1. A resolution conversion apparatus for N-dimensional images (N: a natural number) comprising: a first input unit configured to input target image data which is a set of first coordinate values and first pixel values at the first coordinate values; a second input unit configured to input search image pattern data which is a set of second coordinate values and second pixel values at the second coordinate values; a third input unit configured to input an ideal corresponding point density function which uses N-dimensional coordinate values and calculates density values of ideal corresponding points; an allocating unit configured to allocate on the N-dimensional space a set of the ideal corresponding points according to the density values; a first acquisition unit configured to acquire, from the target image data, an input image pattern including pixel values within a predetermined range with reference to each of the ideal corresponding points; a second acquisition unit configured to acquire, as a plurality of candidate image patterns, from the search image pattern data, a first candidate image pattern including pixel values within the predetermined range, which corresponding to the predetermined range used in the first acquisition unit, with reference to each of the second coordinate values; a finding unit configured to find, from the search image pattern data, an estimated image pattern as a second candidate image pattern of the candidate image patterns which has a smaller difference from the input image pattern than other candidate image patterns; a first setting unit configured to set pixel values of positions corresponding to the ideal corresponding points in the estimated image pattern as pixel values at the ideal corresponding points; and a conversion unit configured to convert a resolution of the target image data using the N-dimensional coordinate values and the pixel values corresponding to the N-dimensional coordinate values.