基于四元同质微分的彩色光流估计

摘要

该文通过将颜色3维矢量表示为一个4元数(quaternion)形式的超复数,将彩色图像序列映射为3维时-空空间上定义的4元超复变函数,并以颜色常数模型假设为基础,建立了描述彩色图像序列中运动模式的4元光流方程.为了对超复数4元光流方程中的运动参数进行有效估计,定义了4元同质微分的概念,进而得到了基于4元同质颜色常数模型的光流方程,并给出了该光流方程的优化求解方法.最后,与已有算法的对比实验验证了该文方法的有效性.%Due to representing 3-dimensional color vectors as quaternion hypercomplex numbers, a color image sequences is mapped as a quaternion hypercomplex function in 3-dimensional spatial-temporal space. By underlying hypothesis of Color Constant Model (CCM), a quaternion Optical Flow Equation (OFE) which is used to describe motion in color image sequences is developed. In order to solve this quaternion OFE efficiently, a concept of quaternion homogeneity differential is introduced, thus that a new Quaternion Homogeneity CCM (QHCCM) OFE is built. The mathematic form of the QHCCM OFE is similar with the Brightness Constant Model (BCM) OFE. Because it contains not only luminance information but also chrominance information, the QHCCM OPE can capture motions in color video more accurate than that of the BCM-based method. Finally, some compared experiments are given to show the proposed method's effectiveness.