The blur kernel recovery from the retouched image via Gaussian blur

A novel algorithm for recovering the blur kernel from blur image is proposed in the paper, which is based on the images before and after blurring bearing the isometry in log-Fourier domain, and exploits the Riemannian geodesic for measuring the isometry. Firstly, the images before and after blurring are transformed to the log-Fourier domain, then the Riemannian geodesic is used for evaluating the blurring-invariant quantity between the original image and the blurred one, finally the blur kernel is resolved from the blurring-invariant. The presented method is testified on images convolved by Gaussian blur, median blur, box blur and multiple Gaussian blur, and the kernel could be robustly recovered.