It is theoretically impossible to restore the original fingerprint image from a sequence of line images captured by a line sensor. However, in this paper we propose a unique fingerprint-image-generation algorithm, which derives fingerprint images from sequences of line images captured at different swipe speeds by the line sensor. A continuous image representation, called trajectory, is used in modeling distortion of raw fingerprint images. Sequences of line images captured from the same finger are considered as sequences of points, which are sampled on the same trajectory in N-dimensional vector space. The key point here is not to reconstruct the original image, but to generate identical images from the trajectory, which are independent of the swipe speed of the finger. The method for applying the algorithm in a practical application is also presented. Experimental results on a raw fingerprint image database from a line sensor show that the generated fingerprint images are independent of swipe speed, and can achieve remarkable matching performance with a conventional minutiae matcher.