Coordinate calculating apparatus and method, and an image processing apparatus and method

In the image processing to obtain an image of the perspective projection method to correct the distorted image obtained by imaging using a super-wide-angle optical system such as a fisheye lens or an omnidirectional mirror, a combination of distance from the height and the optical axis of the projection sphere calculating a synthetic index (Rn) (301), using a synthetic index (Rn), and calculates the distance (Rf) from the origin in the distorted image (302). Furthermore, using the distance from the origin (Rf) is calculated two-dimensional coordinates in the distorted image (p, q) (303), using the position or pixel in the vicinity thereof in a distorted image identified in two-dimensional coordinate Te obtain the pixel values ​​of the output image. While suppressing the amount of calculation, high precision, it is possible to perform projection, i.e. the calculation of the coordinates on the coordinate plane to the imaging plane from the projection sphere.