1. An image processing device comprising: an image input unit adapted to obtain a cone-beam CT image from a detector detecting X-rays that have passed through a subject; a designation unit adapted to designate plural slice positions of the subject; an extraction unit adapted to extract an area necessary for reconstruction of surfaces of the plural slice positions, based on space between the plural slice positions; a convolution processing unit adapted to perform a convolution processing on the extracted area extracted by said extraction unit; and an image processing unit adapted to execute a back projection processing for the reconstruction on the area on which the convolution processing has been performed by said convolution processing unit, wherein, in a case where it is assumed that a difference in height between the center of the area that is the target of the reconstruction and an X-ray source is Zi, a distance in a horizontal direction between the center of the area that is the target of the reconstruction and the X-ray source is D, a distance in a horizontal direction between the center of the area that is the target of the reconstruction and a sensor is S, and a radius of the area that is the target of the reconstruction is R, said extraction unit extracts, as the area necessary for reconstruction, the area from Zi×(D+S)/(D+R) to Zi×(D+S)/(D−R) of the height based on the location of the X-ray source and the sensor.