### Abstract

The standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate. However, one can obtain more accurate results if one applies a filter prior to sampling, a fact well known from sampling theory. The optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space. Unfortunately, the optimal projection prefilter is difficult to implement when sinc or high order spline functions are used. In this paper, we propose to resize the image using an oblique rather than an orthogonal projection operator in order to make use of faster, simpler, and more general algorithms. We show that we can achieve almost the same result as with the orthogonal projection provided that we use the same approximation space. The main advantage is that it becomes perfectly feasible to use higher order models (e.g, splines of degree n ≥ 3). We develop the theoretical background and present a simple and practical implementation procedure using B-splines. Our experiments show that the proposed algorithm consistently outperforms the standard interpolation methods and that it provides essentially the same performance as the optimal procedure (least squares solution) with considerably fewer computations. The method works for arbitrary scaling factors and is applicable to both image enlargement and reduction.

Original language | English |
---|---|

Pages (from-to) | 679-692 |

Number of pages | 14 |

Journal | IEEE Transactions on Image Processing |

Volume | 7 |

Issue number | 5 |

DOIs | |

Publication status | Published - 1998 Dec 1 |

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### All Science Journal Classification (ASJC) codes

- Software
- Computer Graphics and Computer-Aided Design

### Cite this

*IEEE Transactions on Image Processing*,

*7*(5), 679-692. https://doi.org/10.1109/83.668025

}

*IEEE Transactions on Image Processing*, vol. 7, no. 5, pp. 679-692. https://doi.org/10.1109/83.668025

**High-quality image resizing using oblique projection operators.** / Lee, Chulhee; Eden, Murray; Unser, Michael.

Research output: Contribution to journal › Article

TY - JOUR

T1 - High-quality image resizing using oblique projection operators

AU - Lee, Chulhee

AU - Eden, Murray

AU - Unser, Michael

PY - 1998/12/1

Y1 - 1998/12/1

N2 - The standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate. However, one can obtain more accurate results if one applies a filter prior to sampling, a fact well known from sampling theory. The optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space. Unfortunately, the optimal projection prefilter is difficult to implement when sinc or high order spline functions are used. In this paper, we propose to resize the image using an oblique rather than an orthogonal projection operator in order to make use of faster, simpler, and more general algorithms. We show that we can achieve almost the same result as with the orthogonal projection provided that we use the same approximation space. The main advantage is that it becomes perfectly feasible to use higher order models (e.g, splines of degree n ≥ 3). We develop the theoretical background and present a simple and practical implementation procedure using B-splines. Our experiments show that the proposed algorithm consistently outperforms the standard interpolation methods and that it provides essentially the same performance as the optimal procedure (least squares solution) with considerably fewer computations. The method works for arbitrary scaling factors and is applicable to both image enlargement and reduction.

AB - The standard interpolation approach to image resizing is to fit the original picture with a continuous model and resample the function at the desired rate. However, one can obtain more accurate results if one applies a filter prior to sampling, a fact well known from sampling theory. The optimal solution corresponds to an orthogonal projection onto the underlying continuous signal space. Unfortunately, the optimal projection prefilter is difficult to implement when sinc or high order spline functions are used. In this paper, we propose to resize the image using an oblique rather than an orthogonal projection operator in order to make use of faster, simpler, and more general algorithms. We show that we can achieve almost the same result as with the orthogonal projection provided that we use the same approximation space. The main advantage is that it becomes perfectly feasible to use higher order models (e.g, splines of degree n ≥ 3). We develop the theoretical background and present a simple and practical implementation procedure using B-splines. Our experiments show that the proposed algorithm consistently outperforms the standard interpolation methods and that it provides essentially the same performance as the optimal procedure (least squares solution) with considerably fewer computations. The method works for arbitrary scaling factors and is applicable to both image enlargement and reduction.

UR - http://www.scopus.com/inward/record.url?scp=0032071967&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0032071967&partnerID=8YFLogxK

U2 - 10.1109/83.668025

DO - 10.1109/83.668025

M3 - Article

C2 - 18276284

AN - SCOPUS:0032071967

VL - 7

SP - 679

EP - 692

JO - IEEE Transactions on Image Processing

JF - IEEE Transactions on Image Processing

SN - 1057-7149

IS - 5

ER -