Harmonic models of shape transformations in digital images and patterns

Li, Z. C.; Suen, Ching Y.; Bui, Tien D.; Gu, Qing

doi:10.1016/1049-9652(92)90051-x

Cited by 7 publications

(4 citation statements)

References 9 publications

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“…Li et al [18] use a similar functional in an imageindependent patch-warping scenario. At a first glance such a formulation seems to lead to a solution which is not rotation invariant, thus potentially leading to grid artifacts.…”

Section: B Image Scalingmentioning

confidence: 99%

Enhancement by image-dependent warping

Arad

Gotsman

1999

IEEE Trans. on Image Process.

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Abstract-All image warping algorithms to date are imageindependent, namely, relate only to the geometry of the image plane, ignoring the content of the image. We show that taking the image content into account yields elaborate warping schemes which may be used to enhance, sharpen and scale images. Sharpening the image is achieved by "squashing" the pixels in edge areas, and "stretching" the pixels in flat areas. Since image pixels are only moved, not modified, some drawbacks of classical linear filtering methods are avoided. We also lay the mathematical foundation for the use of an image-dependent warping scheme in traditional warping applications, such as distortion minimization.

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Section: B Image Scalingmentioning

confidence: 99%

Enhancement by image-dependent warping

Arad

Gotsman

1999

IEEE Trans. on Image Process.

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“…al. [15]. In our terminology this model proposes to map a single patch by harmonic functions in each coordinate and is implemented by finite elements.…”

Section: Smoothness and Invertibilitymentioning

confidence: 99%

Designing and Implementing a Grid‐Distortion Mapping Based on Variational Principles

Arad

1994

Computer Graphics Forum

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A grid‐distortion mapping based on variational principles is described. The mapping is first defined between any two equivalent regular grids with minor geometric restrictions, and is then optimally extended to the interior of the source grid in a sense to be defined. The result is independent of the particular representation of the curves, and depends only on geometric properties of the grids. We then proceed to construct an approximation to the mapping defined and demonstrate its implementation. Finally, this algorithm is compared to several competing ones, in particular separable (scanline) algorithms.

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“…The harmonic model was first proposed in [13] and [15] for image transformation and analyzed in [9] for combination of the splitting-shooting-integrating method (CSIM).…”

Section: A Descriptions Of the Modelsmentioning

confidence: 99%

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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Harmonic models of shape transformations in digital images and patterns

Cited by 7 publications

References 9 publications

Enhancement by image-dependent warping

Enhancement by image-dependent warping

Designing and Implementing a Grid‐Distortion Mapping Based on Variational Principles

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

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