基于四元数的局部傅里叶变换

为了分析二维四元数函数表示的彩色图像，文中利用了把空间、频率同时作为参数的基于四元数的局部S变换，该变换同时决定了彩色图像的局部频谱。文中给出了QS变挽的精确定义，其定义使用了一个二维高斯局部窗函数，窗宽度与频率成比例；并验证了QS变换的旋转不变性，可逆性。文中通过利用Hartley变换的简便QS变换计算方法，求得彩色图像的QS变换四元数生成式，并由生成式系数计算出彩色图像的能量谱。从实验结果可以得出：QS变换能量谱可以成为分析彩色图像纹理与样式的有力工具。

Local Quaternion Fourier Transform

In order to analyse quaternion images, a joint space-wavenumber localized quaternion S transform （QS） is presented in this study because color images can be treated as two-dimensional quatemion functions,it determines the local color image spectra. The QS transform uses a two-dimensional Ganssian localizing window and window width scales with wavenumbers. Rotation invariance, invert- ibility and computational aspects of the QS transform are discusse, d. In this paper, use Hartley transform to simply QS transform and obtained power map of the QS transform of colour image. Experiment results show that the power map of the QS transform is presented here as a powerful tool in color image texture and pattern analysis.