Mathematical elements for computer graphics (2nd ed.)
Mathematical elements for computer graphics (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Computer graphics: principles and practice (2nd ed.)
Discrete techniques for computer transformations of digital images and patterns
Pattern Recognition
Digital image processing (2nd ed.)
Digital image processing (2nd ed.)
Harmonic models of shape transformation in digital images and patterns
CVGIP: Graphical Models and Image Processing
Advanced splitting-integrating methods with high convergence rates for restoring images and patterns
Journal of Scientific Computing
Probabilistic analysis on the splitting-shooting method for image transformations
Journal of Computational and Applied Mathematics
The finite volume method and application in combinations
Journal of Computational and Applied Mathematics
Computer animation: algorithms and techniques
Computer animation: algorithms and techniques
Digital Image Processing
Numerical algorithms for image geometric transformations and applications
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
Enhancing Human Face Detection by Resampling Examples Through Manifolds
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
3-D face structure extraction and recognition from images using 3-D morphing and distance mapping
IEEE Transactions on Image Processing
Hex-splines: a novel spline family for hexagonal lattices
IEEE Transactions on Image Processing
Image interpolation by two-dimensional parametric cubic convolution
IEEE Transactions on Image Processing
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To carry out face transformation, this paper presents new numerical algorithms, which consist of two parts, namely, the harmonic models for changes of face characteristics and the splitting techniques for grayness transition. The main method in this paper is a combination of the finite-volume method (FVM) with Delaunay triangulation to solve the Laplace equations in the harmonic transformation of face images. The advantages of the FVM with Delaunay triangulation are given as follows: 1) easy to formulate the linear algebraic equations; 2) good in retaining the pertinent geometric and physical need; and 3) less central processing unit time needed. Numerical and graphical experiments have been conducted for the face transformation from a female (woman) to a male (man), and vice versa. The computed sequential errors are O(N-(3/2)), where N2 is the division number of a pixel into subpixels. These computed errors coincide with the analysis on the splitting-shooting method (SSM) with piecewise constant interpolation in the previous paper of Li and Bai. In computation, the average absolute errors of restored pixel grayness can be smaller than 2 out of 256 grayness levels. The FVM is as simple as the finite-difference method (FDM) and as flexible as the finite-element method (FEM). Hence, the FVM is particularly useful when dealing with large face images with a huge number of pixels in shape distortion. The numerical transformation of face images in this paper can be used not only in pattern recognition but also in resampling, image morphing, and computer animation.