Resolution conversion method with arbitrary rational values for transform‐coded images

Abstract

AbstractThe decimation and interpolation (contraction and expansion) processings of the image based on the orthogonal transform are simple and useful in the communication and storage of the digital image data. Consequently, their application to the resolution conversion of the image is expected. The conversion factor in this type of resolution conversion can be seas an arbitrary rational number if the size of the matrices in the forward and backward transforms can be set arbitrarily.On the other hand, the size of the transform matrix in the encoding is specified by the international standard and other specifications and it is not possible to set the conversion factor arbitrarily on the decoding side. When the transform matrix has the size of N, for example, the conversion factor is restricted to be the integer multiple of 1/N.From such a viewpoint, this paper proposes a method that can realize a resolution conversion with an arbitrary conversion factor even if the transform matrix size in the encoding is already specified. The basic principle of the proposed method is to combine the conventional method and the decimation processing and can be characterized as a more general method than the conventional method.By a discussion based on the filter bank and multi‐rate system, the effective configuration for the proposed method is shown. It is shown also as a result that the conversion with an arbitrary rational factor can be executed with nearly the same computational complexity as in the conventional method. A simulation is executed using DCT and LOT and the effectiveness of the proposed method is demonstrated while indicating the problems in DCT.