A Variational Approach to Scene Reconstruction and Image Segmentation from Motion-Blur Cues

Abstract

In this paper we are interested in the joint reconstruction of geometry and photometry of scenes with multiple moving objects from a collection of motion-blurred images. We make simplifying assumptions on the photometry of the scene (we neglect complex illumination effects) and infer the motion field of the scene, its depth map, and its radiance. In particular, we choose to partition the image into regions where motion is well approximated by a simple planar translation. We model motion-blurred images as the solution of an anisotropic diffusion equation, whose initial conditions depend on the radiance and whose diffusion tensor encodes the depth map of the scene and the motion field. We propose an algorithm to infer the unknowns of the model by minimizing the discrepancy between the measured images and the ones synthesized via diffusion. Since the problem is ill-posed, we also introduce additional Tikhonov regularization terms.