A novel interpolation method for preserving image details by using the fuzzy technique

Abstract

AbstractEnlargement processing of digital images is usually carried out by means of an interpolation function obtained by simplification of the sinc function. However, in such an interpolation method, restoration of the high‐frequency components lost in digitizing the images is not carried out at all. Hence, the enlargement causes blurring for images with many edges and detailed signals. For one‐dimensional signals, Carrato and colleagues have proposed an interpolation method in which the discontinuities of the step edge signals are preserved while other signals are linearly interpolated. In this method, no blurring occurs in the expansion processing of strong frames of the images. However, Carrato's method has the following problems. (1) Only the step edges in the image signals are taken into account so that consideration of the detailed signals is insufficient. (2) Extension of the one‐dimensional interpolation method given by Carrato to a two‐dimensional interpolation method has a problem in interpolation at the center of the lattice. In this paper, a method is proposed to accomplish improvement of Carrato's method. With regard to problem (1), the interpolation not only is effective for the step edge signals but also preserves the apex of the peak and valley signals. With regard to problem (2), improvement is planned by directly deriving the interpolation value from the original signals. The proposed interpolation processing is accomplished by describing the processing sequence by a rule. The proposed method consists of two sets of fuzzy reasoning. The proposed method and the conventional interpolation method are compared from the numerical and visual perspectives and the effectiveness of the proposed method is clarified. © 2002 Wiley Periodicals, Inc. Electron Comm Jpn Pt 3, 86(3): 57–66, 2003; Published online in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/ecjc.1140