A Theoretical Analysis of Camera Response Functions in Image Deblurring

Motion deblurring is a long standing problem in computer vision and image processing. In most previous approaches, the blurred image is modeled as the convolution of a latent intensity image with a blur kernel. However, for images captured by a real camera, the blur convolution should be applied to scene irradiance instead of image intensity and the blurred results need to be mapped back to image intensity via the camera’s response function (CRF). In this paper, we present a comprehensive study to analyze the effects of CRFs on motion deblurring. We prove that the intensity-based model closely approximates the irradiance model at low frequency regions. However, at high frequency regions such as edges, the intensity-based approximation introduces large errors and directly applying deconvolution on the intensity image will produce strong ringing artifacts even if the blur kernel is invertible. Based on the approximation error analysis, we further develop a dualimage based solution that captures a pair of sharp/blurred images for both CRF estimation and motion deblurring. Experiments on synthetic and real images validate our theories and demonstrate the robustness and accuracy of our approach.