New Explorations on Cannon’s Contributions and Generalized Solutions for Uniform Linear Motion Blur Identification

Existing frequency-domain-oriented methods of parameter identification for uniform linear motion blur (ULMB) images usually dealt with special scenarios. For example, blur-kernel directions were horizontal or vertical, or degraded images were of foursquare dimension. This excludes those identification methods from being applied to real images, especially to estimate undersized or oversized blur kernels. Pointing against the limitations of blur-kernel identifications, discrete Fourier transform (DFT)-based blur-kernel estimation methods are proposed in this paper. We analyze in depth the Fourier frequency response of generalized ULMB kernels, demonstrate in detail its related phase form and properties thereof, and put forward the concept of quasi-cepstrum. On this basis, methods of estimating ULMB-kernel parameters using amplitude spectrum and quasi-cepstrum are presented, respectively. The quasi-cepstrum-oriented approach increases the identifiable blur-kernel length, up to a maximum of half the diagonal length of the image. Meanwhile, directing toward the image of undersized ULMB, an improved method based on quasi-cepstrum is presented, which ameliorates the identification quality of undersized ULMB kernels. The quasi-cepstrum-oriented approach popularizes and applies the simulation-experiment-focused DFT theory to the estimation of real ULMB images. Compared against the amplitude-spectrum-oriented method, the quasi-cepstrum-oriented approach is more convenient and robust, with lower identification errors and of better noise-immunity.