In this chapter we discuss modeling and removing spatially-variant blur from photographs. We describe a compact global parameterization of camera shake blur, based on the 3D rotation of the camera during the exposure. Our model uses three-parameter homographies to connect camera motion to image motion and, by assigning weights to a set of these homographies, can be seen as a generalization of the standard, spatially-invariant convolutional model of image blur. As such we show how existing

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... thms, designed for spatially-invariant deblurring, can be "upgraded" in a straightforward manner to handle spatially-variant blur instead. We demonstrate this with algorithms working on real images, showing results for blind estimation of blur parameters from single images, followed by non-blind image restoration using these parameters. Finally, we introduce an efficient approximation to the global model, which significantly reduces the computational cost of modeling the spatially-variant blur. By approximating the blur as locally-uniform, we can take advantage of fast Fourier-domain convolution and deconvolution, reducing the time required for blind deblurring by an order of magnitude. 1.1 2 O Whyte, J Sivic, A Zisserman and J Ponce model must be estimated, and finally the restored image can be reconstructed, given the model and the estimated parameters. This chapter is principally concerned with the first of these stages: a geometrically motivated model of spatially-variant image blur due to camera shake, which we show can be (mostly) attributed to the rotation of the camera during exposure. We develop a global descriptor for the generative model parameters of this non-uniform blur, analogous to (but different from) a convolution kernel, and show that a more general class of blurs can be modelled than uniform. Several authors have proposed models for spatially-variant blur, under different assumptions about the scene and the camera, e.g. simple scene models with unconstrained camera motion