Discrete techniques for computer transformations of digital images and patterns

Li, Z. C.

doi:10.1016/0031-3203(90)90120-a

Cited by 16 publications

(10 citation statements)

References 8 publications

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“…In [7], [9], [13], and [17], the combination of SSM and SIM is referred to as CSIM. Since nonlinear solutions are not involved in the cycle conversion T −1 T of images, the CSIM is remarkably advantageous over other methods in image transformations of Dougherty and Glardina [3], Foley et al [4], Gonzalez and Woods [5], Pratt [21], and Rogers and Adams [22].…”

Section: Splitting Methods In Digitized Imagesmentioning

confidence: 99%

“…In [7], [8], [11]- [13], and [17], the SSM and the splittingintegrating method (SIM) are used to approximate (3.18) under T and (3.17) under T −1 , respectively. In [7], [9], [13], and [17], the combination of SSM and SIM is referred to as CSIM.…”

Section: Splitting Methods In Digitized Imagesmentioning

confidence: 99%

“…We carry out the face transformations by means of numerical methods and numerical analysis [7], [13], [17]. Define a nonlinear transformation where the continuous functions are…”

mentioning

confidence: 99%

“…Hence, the functionsx andȳ are obtained, and the solutions x(ξ, η) and y(ξ, η) in (1.7) and (1.8) can be determined uniquely. In practice, we apply numerical methods [7], [13], [17] to seek an approximate solution of (1.7) and (1.8). In [1] and [18], the finite-difference method (FDM) and the finiteelement method (FEM) were used for face transformation; in this paper, we choose the finite-volume method (FVM) with Delaunay triangulation to better solve (1.7) and (1.8).…”

mentioning

confidence: 99%

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Face Transformation With Harmonic Models by the Finite-Volume Method With Delaunay Triangulation

Chiang

Suen

2010

IEEE Trans. Syst., Man, Cybern. B

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Abstract-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 N 2 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.

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Section: Splitting Methods In Digitized Imagesmentioning

confidence: 99%

Section: Splitting Methods In Digitized Imagesmentioning

confidence: 99%

“…We carry out the face transformations by means of numerical methods and numerical analysis [7], [13], [17]. Define a nonlinear transformation where the continuous functions are…”

mentioning

confidence: 99%

mentioning

confidence: 99%

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Face Transformation With Harmonic Models by the Finite-Volume Method With Delaunay Triangulation

Chiang

Suen

2010

IEEE Trans. Syst., Man, Cybern. B

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“…Previous research (Li, 1990) proposed the area method to carry out linear transformations using exact integration. However, for nonlinear transformations, splitting a pixel into N 2 subpixels produces approximate integration and results in sequential errors of O(1/N p ) with the power p !…”

mentioning

confidence: 99%

New splitting algorithms for geometric transformations of digital images and their error analysis

Chiang

Suen

2011

Int J Imaging Syst Tech

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For digital images and patterns under the nonlinear geometric transformation, T: (n, h) ? (x, y), this study develops the splitting algorithms (i.e., the pixel-division algorithms) that divide a 2D pixel into N 3 N subpixels, where N is a positive integer chosen as N 5 2 k (k ! 0) in practical computations. When the true intensity values of pixels are known, this method makes it easy to compute the true intensity errors. As true intensity values are often unknown, the proposed approaches can compute the sequential intensity errors based on the differences between the two approximate intensity values at N and N/2. This article proposes the new splitting-shooting method, new splitting integrating method, and their combination. These methods approximate results show that the true errors of pixel intensity are O(H), where H is the pixel size. Note that the algorithms in this article do not produce any sequential errors as N ! N 0 , where N 0 (!2) is an integer independent of N and H. This is a distinctive feature compared to our previous papers on this subject. The other distinct feature of this article is that the true error bound O(H) is well suited to images with all kinds of discontinuous intensity, including scattered pixels.

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Splitting-integrating method for inverse transformation ofn-dimensional digital images and patterns

1995

Numer Algor

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Discrete techniques for computer transformations of digital images and patterns

Cited by 16 publications

References 8 publications

Face Transformation With Harmonic Models by the Finite-Volume Method With Delaunay Triangulation

Face Transformation With Harmonic Models by the Finite-Volume Method With Delaunay Triangulation

New splitting algorithms for geometric transformations of digital images and their error analysis

Splitting-integrating method for inverse transformation ofn-dimensional digital images and patterns

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