1. An image processing apparatus for generating, from a frame image, first to Nth (N≧2) sub-frame images for NX-speed driving display, the apparatus comprising: an input unit configured to input the frame image; a generation unit configured to generate, from the frame image, first to Nth intermediate images; a holding unit configured to hold first to Nth sub-filters that have been generated by dividing an original filter, and relative position information of pixels referred to by each of the sub-filters; a collection unit configured to collect pixel values of pixels in an ith intermediate image (1≦i≦N), the pixels being at relative positions indicated by the relative position information for an ith sub-filter with respect to a pixel of interest in the ith intermediate image; and a calculation unit configured to create the N sub-frame images by obtaining a pixel value of the pixel of interest in an ith sub-frame image from a calculation value obtained using the ith sub-filter with respect to the pixel values collected by the collection unit, wherein an average value of pixel values of a pixel in the N sub-frame images is the same as a value of that pixel obtained using the original filter with respect to the frame image, and wherein at least one of the units is implemented by a computer.