Fractional directional derivative and identification of blur parameters of motion-blurred image

The blur direction and extent of motion-blurred image, which is degraded by the relative motion between the camera and object scene, are needed in the methods of image restoration, such as blind deconvolution. The recently developed identification method is based on integer-order derivative, which can directly extract the blur angle and extent from blurred image itself. However, this method is sensitive to noise. As an extension to the fractional-order derivative, a noncausal fractional-order directional derivative operator is derived. Based on this new operator, a novel method identifying blur parameters is developed in this work. The performance comparison between the fractional-order and integer-order methods are also presented, which demonstrate that the former provides better immunity to noise and capacity to identify the motion-blur direction and extent.