New fast algorithm for hypercomplex decomposition and hypercomplex cross-correlation

In order to calculate the cross-correlation of two color images treated as vector in a holistic manner, a rapid vertical/parallel decomposition algorithm for quaternion is  resented. The calculation for decomposition is reduced from 21 times to 4 times real number multiplications with the same results. An algorithm for cross-correlation of color images based on decomposition in time domain is put forward, in which some properties pointed out in this paper can be utilized to reduce the computational complexity. Simulation results show the effectiveness and superiority of the proposed method.     

一种超复数鲁棒相关图像配准算法

为解决实际应用中彩色图像配准问题,针对已有的超复数互相关方法没有办法处理存在粗差的情况,在超复数互相关方法的基础上,结合鲁棒核函数,提出了一种超复数鲁棒相关的方法.该方法在频域中能使用快速傅里叶变换实现,在满足鲁棒性、实时性和准确性的同时,能通过遍历搜索去获得图像配准的全局解.即使在配准图像间存在粗差或者色彩旋转的情况下,该方法也能获得正确的配准结果.实验结果证明了该方法的有效性.     

基于超复数计算的3D径向坐标可视化映射方法

提出一种多维数据3D空间可视化方法。在二维径向坐标映射基础上,引入雷达图的面积特征作为第三维,构成三维径向坐标映射。基于超复数实现径向坐标在3D空间的计算。实验结果表明,三维映射较二维映射更能反映数据结构信息,有效处理了二维径向坐标映射中映射数据点易堆叠的问题。