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Enlarging Image by Constrained Least Square Approach with Shape Preserving

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Abstract

From a visual point of view, the shape of an image is mainly determined by the edges. Conventional polynomial interpolation of image enlarging methods would produce blurred edges, while edge-directed interpolation based methods would cause distortion in the non-edge areas. A new method for image enlarging is presented. The image is enlarged in two steps. In the first step, a fitting surface is constructed to interpolate the image data. To remove the zigzagging artifact, for each pixel, a fitting patch is constructed using edge information as constraints. The combination of all the patches forms the fitting surface which has the shape suggested by image data. Each point on the fitting surface can be regarded as a sampling point taken from a unit square domain, which means that when the fitting surface is used to enlarge the image, each sampling domain of the enlarged pixels is also a unit square, causing the enlarged image to lose some details. To make the enlarged image keep the details as many as possible, the sampling domain of the enlarged pixels should be less than a unit square. Then, in the second step, using the points taken from the fitting surface, new pixels are computed using constrained optimization technique to form the enlarged image, and the size of the sampling domain of the enlarged pixels is inversely proportional to the size of the enlarged image. The image enlarged by the new method has a quadratic polynomial precision. Comparison results show that the new method produces resized image with better quality.

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Authors and Affiliations

  1. School of Computer Science and Technology, Shandong University, Jinan, 250101, China

    Fan Zhang, Xin Zhang, Xue-Ying Qin & Cai-Ming Zhang

  2. Shandong Provincial Key Laboratory of Digital Media Technology, Shandong University of Finance and Economics, Jinan, 250014, China

    Cai-Ming Zhang

Authors
  1. Fan Zhang
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  2. Xin Zhang
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  3. Xue-Ying Qin
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  4. Cai-Ming Zhang
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Corresponding author

Correspondence to Cai-Ming Zhang.

Additional information

This work was supported by the National Natural Science Foundation of China under Grant Nos. 61020106001, 61332015, 61272430, and 61373078.

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Zhang, F., Zhang, X., Qin, XY. et al. Enlarging Image by Constrained Least Square Approach with Shape Preserving. J. Comput. Sci. Technol. 30, 489–498 (2015). https://doi.org/10.1007/s11390-015-1539-9

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  • DOI: https://doi.org/10.1007/s11390-015-1539-9

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