Research Paper

Science China Information Sciences

, Volume 56, Issue 11, pp 1-12

First online:

Boundary-representable partition of unity for image magnification

  • Yukie NagaiAffiliated withSchool of Engineering, The University of Tokyo Email author 
  • , Yutaka OhtakeAffiliated withSchool of Engineering, The University of Tokyo
  • , Hideo YokotaAffiliated withBio-Research Infrastructure Construction Team, ASI, RIKEN
  • , Hiromasa SuzukiAffiliated withRCAST, The University of Tokyo

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This paper proposes a simple yet effective algorithm to magnify 2D/3D images with preserving discontinuities of intensity. Our algorithm is based on the partition of unity (PU) approximation, which offers many advantages such as smooth representation, noise-robustness, and precise representation. Unfortunately, PU encounters difficulties when scaling images and maintaining boundaries within images owing to the nature of its approximation. To overcome this problem, we propose an approximation that preserves discontinuities. This is realized by dividing the local spherical support of PU into two parts along a locally detected discontinuity and by individually approximating intensities on each side of the discontinuity. This algorithm is suitable for magnifying a variety of images, including scanned documents, pictures, and CT-scanned images. To demonstrate the effectiveness of the proposed method, we show some experimental results for 2D/3D images.


image approximation partition of unity piecewise smooth function volume data magnification