1. An image processing apparatus which performs transformation processing for an input image, and performs filter processing for a transformed image including the transformed input image in an image area, thereby generating an output image, comprising: an acquisition unit configured to acquire the input image; a determination unit configured to determine whether a pixel position to be mapped to a pixel of interest position in the transformed image by the transformation processing is present among pixel positions in the input image; a transformation unit configured to set a pixel value at the pixel position in the input image, to be mapped to the pixel of interest position in the transformed image, as a pixel value of a pixel at the pixel of interest position in the transformed image if the determination unit determines that the pixel position to be mapped is present, and set a predetermined value as the pixel value of the pixel at the pixel of interest position if the determination unit determines that the pixel position to be mapped is absent; a calculation unit configured to calculate a pixel value of a pixel at a processing pixel position in the output image from the transformed image obtained by setting a pixel value for each pixel position which forms the transformed image by the transformation unit, wherein the calculation unit is further configured to: set a pixel value, obtained by a convolution operation between filter coefficients and pixel values of pixels near the processing pixel position in the transformed image, as the pixel value of the pixel at the processing pixel position in the output image if the determination unit determines that the pixel position to be mapped is present, and set one of a predetermined pixel value and the pixel value of the pixel at the processing pixel position in the transformed image as the pixel value of the pixel at the processing pixel position in the output image if the determination unit determines that the pixel position to be mapped is absent; and an output unit configured to output the output image obtained by setting a pixel value for each pixel position in the output image by the calculation unit.