1. An image processing apparatus comprising: a calculation section configured to calculate filtering coefficients of a filter with a first area in an image, the image being partitioned into a plurality of first areas including the first area, the image being partitioned differently into a plurality of second areas, each one of the second areas being covered by several of the first areas, to calculate a convoluted image of the one of the second areas using the filtering coefficients calculated with the one of the first areas covering a part of the one of the second areas, the calculation being executed for the several of the first areas covering distinct parts of the one of the second areas, respectively; and an interpolation section configured to interpolate a pixel in the one of the second areas using pixels at the same position in the convoluted images of the second area which are convoluted with the respective filtering coefficients.