distortion models consisting of two forward and backward reciprocating planes that let a corrected image correspond to an uncorrected image for each scanning direction are constituted to let an uncorrected satellite image scanned by a reciprocating scanning sensor with scanning overlap or scanning underlap correspond to a corrected image after distortion correction , by means of a continuous mapping function on a 1 : 1 basis . it is determined whether each point on the corrected image is a point on an overlapping scan or on an underlapping scan or on a normal scan from the existence of a real point on the distortion models .