Edge detection of colour image based on quaternion fractional differential

According to the development of the real fractional differential and its applications in the modern signal processing, the authors extend it to quaternion body and put forward a new concept: quaternion fractional differential (QFD), and apply it to edge detection of colour image. This method is called edge detection based on QFD. Simulation experiments indicate that this method has special advantages. Furthermore, the authors give an indicator to evaluate the effectiveness of different edge filters. Comparing with Sobel and mix edges of real fractional differential to every channels of colour image, they discover that QFD has fewer false negatives in the textured regions and is also better at detecting edges that are partially defined by texture, which means the authors can obtain much better results in the interesting regions using QFD and is more consistent with the characteristics of human visual system.