1. An image processing apparatus which reduces an image-shake of an image caused by a shake of an image pickup apparatus, the image processing apparatus comprising: a shake detector configured to detect the shake applied to the image pickup apparatus; a decomposer configured to decompose the shake detected by the shake detector to a plurality of shake components including at least translation, rotation, and tilt components; calculator configured to calculate a filtering process parameter for each of the plurality of components, each of which are different in each of the plurality of shake components and each of which are determined by characteristics of one of the plurality of shake components; and a processor configured to perform a filtering process using a filtering process parameter calculated for each of the shake components to calculate a shake correction amount, and perform a shake correction process based on the shake correction amount, with respect to the image.