1. An image processing apparatus for converting a spatial resolution of an original image by multiplying the spatial resolution by a factor of a real number Z in one of a vertical direction and a horizontal direction or in both of the directions, comprising: a diagonal weight setting means for setting a weight for a statistical diagonal interpolation pixel generated by interpolation on the basis of a slope at a position of a pixel of interest having the statistically highest confidence level; a combining interpolation means for combining the statistical diagonal interpolation pixel with a different pixel interpolated by a different interpolation to generate a combined interpolated pixel as a pixel at the position of a pixel of interest on the basis of the weight of the statistical diagonal interpolation pixel set by the diagonal weight setting means; an edge strength information generation means for generating information used for quantitatively evaluating the strength of an edge at the position of the pixel of interest; a texture strength information generation means for generating information used for quantitatively evaluating the strength of texture at the position of the pixel of interest; a texture-adaptive mixing means for generating a texture mixed pixel by combining the combined interpolated pixel at the position of the pixel of interest with a texture pixel generated by performing texture filtering on the pixel of interest on the basis of the texture strength information generated by the texture strength information generation means; an edge-adaptive mixing means for generating an edge mixed pixel as a pixel at the position of the pixel of interest by combining an edge pixel generated by performing filtering on the pixel of interest with the generated texture mixed pixel on the basis of the edge strength information generated by the edge strength information generation means; a slope selection means for selecting a slope at the position of the pixel of interest having the highest confidence level on the basis of a directional distribution of slopes of a plurality of pixels corresponding to the position of the pixel of interest and the confidence level; and a statistical diagonal interpolation means for generating the statistical diagonal interpolation pixel at the position of the pixel of interest by interpolation on the basis of the slope selected by the slope selection means; wherein the diagonal weight setting means sets a weight of the statistical diagonal interpolation pixel generated by the statistical diagonal interpolation means on the basis of a slope having the statistically highest confidence level at the position of the pixel of interest; and wherein the combining interpolation means generates a combined interpolated pixel as the pixel of interest by computing a linear sum of the pixel generated by the different interpolation and the statistical diagonal interpolation pixel generated by the statistical diagonal interpolation means using a coefficient corresponding to the weight set by the diagonal weight setting means.