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Three-dimensional magnetic resonance medical images may contain scanner- and patient-induced geometric distortion. For qualitative diagnosis, geometric errors of a few millimeters are often tolerated. However, quantitative applications such as image-guided neurosurgery and radiotherapy can require an accuracy of a millimeter or better. We have developed a method to accurately measure scanner-induced geometric distortion and to correct the MR images for this type of distortion. The method involves a number of steps. First, a specially designed phantom is scanned that contains a large number of reference structures on positions with a manufacturing error of less than 0.05 mm. Next, the positions of the reference structures are automatically detected in the scanned images and a higher-order polynomial distortion-correction transformation is estimated. Then the patient is scanned and the transformation is applied to correct the patient images for the detected distortion. The distortion-correction method is explained in detail in this paper. The accuracy of the method has been measured with synthetically generated phantom scans that contain an exactly-known amount and type of distortion. The reproducibility of the method has been measured by applying it to a series of consecutive phantom scans. Validation results are briefly described in this paper, a more-detailed description is given in another submission to SPIE Medical Imaging 2001.