1. An image processing device, comprising: a motion vector detection unit configured to detect, from frame image data made up of frame images, motion vectors representing motion of said frame images; a modeling unit configured to model said motion vector, detected by said motion vector detection unit, to a component separation expression in which a camera motion component and a focal plane distortion component are separated, using unknown component parameters respectively representing camera motion which is motion of a camera, and an amount in change in focal plane distortion; a component calculation unit configured to calculate said component parameters used in said component separation expression, thereby calculating said camera motion component in said motion vector; and a correction unit configured to correct blurring in said frame image, based on said camera motion component, said correction unit including: camerawork component calculation unit configured to calculate the camerawork component which is camera motion intended by the user, based on said camera motion component; a blurring amount calculation unit configured to calculate an amount of said blurring, by subtracting said camerawork component from said camera motion component; a correction vector generating unit configured to generate a correction vector for correcting said blurring in said motion vector, based on said amount of blurring calculated by said blurring amount calculation unit; and a motion compensation unit configured to apply said correction vector generated by said correction vector generating unit to said motion vector, wherein said correction vector generating unit generates a matrix expression including an inverse matrix of said amount of blurring, as said correction vector.