsaihuang faceboundaryformulationforharmonicmodelsfaceimageresembling AT zicaili faceboundaryformulationforharmonicmodelsfaceimageresembling AT yiminwei faceboundaryformulationforharmonicmodelsfaceimageresembling AT chingyeesuen faceboundaryformulationforharmonicmodelsfaceimageresembling |