1. An image processing apparatus, for correcting a blur due to an optical system of an image capturing apparatus, the image processing apparatus comprising: an obtaining unit configured to obtain 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 obtain a plurality of representative pixel values by applying 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 by operating a weighting addition of the plurality of representative pixel values based on a positional relationship between each of filter position corresponding to the selected representative filter and the pixel position of the pixel of interest.