An image processing apparatus which can increase processing speed, reduce memory access load, and enhance ease of control in image processing. Coordinate computations through different geometric deformations are performed on respective pixels of an input image, thus calculating post-geometric deformation coordinates and coordinate moving vectors. Geometric deformation parameters for geometric deformations are output to a plurality of coordinate computation units connected in series. The coordinate moving vectors are collectively combined together to generate combined coordinate moving vectors, based on which coordinates of pixels in an image to be output are converted into coordinates of the pixels of the input image. The coordinate computations are performed based on the coordinates of the pixels of the input image and the geometric deformation parameters. The post-geometric deformation coordinates output from the preceding coordinate computation units are input as coordinates of the pixels of the image to the second and subsequent coordinate computation units.