1. An image processing apparatus comprising a projection image generation means for setting a plurality of search points in a three-dimensional image along a plurality of visual lines, each connecting each pixel on a projection plane on which the three-dimensional image is projected and an arbitrary viewpoint, calculating a pixel value of each search point by an interpolation operation based on pixel values of adjacent pixels of each search point, determining a pixel value of each pixel on the projection plane with respect to each visual line based on the pixel values of the search points, and generating a projection image formed of each pixel on the projection plane, wherein: the three-dimensional image is an image divided into an intended setting area in which the search points are intended to be set and the image is displayed and an unintended setting area in which the search points are not intended to be set and the image is not displayed; the search points are in the intended setting area; and the projection image generation means calculates the pixel value of the search point such that the pixel value of an adjacent pixel of the search point does not contribute to the calculation only on condition that the adjacent pixel is a pixel in the unintended setting area.