1. An image processing apparatus comprising: an acquisition unit which acquires three-dimensional deformation information indicating three-dimensional deformation of a two-dimensional object in a three-dimensional space; a determination unit which determines, based on the three-dimensional deformation information, whether or not it is possible to transform the three-dimensional deformation into two-dimensional deformation for the two-dimensional object; a generation unit which generates, when said determination unit determines that it is possible to transform the three-dimensional deformation into the two-dimensional deformation, a transformed two-dimensional object by applying the two-dimensional deformation to the two-dimensional object; and a laying-out unit which utilizes, when said determination unit determines that it is impossible to transform the three-dimensional deformation into the two-dimensional deformation, the three-dimensional deformation information to lay-out the two-dimensional object on the three-dimensional space, wherein when a distance between a position of the projection plane and a layout position of the two-dimensional object indicated by the three-dimensional deformation information is larger than a threshold, and a rotation angle about a prescribed axis specified by the three-dimensional deformation information falls within a prescribed range, said determination unit determines that it is possible to achieve a deformation equivalent to the three-dimensional deformation indicated by the three-dimensional deformation information by only two-dimensional affine transformation for the two-dimensional object.