Discernment of blur parameters from blurred image caused by two linear motions

The method of how to find the blur parameters on an image was suggested when blurring factors of high frequency vibration and uniform linear motion happen simultaneously. Blurred images with various composite motion blur parameters were synthesized and analyzed using existing algorithms. It was found that cepstral analysis was capable of discerning the motion angles accurately when the directions of two motions are different. Along the motion angle, if the autocorrelation function of derivative image exists two close extreme points with positive and negative values separately and the space between two peak points is less than 4~5 pixels, the image would be blurred by high frequency motion, otherwise it would be blurred by uniform linear motion. Having determined the motion angle and motion style, the quadratic radon transform is the best way to obtain the blur amplitude for high frequency vibration. As for the uniform linear motion, the autocorrelation of image derivative is the best algorithm to obtain the blur length.