1. An image processing apparatus, for correcting a blur due to an optical system of an image capturing apparatus, the image processing apparatus comprising: a storage unit configured to store a plurality of representative filters; a selection unit configured to select a subset of representative filters from the plurality of representative filters based on a pixel position of a pixel of interest in an image; a filtering unit configured to apply each of the selected representative filter to a pixel value of the pixel of interest; and a correction unit configured to correct the pixel value of the pixel of interest based on (a) a result of the application of filters by the filtering unit, and (b) the pixel position of the pixel of interest.