Local Quaternion Fourier Transform And Application

This paper presents a new Fourier transform which is namely quaternion S transform and it applied to the analysis of color images. QS is essentially a windowed (localization) quaternions Fourier transform. This QS transform includes a circularly symmetricl Gaussian window to assure the rotation invariance of the transform, and window width is proportional to frequency.Different from traditional QFT which uses Quaternion Symplectic Decomposition method, In this study we use Hartley convolutions to realize fast calculation of QST and find out the power map of QS transform. Power map of QST is4D function under plane and frequency domain, It not only to retain the spatial texture characteristics also provides a way to process power map in frequency domain. Next we sunmate power map of QS in frequency domain to realize visual power map of QS. QS power map visualization of color image is similar to the gray color image. According to example, QS power map can be used to extract texture characteristics of color image.We use QS power map for color image retrieval, QS power map of Color images can be seen as gray image of color images and is used for calculating gray level cooccurrence matrix to extract texture characteristics. At last, by contrast texture feature of gray level cooccurrence matrix calculating similar distance for color image retrieval. The experiment educe some results:In searching the same image result of QS retrieval is good as ordinary retrieval, but in the similar or sparse image retrieval QS retrieval is better than ordinary, and similar distance of QS retrieval trend to smooth linear, makes it easier to control similar "threshold value".