Improved direction estimation for Di Zenzo's multichannel image gradient operator

Gradient estimation is one of the most important tasks in image/video processing. For multichannel images, a classical and widely-used gradient method is Di Zenzo's gradient operator, which is based on the measure of squared local contrast variation of multichannel images. However, up to now, the indetermination of Di Zenzo's gradient direction has not been well solved, which results in errors occurring in most of the subsequent studies in which Di Zenzo's vector gradient is used. In this paper, this problem is solved thoroughly. Furthermore, the ranges of the values that the gradient angle should take in various cases are also analyzed. As an application in color image processing, a color version of Canny edge detector is implemented by introducing the new gradient estimator to the traditional grayscale image Canny operator. The experimental results indicate that the improved Di Zenzo's gradient operator is currently one of the best color gradient estimators and outperforms other state-of-the-art color image gradient methods. The improved multichannel gradient operator not only provides accurate gradient estimation but also is efficient and easy to implement.